qu.1.topic=hyperbolic graphs@

qu.1.1.mode=Multiple Choice@
qu.1.1.name=choose hyperbolic graph@
qu.1.1.comment=@
qu.1.1.editing=useHTML@
qu.1.1.solution=@
qu.1.1.algorithm=$num=rint(20)+1;
$M=maple("
for  i from 0 to $num do  
which:=combinat[randperm](5):
end do:
which;
");
$z1=switch(0,$M);
$z2=switch(1,$M);
$z3=switch(2,$M);
$z4=switch(3,$M);
$z5=switch(4,$M);
$f=switch($z1 , "sinh(x)","cosh(x)","tanh(x)","exp(x)","exp(-x)");
$B=switch($z2 , "sinh(x)","cosh(x)","tanh(x)","exp(x)","exp(-x)");
$C=switch($z3 , "sinh(x)","cosh(x)","tanh(x)","exp(x)","exp(-x)");
$D=switch($z4 , "sinh(x)","cosh(x)","tanh(x)","exp(x)","exp(-x)");
$E=switch($z5 , "sinh(x)","cosh(x)","tanh(x)","exp(x)","exp(-x)");
$F=maple("printf(MathML[ExportPresentation]($f))");
$pa=plotmaple("plot($f,x=-2..2,y=-2..2,thickness=2),plotdevice='gif', plotoptions='height=250,width=250'");
$pb=plotmaple("plot($B,x=-2..2,y=-2..2,thickness=2),plotdevice='gif', plotoptions='height=250,width=250'");
$pc=plotmaple("plot($C,x=-2..2,y=-2..2,thickness=2),plotdevice='gif', plotoptions='height=250,width=250'");
$pd=plotmaple("plot($D,x=-2..2,y=-2..2,thickness=2),plotdevice='gif', plotoptions='height=250,width=250'");
$pe=plotmaple("plot($E,x=-2..2,y=-2..2,thickness=2),plotdevice='gif', plotoptions='height=250,width=250'");@
qu.1.1.uid=9837bfef-7db9-4e7d-97b8-510ebc9771ad@
qu.1.1.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=Graphs;
@
qu.1.1.question=<p>Which of the following is the graph of <math><mrow><mi>y</mi><mo>=</mo></mrow></math>$F?</p>@
qu.1.1.answer=1@
qu.1.1.choice.1=$pa@
qu.1.1.choice.2=$pb@
qu.1.1.choice.3=$pc@
qu.1.1.choice.4=$pd@
qu.1.1.choice.5=$pe@
qu.1.1.fixed=@

qu.2.topic=HyperbolicTheory@

qu.2.1.mode=Multiple Choice@
qu.2.1.name=sinh(ax)=@
qu.2.1.comment=@
qu.2.1.editing=useHTML@
qu.2.1.solution=@
qu.2.1.algorithm=$a=rand(2,8,1);
$b=2*$a;@
qu.2.1.uid=d68e2e02-dfc0-4580-8a2c-7cc61352e8a3@
qu.2.1.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=Theory;
@
qu.2.1.question=<p>Algebraically, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>sinh</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><msup><mi>e</mi><mrow><mi>x</mi></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msup><mi>e</mi><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>x</mi></mrow></msup></mrow><mrow><mn>2</mn></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><msup><mi>e</mi><mrow><mn>2</mn><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>x</mi></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow><mrow><mn>2</mn><msup><mi>e</mi><mrow><mi>x</mi></mrow></msup></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&period;</mo></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mstyle></math>Using this, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>sinh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo></mrow></mstyle></math></p>@
qu.2.1.answer=1@
qu.2.1.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mrow><mfenced><mrow><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$b</mi></msup></mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mn    mathvariant='normal' >1</mn></mrow></mfenced></mrow><mrow><mn    mathvariant='normal' >2</mn><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$a</mi></msup></mrow></mrow></mfrac></mrow></math>@
qu.2.1.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mrow><mfenced><mrow><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$b</mi></msup><mo    mathvariant='normal'             >&plus;</mo></mrow><mn    mathvariant='normal' >1</mn></mrow></mfenced></mrow><mrow><mn    mathvariant='normal' >2</mn><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$a</mi></msup></mrow></mrow></mfrac></mrow></math>@
qu.2.1.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mrow><mfenced><mrow><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$b</mi></msup></mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mn    mathvariant='normal' >1</mn></mrow></mfenced></mrow><mrow><mn    mathvariant='normal' >2</mn><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$b</mi></msup></mrow></mrow></mfrac></mrow></math>@
qu.2.1.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mrow><mfenced><mrow><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$b</mi></msup><mo    mathvariant='normal'             >&plus;</mo></mrow><mn    mathvariant='normal' >1</mn></mrow></mfenced></mrow><mrow><mn    mathvariant='normal' >2</mn><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$b</mi></msup></mrow></mrow></mfrac></mrow></math>@
qu.2.1.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mrow><mfenced><mrow><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$a</mi></msup></mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mn    mathvariant='normal' >1</mn></mrow></mfenced></mrow><mrow><mn    mathvariant='normal' >2</mn><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$a</mi></msup></mrow></mrow></mfrac></mrow></math>@
qu.2.1.fixed=@

qu.2.2.mode=Multiple Choice@
qu.2.2.name=cosh(ax)=@
qu.2.2.comment=@
qu.2.2.editing=useHTML@
qu.2.2.solution=@
qu.2.2.algorithm=$a=rand(2,8,1);
$b=2*$a;@
qu.2.2.uid=7be18778-b88c-4c13-a043-328941ed8bbb@
qu.2.2.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=Theory;
@
qu.2.2.question=<p>Algebraically, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>cosh</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><msup><mi>e</mi><mrow><mi>x</mi></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><msup><mi>e</mi><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>x</mi></mrow></msup></mrow><mrow><mn>2</mn></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><msup><mi>e</mi><mrow><mn>2</mn><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>x</mi></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>1</mn></mrow><mrow><mn>2</mn><msup><mi>e</mi><mrow><mi>x</mi></mrow></msup></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&period;</mo></mrow></mstyle></math> Using this, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>cosh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo></mrow></mstyle></math></p>@
qu.2.2.answer=2@
qu.2.2.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mrow><mfenced><mrow><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$b</mi></msup></mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mn    mathvariant='normal' >1</mn></mrow></mfenced></mrow><mrow><mn    mathvariant='normal' >2</mn><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$a</mi></msup></mrow></mrow></mfrac></mrow></math>@
qu.2.2.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mrow><mfenced><mrow><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$b</mi></msup><mo    mathvariant='normal'             >&plus;</mo></mrow><mn    mathvariant='normal' >1</mn></mrow></mfenced></mrow><mrow><mn    mathvariant='normal' >2</mn><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$a</mi></msup></mrow></mrow></mfrac></mrow></math>@
qu.2.2.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mrow><mfenced><mrow><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$b</mi></msup></mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mn    mathvariant='normal' >1</mn></mrow></mfenced></mrow><mrow><mn    mathvariant='normal' >2</mn><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$b</mi></msup></mrow></mrow></mfrac></mrow></math>@
qu.2.2.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mrow><mfenced><mrow><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$b</mi></msup><mo    mathvariant='normal'             >&plus;</mo></mrow><mn    mathvariant='normal' >1</mn></mrow></mfenced></mrow><mrow><mn    mathvariant='normal' >2</mn><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$b</mi></msup></mrow></mrow></mfrac></mrow></math>@
qu.2.2.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mrow><mfenced><mrow><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$a</mi></msup></mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mn    mathvariant='normal' >1</mn></mrow></mfenced></mrow><mrow><mn    mathvariant='normal' >2</mn><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$a</mi></msup></mrow></mrow></mfrac></mrow></math>@
qu.2.2.fixed=@

qu.2.3.mode=Multiple Selection@
qu.2.3.name=Properties@
qu.2.3.comment=@
qu.2.3.editing=useHTML@
qu.2.3.solution=@
qu.2.3.algorithm=@
qu.2.3.uid=fe14c5bd-4807-4016-b114-2aa15e0d335e@
qu.2.3.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=Theory;
@
qu.2.3.question=<p>One or more of the following five choices are true. Which?</p>
<p><img alt="" src=" __BASE_URI__gifs/HyperbolicPropertiesgif.GIF " /><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='newline'></mspace></mrow></math></p>@
qu.2.3.answer=1, 2, 4@
qu.2.3.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi mathvariant='normal'>cosh</mi><mn>2</mn></msup><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msup><mi mathvariant='normal'>sinh</mi><mn>2</mn></msup><mfenced open='(' close=')' separators=','><mrow><mrow><mi mathvariant='normal'></mi></mrow><mi>&theta;</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow></mstyle></math>@
qu.2.3.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>x</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>cosh</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math> and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>y</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>sinh</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>@
qu.2.3.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>x</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>cos</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math> and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>y</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>sin</mi><mfenced open='(' close=')' separators=','><mrow><mi>&theta;</mi></mrow></mfenced></mrow></mstyle></math>@
qu.2.3.choice.4=the shaded area<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>&theta;</mi></mrow></mstyle></math>@
qu.2.3.choice.5=the arc length along the hyperbola from <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mn>1</mn><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mn>0</mn></mrow></mfenced></mrow></mstyle></math> to <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfenced open='(' close=')' separators=','><mrow><mi>x</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mi>y</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>&theta;</mi></mrow></mstyle></math>@
qu.2.3.fixed=@

qu.2.4.mode=Multiple Choice@
qu.2.4.name=tanh(ax)=@
qu.2.4.comment=@
qu.2.4.editing=useHTML@
qu.2.4.solution=@
qu.2.4.algorithm=$a=rint(9)+2;
$b=2*$a;@
qu.2.4.uid=1a0849f5-092c-45e6-b2f5-fb710f24063b@
qu.2.4.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=Theory;
@
qu.2.4.question=<p>Algebraically, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>tanh</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><msup><mi>e</mi><mrow><mi>x</mi></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msup><mi>e</mi><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>x</mi></mrow></msup></mrow><mrow><msup><mi>e</mi><mrow><mi>x</mi></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><msup><mi>e</mi><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>x</mi></mrow></msup></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><msup><mi>e</mi><mrow><mn>2</mn><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>x</mi></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow><mrow><msup><mi>e</mi><mrow><mn>2</mn><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi>x</mi></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>1</mn></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&period;</mo></mrow></mstyle></math>Using this, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>tanh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo></mrow></mstyle></math></p>@
qu.2.4.answer=2@
qu.2.4.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mrow><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$b</mi></msup><mo    mathvariant='normal'             >&plus;</mo></mrow><mn    mathvariant='normal' >1</mn></mrow><mrow><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$b</mi></msup><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo></mrow><mn    mathvariant='normal' >1</mn></mrow></mfrac></mrow></math>@
qu.2.4.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mrow><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$b</mi></msup></mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mn    mathvariant='normal' >1</mn></mrow><mrow><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$b</mi></msup></mrow><mo    mathvariant='normal'             >&plus;</mo><mn    mathvariant='normal' >1</mn></mrow></mfrac></mrow></math>@
qu.2.4.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mrow><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$a</mi></msup></mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mn    mathvariant='normal' >1</mn></mrow><mrow><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$a</mi></msup></mrow><mo    mathvariant='normal'             >&plus;</mo><mn    mathvariant='normal' >1</mn></mrow></mfrac></mrow></math>@
qu.2.4.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mrow><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$a</mi></msup><mo    mathvariant='normal'             >&plus;</mo></mrow><mn    mathvariant='normal' >1</mn></mrow><mrow><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$a</mi></msup><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo></mrow><mn    mathvariant='normal' >1</mn></mrow></mfrac></mrow></math>@
qu.2.4.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mrow><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$a</mi></msup><mo    mathvariant='normal'             >&plus;</mo></mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mrow><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$a</mi></msup></mrow></mrow></mfrac></mrow><mrow><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$a</mi></msup><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo></mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mrow><mrow><msup ><mi    mathvariant='italic' >e</mi><mi    mathvariant='normal' >$a</mi></msup></mrow></mrow></mfrac></mrow></mfrac></mrow></math>@
qu.2.4.fixed=@

qu.3.topic=hyp(arcDIFFERENThyp)@

qu.3.1.mode=Multiple Choice@
qu.3.1.name=coth-FINDcsch@
qu.3.1.comment=<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi mathvariant='normal'>coth</mi><mrow><mn>2</mn></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msup><mi mathvariant='normal'>csch</mi><mrow><mn>2</mn></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msup><mi mathvariant='normal'>csch</mi><mrow><mn>2</mn></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced></mrow></mstyle></math></p>
<p>since <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>coth</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&lt;</mo><mn>0</mn></mrow></mstyle></math>we know <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>x</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&lt;</mo><mn>0</mn></mrow></mstyle></math>, which means<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>csch</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&lt;</mo><mn>0</mn></mrow></mstyle></math> . Therefore,</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>csch</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mrow><msqrt><mrow><mi mathvariant='normal'>$d</mi></mrow></msqrt></mrow></mrow></mstyle></math></p>
<p>&nbsp;</p>@
qu.3.1.editing=useHTML@
qu.3.1.solution=@
qu.3.1.algorithm=$a=range(-10,-2,1);
condition:not(eq($a,1));
$c=1+$a^2;
$d=$a^2-1;@
qu.3.1.uid=9a9b26fc-a82b-4f00-b9d5-fca607e0c4d8@
qu.3.1.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=Hyperbolic Identities;
@
qu.3.1.question=<p>If <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>coth</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$a</mi></mrow></mstyle></math> then <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>csch</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo></mrow></mstyle></math></p>
<p>(Remember that <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>coth</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&lt;</mo><mn>0</mn></mrow></mstyle></math> only when <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>x</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&lt;</mo><mn>0.</mn></mrow></mstyle></math>Use <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><msup><mi mathvariant='normal'>coth</mi><mrow><mn>2</mn></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msup><mi mathvariant='normal'>csch</mi><mrow><mn>2</mn></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&period;</mo></mrow></mstyle></math>)</p>@
qu.3.1.answer=4@
qu.3.1.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msqrt><mrow><mi mathvariant='normal'>$c</mi></mrow></msqrt></mrow></mstyle></math>@
qu.3.1.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mrow><msqrt><mrow><mi mathvariant='normal'>$c</mi></mrow></msqrt></mrow></mrow></mstyle></math>@
qu.3.1.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msqrt><mrow><mi mathvariant='normal'>$d</mi></mrow></msqrt></mrow></mstyle></math>@
qu.3.1.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mrow><msqrt><mrow><mi mathvariant='normal'>$d</mi></mrow></msqrt></mrow></mrow></mstyle></math>@
qu.3.1.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>both</mi><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><msqrt><mrow><mi mathvariant='normal'>$c</mi></mrow></msqrt><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mo mathvariant='bold' fontweight='bold' lspace='0.0em' rspace='0.0em'>and</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msqrt><mrow><mi mathvariant='normal'>$c</mi></mrow></msqrt></mrow></mstyle></math>@
qu.3.1.choice.6=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>both</mi><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><msqrt><mrow><mi mathvariant='normal'>$d</mi></mrow></msqrt><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo mathvariant='bold' fontweight='bold' lspace='0.0em' rspace='0.0em'>and</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msqrt><mrow><mi mathvariant='normal'>$d</mi></mrow></msqrt></mrow></mstyle></math>@
qu.3.1.fixed=@

qu.3.2.mode=Multiple Choice@
qu.3.2.name=coth+FINDcsch@
qu.3.2.comment=<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi mathvariant='normal'>coth</mi><mrow><mn>2</mn></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msup><mi mathvariant='normal'>csch</mi><mrow><mn>2</mn></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced></mrow><mrow><mi></mi></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msup><mi mathvariant='normal'>csch</mi><mrow><mn>2</mn></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced></mrow></mstyle></math></p>
<p>since <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>coth</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&gt;</mo><mn>0</mn></mrow></mstyle></math>we know <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>x</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&gt;</mo><mn>0</mn></mrow></mstyle></math>, which means . Therefore,</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi mathvariant='normal'>csch</mi><mrow></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><msqrt><mrow><mi mathvariant='normal'>$d</mi></mrow></msqrt></mrow></mrow></mstyle></math></p>
<p>&nbsp;</p>@
qu.3.2.editing=useHTML@
qu.3.2.solution=@
qu.3.2.algorithm=$a=range(2,10,1);
condition:not(eq($a,1));
$c=1+$a^2;
$d=$a^2-1;@
qu.3.2.uid=7201e0b0-1a1e-45f6-8ce4-54cf19f7c9d0@
qu.3.2.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=Hyperbolic Identities;
@
qu.3.2.question=<p>If <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>coth</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$a</mi></mrow></mstyle></math> then <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>csch</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo></mrow></mstyle></math></p>
<p>(Remember that <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>coth</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&gt;</mo><mn>0</mn></mrow></mstyle></math>&nbsp;only when <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>x</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&gt;</mo><mn>0.</mn></mrow></mstyle></math>Use <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><msup><mi mathvariant='normal'>coth</mi><mrow><mn>2</mn></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msup><mi mathvariant='normal'>csch</mi><mrow><mn>2</mn></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&period;</mo></mrow></mstyle></math>)</p>@
qu.3.2.answer=3@
qu.3.2.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msqrt><mrow><mi mathvariant='normal'>$c</mi></mrow></msqrt></mrow></mstyle></math>@
qu.3.2.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mrow><msqrt><mrow><mi mathvariant='normal'>$c</mi></mrow></msqrt></mrow></mrow></mstyle></math>@
qu.3.2.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msqrt><mrow><mi mathvariant='normal'>$d</mi></mrow></msqrt></mrow></mstyle></math>@
qu.3.2.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mrow><msqrt><mrow><mi mathvariant='normal'>$d</mi></mrow></msqrt></mrow></mrow></mstyle></math>@
qu.3.2.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>both</mi><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><msqrt><mrow><mi mathvariant='normal'>$c</mi></mrow></msqrt><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mo mathvariant='bold' fontweight='bold' lspace='0.0em' rspace='0.0em'>and</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msqrt><mrow><mi mathvariant='normal'>$c</mi></mrow></msqrt></mrow></mstyle></math>@
qu.3.2.choice.6=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>both</mi><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><msqrt><mrow><mi mathvariant='normal'>$d</mi></mrow></msqrt><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo mathvariant='bold' fontweight='bold' lspace='0.0em' rspace='0.0em'>and</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msqrt><mrow><mi mathvariant='normal'>$d</mi></mrow></msqrt></mrow></mstyle></math>@
qu.3.2.fixed=@

qu.3.3.mode=Multiple Choice@
qu.3.3.name=sinhFINDcosh@
qu.3.3.comment=<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi mathvariant='normal'>cosh</mi><mrow><mn>2</mn></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msup><mi mathvariant='normal'>sinh</mi><mrow><mn>2</mn></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi mathvariant='normal'>cosh</mi><mrow><mn>2</mn></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi mathvariant='normal'>cosh</mi><mrow><mn>2</mn></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$c</mi></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi mathvariant='normal'>cosh</mi><mrow></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><msqrt><mrow><mi mathvariant='normal'>$c</mi></mrow></msqrt></mrow></mrow></mstyle></math></p>
<p>Remember <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>cosh</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&GreaterEqual;</mo><mn>1</mn><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mstyle></math>for all <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>x</mi></mrow></mstyle></math>, so we cannot use the negative root.</p>@
qu.3.3.editing=useHTML@
qu.3.3.solution=@
qu.3.3.algorithm=$a=range(-10,10,1);
condition:not(eq($a,1));
condition:not(eq($a,-1));
$c=1+$a^2;
$d=$a^2-1;@
qu.3.3.uid=40fcb0b7-a37c-4a04-9f90-f0ff8648068f@
qu.3.3.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=Hyperbolic Identities;
@
qu.3.3.question=<p>Remember that <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi mathvariant='normal'>cosh</mi><mrow><mn>2</mn></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msup><mi mathvariant='normal'>sinh</mi><mrow><mn>2</mn></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1.</mn></mrow></mstyle></math>If <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>sinh</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo></mrow><mrow><mi mathvariant='normal'>$a</mi></mrow></mstyle></math> then <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>cosh</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo></mrow></mstyle></math></p>@
qu.3.3.answer=1@
qu.3.3.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi></mi></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msqrt><mrow><mi mathvariant='normal'>$c</mi></mrow></msqrt></mrow></mstyle></math>@
qu.3.3.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi></mi></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msqrt><mrow><mi mathvariant='normal'>$c</mi></mrow></msqrt></mrow></mstyle></math>@
qu.3.3.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msqrt><mrow><mi mathvariant='normal'>$d</mi></mrow></msqrt></mrow></mstyle></math>@
qu.3.3.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mrow><msqrt><mrow><mi mathvariant='normal'>$d</mi></mrow></msqrt></mrow></mrow></mstyle></math>@
qu.3.3.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>both</mi><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><msqrt><mrow><mi mathvariant='normal'>$c</mi></mrow></msqrt><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mo mathvariant='bold' fontweight='bold' lspace='0.0em' rspace='0.0em'>and</mo><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><msqrt><mrow><mi mathvariant='normal'>$c</mi></mrow></msqrt></mrow></mrow></mstyle></math>@
qu.3.3.choice.6=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>both</mi><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mrow><msqrt><mrow><mi mathvariant='normal'>$d</mi></mrow></msqrt></mrow><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mo mathvariant='bold' fontweight='bold' lspace='0.0em' rspace='0.0em'>and</mo><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><msqrt><mrow><mi mathvariant='normal'>$d</mi></mrow></msqrt></mrow></mrow></mstyle></math>@
qu.3.3.fixed=@

qu.3.4.mode=Multiple Choice@
qu.3.4.name=coshFINDsinh@
qu.3.4.comment=<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi mathvariant='normal'>cosh</mi><mrow><mn>2</mn></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msup><mi mathvariant='normal'>sinh</mi><mrow><mn>2</mn></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msup><mi mathvariant='normal'>sinh</mi><mrow><mn>2</mn></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1</mn></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>sinh</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mrow><mo lspace='0.0em' rspace='0.0em'>&plusmn;</mo></mrow><mrow><msqrt><mrow><mi mathvariant='normal'>$d</mi></mrow></msqrt></mrow></mrow></mstyle></math></p>@
qu.3.4.editing=useHTML@
qu.3.4.solution=@
qu.3.4.algorithm=$a=range(2,10,1);
$c=1+$a^2;
$d=$a^2-1;@
qu.3.4.uid=26ca668f-fbfc-4369-86f4-ca6f00dfb47c@
qu.3.4.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=Hyperbolic Identities;
@
qu.3.4.question=<p>Remember that <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi mathvariant='normal'>cosh</mi><mrow><mn>2</mn></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msup><mi mathvariant='normal'>sinh</mi><mrow><mn>2</mn></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mn>1.</mn></mrow></mstyle></math>If <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>cosh</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo></mrow><mrow><mi mathvariant='normal'>$a</mi></mrow></mstyle></math> then <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>sinh</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo></mrow></mstyle></math></p>@
qu.3.4.answer=6@
qu.3.4.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi></mi></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msqrt><mrow><mi mathvariant='normal'>$c</mi></mrow></msqrt></mrow></mstyle></math>@
qu.3.4.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi></mi></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msqrt><mrow><mi mathvariant='normal'>$c</mi></mrow></msqrt></mrow></mstyle></math>@
qu.3.4.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msqrt><mrow><mi mathvariant='normal'>$d</mi></mrow></msqrt></mrow></mstyle></math>@
qu.3.4.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mrow><msqrt><mrow><mi mathvariant='normal'>$d</mi></mrow></msqrt></mrow></mrow></mstyle></math>@
qu.3.4.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>both</mi><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><msqrt><mrow><mi mathvariant='normal'>$c</mi></mrow></msqrt><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mo mathvariant='bold' fontweight='bold' lspace='0.0em' rspace='0.0em'>and</mo><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><msqrt><mrow><mi mathvariant='normal'>$c</mi></mrow></msqrt></mrow></mrow></mstyle></math>@
qu.3.4.choice.6=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>both</mi><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mrow><msqrt><mrow><mi mathvariant='normal'>$d</mi></mrow></msqrt></mrow><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mo mathvariant='bold' fontweight='bold' lspace='0.0em' rspace='0.0em'>and</mo><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mrow><msqrt><mrow><mi mathvariant='normal'>$d</mi></mrow></msqrt></mrow></mrow></mstyle></math>@
qu.3.4.fixed=@

qu.4.topic=DerHypXchoice@

qu.4.1.mode=Multiple Choice@
qu.4.1.name=dersinhXChoice@
qu.4.1.comment=<p>Remember + + + - - -</p>
<p><img width="410" height="268" alt="" src="__BASE_URI__pictures/archyp.png" /></p>@
qu.4.1.editing=useHTML@
qu.4.1.solution=@
qu.4.1.algorithm=$a=range(2,9,2);
$b=range(1,10,1);@
qu.4.1.uid=ff4abeac-e215-4ffa-8bc7-4fbc66c34534@
qu.4.1.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=Derivatives;
@
qu.4.1.question=<p>Find the derivative: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mfrac><mi mathvariant='normal'>sinh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math></p>@
qu.4.1.answer=1@
qu.4.1.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>cosh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced></mrow></mstyle></math>@
qu.4.1.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mrow></mrow></mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>cosh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced></mrow></mstyle></math>@
qu.4.1.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mn>1</mn><mi mathvariant='normal'>$a</mi></mfrac><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>cosh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mstyle></math>@
qu.4.1.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mfrac><mn>1</mn><mi mathvariant='normal'>$a</mi></mfrac><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>cosh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mstyle></math>@
qu.4.1.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mn>1</mn><mi mathvariant='normal'>$a</mi></mfrac><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>cosh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced></mrow></mstyle></math>@
qu.4.1.fixed=@

qu.4.2.mode=Multiple Choice@
qu.4.2.name=dercoshXChoice@
qu.4.2.comment=<p>Remember&nbsp; + + + - - -</p>
<p><img width="410" height="268" alt="" src="__BASE_URI__pictures/archyp.png" /></p>@
qu.4.2.editing=useHTML@
qu.4.2.solution=@
qu.4.2.algorithm=$a=range(2,10,1);
$b=range(1,10,1);
$c=range(2,9,2);@
qu.4.2.uid=5dda2650-e8a0-4b38-96a5-c6dee361e577@
qu.4.2.info=  Author=Jack Weiner, Gord Clement;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=Derivatives;
  Difficulty=Easy;
@
qu.4.2.question=<p>Find the derivative: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mfrac><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mfrac></mrow><mrow><mi mathvariant='normal'>cosh</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced></mrow></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math></p>@
qu.4.2.answer=1@
qu.4.2.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mrow><mi    mathvariant='normal' >sinh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mrow></math>@
qu.4.2.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mrow></mrow></mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'     lspace='thickmathspace' rspace='thickmathspace'       >&minus;</mo><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='thickmathspace' rspace='thickmathspace'       >&sdot;</mo><mrow><mi    mathvariant='normal' >sinh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mrow></math>@
qu.4.2.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mrow><mi    mathvariant='normal' >sinh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.4.2.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mrow><mi    mathvariant='normal' >sinh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></mrow></math>@
qu.4.2.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mi    mathvariant='normal' >sinh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mrow></math>@
qu.4.2.fixed=@

qu.4.3.mode=Multiple Choice@
qu.4.3.name=dertanhXChoice@
qu.4.3.comment=<p>Remember + + + - - -</p>
<p><img width="410" height="268" alt="" src="__BASE_URI__pictures/archyp.png" /></p>@
qu.4.3.editing=useHTML@
qu.4.3.solution=@
qu.4.3.algorithm=$a=range(2,9,2);
$b=range(1,10,1);
$X=mathml("$a*x+$b");@
qu.4.3.uid=b57ab012-7753-4e17-abb2-b20ab0e49355@
qu.4.3.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=Derivatives;
@
qu.4.3.question=<p>Find the derivative: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mfrac><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mfrac></mrow><mrow><mi mathvariant='normal'>tanh</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced></mrow></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math></p>@
qu.4.3.answer=1@
qu.4.3.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mrow><msup ><mi    mathvariant='normal' >sech</mi><mn    mathvariant='normal' >2</mn></msup><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mrow></math>@
qu.4.3.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mrow></mrow></mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='thickmathspace' rspace='thickmathspace'       >&sdot;</mo><mrow><msup ><mi    mathvariant='normal' >sech</mi><mn    mathvariant='normal' >2</mn></msup><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mrow></math>@
qu.4.3.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mi    mathvariant='normal' >sech</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&sdot;</mo><mrow><mi    mathvariant='normal' >tanh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mrow></math>@
qu.4.3.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'             >&minus;</mo><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mrow><mi    mathvariant='normal' >sech</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&sdot;</mo><mrow><mi    mathvariant='normal' >tanh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mrow></math>@
qu.4.3.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mo    mathvariant='normal'             >&sdot;</mo><mrow><mi    mathvariant='normal' >ln</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mrow><mfenced open='&LeftBracketingBar;' close='&RightBracketingBar;'><mrow><mrow><mi    mathvariant='normal' >cosh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mrow></mfenced></mrow></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.4.3.fixed=@

qu.4.4.mode=Multiple Choice@
qu.4.4.name=dersechXChoice@
qu.4.4.comment=<p>Remember&nbsp; + + + - - -</p>
<p>
<table border="1" cellspacing="1" cellpadding="1" width="200">
    <tbody>
        <tr>
            <td>
            <p align="center"><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>y</mi></mrow></mstyle></math></p>
            </td>
            <td>
            <p align="center"><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>y</mi></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mfrac></mrow></mstyle></math></p>
            </td>
        </tr>
        <tr>
            <td>sinh(x)</td>
            <td>cosh(x)</td>
        </tr>
        <tr>
            <td>cosh(x)</td>
            <td>sinh(x)</td>
        </tr>
        <tr>
            <td>tanh(x)</td>
            <td><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msup><mi mathvariant='normal'>sech</mi><mrow><mn>2</mn></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced></mrow></mstyle></math></td>
        </tr>
        <tr>
            <td>csch(x)</td>
            <td><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>csch</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>coth</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced></mrow></mstyle></math></td>
        </tr>
        <tr>
            <td>sech(x)</td>
            <td><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>sech</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>tanh</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced></mrow></mstyle></math></td>
        </tr>
        <tr>
            <td>coth(x)</td>
            <td><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msup><mi mathvariant='normal'>csch</mi><mrow><mn>2</mn></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced></mrow></mstyle></math></td>
        </tr>
    </tbody>
</table>
</p>@
qu.4.4.editing=useHTML@
qu.4.4.solution=@
qu.4.4.algorithm=$a=range(2,9,2);
$b=range(1,10,1);
$X=mathml("$a*x+$b");@
qu.4.4.uid=37d14ec8-29a4-4409-bcd1-6a33a9107096@
qu.4.4.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=Derivatives;
@
qu.4.4.question=<p>Find the derivative: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mfrac><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mfrac></mrow><mrow><mi mathvariant='normal'>sech</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced></mrow></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math></p>@
qu.4.4.answer=4@
qu.4.4.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >tan</mi><mrow><msup ><mi    mathvariant='normal' >h</mi><mn    mathvariant='normal' >2</mn></msup><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mrow></math>@
qu.4.4.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mrow></mrow></mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='thickmathspace' rspace='thickmathspace'       >&sdot;</mo><mrow><msup ><mi    mathvariant='normal' >tanh</mi><mn    mathvariant='normal' >2</mn></msup><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mrow></math>@
qu.4.4.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mi    mathvariant='normal' >sech</mi><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&sdot;</mo><mrow><mi    mathvariant='normal' >tanh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mrow></math>@
qu.4.4.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'             >&minus;</mo><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mrow><mi    mathvariant='normal' >sech</mi><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&sdot;</mo><mrow><mi    mathvariant='normal' >tanh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mrow></math>@
qu.4.4.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mrow><mi    mathvariant='normal' >csch</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mrow></math>@
qu.4.4.fixed=@

qu.4.5.mode=Multiple Choice@
qu.4.5.name=dercothXChoice@
qu.4.5.comment=<p>Remember&nbsp; + + + - - -</p>
<p><img width="410" height="268" alt="" src="__BASE_URI__pictures/archyp.png" /></p>@
qu.4.5.editing=useHTML@
qu.4.5.solution=@
qu.4.5.algorithm=$a=range(2,9,2);
$b=range(1,10,1);
$X=mathml("$a*x+$b");@
qu.4.5.uid=83791fca-eec8-4544-bb2a-a63a056187f4@
qu.4.5.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=Derivatives;
@
qu.4.5.question=<p>Find the derivative: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mfrac><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mfrac></mrow><mrow><mi mathvariant='normal'>coth</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced></mrow></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math></p>@
qu.4.5.answer=1@
qu.4.5.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mrow><msup ><mi    mathvariant='normal' >csch</mi><mn    mathvariant='normal' >2</mn></msup><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mrow></math>@
qu.4.5.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mrow></mrow></mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='thickmathspace' rspace='thickmathspace'       >&sdot;</mo><mrow><msup ><mi    mathvariant='normal' >csch</mi><mn    mathvariant='normal' >2</mn></msup><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mrow></math>@
qu.4.5.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mi    mathvariant='normal' >csch</mi><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&sdot;</mo><mrow><mi    mathvariant='normal' >coth</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mrow></math>@
qu.4.5.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'             >&minus;</mo><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mrow><mi    mathvariant='normal' >csch</mi><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&sdot;</mo><mrow><mi    mathvariant='normal' >coth</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mrow></math>@
qu.4.5.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mo    mathvariant='normal'             >&sdot;</mo><mrow><mi    mathvariant='normal' >ln</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mrow><mfenced open='&LeftBracketingBar;' close='&RightBracketingBar;'><mrow><mrow><mi    mathvariant='normal' >sinh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mrow></mfenced></mrow></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.4.5.fixed=@

qu.4.6.mode=Multiple Choice@
qu.4.6.name=dercschXChoice@
qu.4.6.comment=<p>Remember + + + - - -</p>
<p><img width="410" height="268" alt="" src="__BASE_URI__pictures/archyp.png" /></p>@
qu.4.6.editing=useHTML@
qu.4.6.solution=@
qu.4.6.algorithm=$a=range(2,9,2);
$b=range(1,10,1);
$X=mathml("$a*x+$b");@
qu.4.6.uid=d4b44970-8ee7-46a2-bb39-4bf566715ce5@
qu.4.6.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=Derivatives;
@
qu.4.6.question=<p>Find the derivative: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mfrac><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mfrac></mrow><mrow><mi mathvariant='normal'>csch</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced></mrow></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math></p>@
qu.4.6.answer=4@
qu.4.6.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mrow><msup ><mi    mathvariant='normal' >coth</mi><mn    mathvariant='normal' >2</mn></msup><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mrow></math>@
qu.4.6.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mrow></mrow></mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='thickmathspace' rspace='thickmathspace'       >&sdot;</mo><mrow><msup ><mi    mathvariant='normal' >coth</mi><mn    mathvariant='normal' >2</mn></msup><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mrow></math>@
qu.4.6.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mi    mathvariant='normal' >csch</mi><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&sdot;</mo><mrow><mi    mathvariant='normal' >coth</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mrow></math>@
qu.4.6.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'             >&minus;</mo><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mrow><mi    mathvariant='normal' >csch</mi><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&sdot;</mo><mrow><mi    mathvariant='normal' >coth</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mrow></math>@
qu.4.6.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mrow><mi    mathvariant='normal' >sech</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mrow></math>@
qu.4.6.fixed=@

qu.5.topic=HyperDerWritten@

qu.5.1.question=<p>Find <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mfrac></mrow></mstyle></math>$display</p>@
qu.5.1.maple=evalb(simplify(($ANS)-($RESPONSE))=0);@
qu.5.1.allow2d=1@
qu.5.1.maple_answer=$ANSD@
qu.5.1.type=formula@
qu.5.1.mode=Maple@
qu.5.1.name=HyperDer@
qu.5.1.comment=<p>Remember + + + - - -</p>
<p><img width="410" height="268" alt="" src="__BASE_URI__pictures/archyp.png" /></p>@
qu.5.1.editing=useHTML@
qu.5.1.solution=@
qu.5.1.algorithm=$a=rint(2,9);
$b=rint(2,10);
$z=rint(2);
$f=switch($z,"sinh(($a)*x+($b))","cosh(($a)*
x+($b))");
$display=maple("printf(MathML[ExportPresentation]($f))");
$ANSD=switch($z,"$a*cosh(($a)*x+($b))","($a)*sinh(($a)*x+($b))");
$ANS=switch($z,$a*cosh(($a)*x+($b)),($a)*sinh(($a)*x+($b)));@
qu.5.1.uid=7c76ab57-ef0c-4de9-9bf0-743f2b6e1b25@

qu.6.topic=IntegralHyperbolic@

qu.6.1.mode=Multiple Choice@
qu.6.1.name=intcothXChoice@
qu.6.1.comment=<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.0em' rspace='0.0em' stretchy='true' largeop='true'>&Integral;</mo><mi mathvariant='normal'>coth</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='auto'/></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mo lspace='0.0em' rspace='0.0em' stretchy='true' largeop='true'>&Integral;</mo><mfrac><mrow><mi mathvariant='normal'>cosh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced></mrow><mrow><mi mathvariant='normal'>sinh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mn>1</mn><mrow><mi mathvariant='normal'>$a</mi></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>ln</mi><mo fence='true' lspace='0.1666667em' rspace='0.1666667em' stretchy='true'>&lpar;</mo><mfenced open='|' close='|' separators=','><mrow><mi mathvariant='normal'>sinh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced></mrow></mfenced><mo fence='true' lspace='0.1666667em' rspace='0.1666667em' stretchy='true'>&rpar;</mo><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mstyle></math></p>@
qu.6.1.editing=useHTML@
qu.6.1.solution=@
qu.6.1.algorithm=$a=range(2,9);
$b=range(1,10);@
qu.6.1.uid=8f546b60-783a-44cd-a64f-541cb8603156@
qu.6.1.info=  Author=Jack Weiner, Gord Clemet;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=Integration;
@
qu.6.1.question=<p>Find the integral: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.0em' rspace='0.0em' stretchy='true' largeop='true'>&Integral;</mo><mi mathvariant='normal'>coth</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi mathvariant='normal'>x</mi><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='newline'/><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='auto'/></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math></p>@
qu.6.1.answer=3@
qu.6.1.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mfrac><mn>1</mn><mrow><mi mathvariant='normal'>$a</mi></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>csch</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mstyle></math>@
qu.6.1.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mrow></mrow></mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'></mi></mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mfrac><mn>1</mn><mrow><mi mathvariant='normal'>$a</mi></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>ln</mi><mfenced open='(' close=')' separators=','><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mfenced open='|' close='|' separators=','><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi mathvariant='normal'>sinh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mstyle></math>@
qu.6.1.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mrow></mrow></mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'></mi></mrow><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mfrac><mn>1</mn><mrow><mi mathvariant='normal'>$a</mi></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>ln</mi><mfenced open='(' close=')' separators=','><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mfenced open='|' close='|' separators=','><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi mathvariant='normal'>sinh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mstyle></math>@
qu.6.1.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mrow></mrow></mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>ln</mi><mo fence='true' lspace='0.1666667em' rspace='0.1666667em' stretchy='true'>&lpar;</mo><mfenced open='|' close='|' separators=','><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi mathvariant='normal'>sinh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mfenced><mo fence='true' lspace='0.1666667em' rspace='0.1666667em' stretchy='true'>&rpar;</mo><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow></mrow></mstyle></math>@
qu.6.1.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mrow></mrow></mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>ln</mi><mo fence='true' lspace='0.1666667em' rspace='0.1666667em' stretchy='true'>&lpar;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mfenced open='|' close='|' separators=','><mrow><mi mathvariant='normal'>sinh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mfenced><mo fence='true' lspace='0.1666667em' rspace='0.1666667em' stretchy='true'>&rpar;</mo><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mstyle></math>@
qu.6.1.fixed=@

qu.6.2.mode=Multiple Choice@
qu.6.2.name=inttanhXChoice@
qu.6.2.comment=<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.0em' rspace='0.0em' stretchy='true' largeop='true'>&Integral;</mo><mi mathvariant='normal'>tanh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mo lspace='0.0em' rspace='0.0em' stretchy='true' largeop='true'>&Integral;</mo><mfrac><mrow><mi mathvariant='normal'>sinh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo></mrow><mrow><mi mathvariant='normal'>cosh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mn>1</mn><mrow><mi mathvariant='normal'>$a</mi></mrow></mfrac><mi mathvariant='normal'>ln</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>cosh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mstyle></math></p>
<p>Note: we do not need absolute value bars inside the ln since <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>cosh</mi><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.2777778em' rspace='0.2777778em'>&GreaterEqual;</mo><mn>1</mn></mrow></mstyle></math>for all <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>x</mi></mrow></mstyle></math></p>@
qu.6.2.editing=useHTML@
qu.6.2.solution=@
qu.6.2.algorithm=$a=range(2,9,2);
$b=range(1,10,1);@
qu.6.2.uid=13d1854e-29f0-4b50-a69b-fa99e07c944b@
qu.6.2.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=Integration;
@
qu.6.2.question=<p>Find the integral: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.0em' rspace='0.0em'>&Integral;</mo><mrow><mi mathvariant='normal'>tanh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced></mrow><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math></p>@
qu.6.2.answer=3@
qu.6.2.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mo    mathvariant='normal'             >&sdot;</mo><mrow><mi    mathvariant='normal' >sech</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.6.2.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mrow></mrow></mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'     lspace='thickmathspace' rspace='thickmathspace'       >&minus;</mo><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mo    mathvariant='normal'     lspace='thickmathspace' rspace='thickmathspace'       >&sdot;</mo><mrow><mi    mathvariant='normal' >ln</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >cosh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.6.2.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mrow></mrow></mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mo    mathvariant='normal'     lspace='thickmathspace' rspace='thickmathspace'       >&sdot;</mo><mrow><mi    mathvariant='normal' >ln</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >cosh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.6.2.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mrow></mrow></mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'     lspace='thickmathspace' rspace='thickmathspace'       >&minus;</mo><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='thickmathspace' rspace='thickmathspace'       >&sdot;</mo><mrow><mi    mathvariant='normal' >ln</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >cosh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.6.2.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mrow></mrow></mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mrow><mi    mathvariant='normal' >ln</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >cosh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.6.2.fixed=@

qu.6.3.mode=Multiple Choice@
qu.6.3.name=integralsechtanhXChoice@
qu.6.3.comment=<p>Remember + + + - - -</p>
<p><img width="410" height="268" alt="" src="__BASE_URI__pictures/archyp.png" /></p>@
qu.6.3.editing=useHTML@
qu.6.3.solution=@
qu.6.3.algorithm=$a=range(2,9);
$b=range(1,10);
$X=mathml("$a*x+$b");@
qu.6.3.uid=c994ee8f-63f2-4370-920e-cb5f643082f2@
qu.6.3.info=  Author=Jack Weiner, Gord Clemet;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=Integration;
@
qu.6.3.question=<p>Find the integral: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.0em' rspace='0.0em'>&Integral;</mo><mrow><mi mathvariant='normal'>sech</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mrow><mi mathvariant='normal'>tanh</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced></mrow><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math></p>@
qu.6.3.answer=3@
qu.6.3.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'             >&minus;</mo><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mo    mathvariant='normal'             >&sdot;</mo><mrow><mi    mathvariant='normal' >tanh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.6.3.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mrow></mrow></mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='thickmathspace' rspace='thickmathspace'       >&sdot;</mo><mrow><mi    mathvariant='normal' >sech</mi><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.6.3.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mrow></mrow></mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mo    mathvariant='normal'     lspace='thickmathspace' rspace='thickmathspace'       >&sdot;</mo><mrow><mi    mathvariant='normal' >sech</mi><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.6.3.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mrow></mrow></mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mo    mathvariant='normal'     lspace='thickmathspace' rspace='thickmathspace'       >&sdot;</mo><mrow><mi    mathvariant='normal' >sech</mi><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.6.3.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mrow></mrow></mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='thickmathspace' rspace='thickmathspace'       >&sdot;</mo><mrow><mi    mathvariant='normal' >sech</mi><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.6.3.fixed=@

qu.6.4.mode=Multiple Choice@
qu.6.4.name=integralsech^2XChoice@
qu.6.4.comment=<p>Remember + + + - - -</p>
<p><img width="410" height="268" alt="" src="__BASE_URI__pictures/archyp.png" /></p>@
qu.6.4.editing=useHTML@
qu.6.4.solution=@
qu.6.4.algorithm=$a=range(2,9);
$b=range(1,10);
$X=mathml("$a*x+$b");@
qu.6.4.uid=0ea78008-a41a-4ecd-b42c-382c1f624d9e@
qu.6.4.info=  Author=Jack Weier, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=Integration;
@
qu.6.4.question=<p>Find the integral: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.0em' rspace='0.0em'>&Integral;</mo><msup><mi mathvariant='normal'>sech</mi><mn>2</mn></msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math></p>@
qu.6.4.answer=3@
qu.6.4.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mrow><mi    mathvariant='normal' >tanh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.6.4.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mrow></mrow></mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='thickmathspace' rspace='thickmathspace'       >&sdot;</mo><mrow><mi    mathvariant='normal' >tanh</mi><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.6.4.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mrow><mn    mathvariant='normal' >1</mn></mrow><mi    mathvariant='normal' >$a</mi></mfrac><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >tanh</mi><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.6.4.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'             >&minus;</mo><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mo    mathvariant='normal'             >&sdot;</mo><mrow><mi    mathvariant='normal' >tanh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></mrow></math>@
qu.6.4.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mo    mathvariant='normal'             >&sdot;</mo><msup ><mi    mathvariant='normal' >tanh</mi><mn    mathvariant='normal' >2</mn></msup><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.6.4.fixed=@

qu.6.5.mode=Multiple Choice@
qu.6.5.name=intcoshXChoice@
qu.6.5.comment=<p>Remember + + + - - -</p>
<p><img width="410" height="268" alt="" src="__BASE_URI__pictures/archyp.png" /></p>@
qu.6.5.editing=useHTML@
qu.6.5.solution=@
qu.6.5.algorithm=$a=range(2,10);
$b=range(1,10);@
qu.6.5.uid=a8104a98-a0bd-4cfc-ab9e-346ede90ffea@
qu.6.5.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=Integration;
@
qu.6.5.question=<p>Find the integral: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.0em' rspace='0.0em' stretchy='true' largeop='true'>&Integral;</mo><mi mathvariant='normal'>cosh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math></p>@
qu.6.5.answer=3@
qu.6.5.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>sinh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced></mrow></mstyle></math>@
qu.6.5.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mrow></mrow></mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>sinh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mstyle></math>@
qu.6.5.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mn>1</mn><mi mathvariant='normal'>$a</mi></mfrac><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>sinh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mstyle></math>@
qu.6.5.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mfrac><mn>1</mn><mi mathvariant='normal'>$a</mi></mfrac><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>sinh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mstyle></math>@
qu.6.5.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>sinh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mstyle></math>@
qu.6.5.fixed=@

qu.6.6.mode=Multiple Choice@
qu.6.6.name=integralcsch^2XChoice@
qu.6.6.comment=<p>Remember + + + - - -</p>
<p><img width="410" height="268" alt="" src="__BASE_URI__pictures/archyp.png" /></p>@
qu.6.6.editing=useHTML@
qu.6.6.solution=@
qu.6.6.algorithm=$a=range(2,9);
$b=range(1,10);
$X=mathml("$a*x+$b");@
qu.6.6.uid=9db94c2d-3e59-4269-93d0-d5b69976b9fc@
qu.6.6.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=Integration;
@
qu.6.6.question=<p>Find the integral: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.0em' rspace='0.0em'>&Integral;</mo><msup><mi mathvariant='normal'>csch</mi><mn>2</mn></msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math></p>@
qu.6.6.answer=4@
qu.6.6.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mrow><mi    mathvariant='normal' >coth</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.6.6.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mrow></mrow></mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='thickmathspace' rspace='thickmathspace'       >&sdot;</mo><mrow><mi    mathvariant='normal' >coth</mi><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.6.6.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mrow><mn    mathvariant='normal' >1</mn></mrow><mi    mathvariant='normal' >$a</mi></mfrac><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >coth</mi><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.6.6.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'             >&minus;</mo><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mo    mathvariant='normal'             >&sdot;</mo><mrow><mi    mathvariant='normal' >coth</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></mrow></math>@
qu.6.6.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mo    mathvariant='normal'             >&sdot;</mo><msup ><mi    mathvariant='normal' >coth</mi><mn    mathvariant='normal' >2</mn></msup><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.6.6.fixed=@

qu.6.7.mode=Multiple Choice@
qu.6.7.name=integralcschcothXChoice@
qu.6.7.comment=<p>Remember + + + - - -</p>
<p><img width="410" height="268" alt="" src="__BASE_URI__pictures/archyp.png" /></p>@
qu.6.7.editing=useHTML@
qu.6.7.solution=@
qu.6.7.algorithm=$a=range(2,9);
$b=range(1,10);
$X=mathml("$a*x+$b");@
qu.6.7.uid=5fb0f3c0-c090-413c-89ab-c79e63090626@
qu.6.7.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=Integration;
@
qu.6.7.question=<p>Find the integral: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.0em' rspace='0.0em'>&Integral;</mo><mrow><mi mathvariant='normal'>csch</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mrow><mi mathvariant='normal'>coth</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi></mrow></mfenced></mrow><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math></p>@
qu.6.7.answer=3@
qu.6.7.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'             >&minus;</mo><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mo    mathvariant='normal'             >&sdot;</mo><mrow><mi    mathvariant='normal' >coth</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.6.7.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mrow></mrow></mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='thickmathspace' rspace='thickmathspace'       >&sdot;</mo><mrow><mi    mathvariant='normal' >csch</mi><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.6.7.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mrow></mrow></mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mo    mathvariant='normal'     lspace='thickmathspace' rspace='thickmathspace'       >&sdot;</mo><mrow><mi    mathvariant='normal' >csch</mi><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.6.7.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mrow></mrow></mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mo    mathvariant='normal'     lspace='thickmathspace' rspace='thickmathspace'       >&sdot;</mo><mrow><mi    mathvariant='normal' >csch</mi><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.6.7.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mrow></mrow></mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='thickmathspace' rspace='thickmathspace'       >&sdot;</mo><mrow><mi    mathvariant='normal' >csch</mi><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.6.7.fixed=@

qu.6.8.mode=Multiple Choice@
qu.6.8.name=intsinhXChoice@
qu.6.8.comment=<p>Remember + + + - - -</p>
<p><img width="410" height="268" alt="" src="__BASE_URI__pictures/archyp.png" /></p>@
qu.6.8.editing=useHTML@
qu.6.8.solution=@
qu.6.8.algorithm=$a=range(2,9);
$b=range(1,10);@
qu.6.8.uid=a794bde2-6cd2-45d6-9072-1fb3d45eec7b@
qu.6.8.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=Integration;
@
qu.6.8.question=<p>Find the integral: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.0em' rspace='0.0em' stretchy='true' largeop='true'>&Integral;</mo><mi mathvariant='normal'>sinh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$b</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math></p>@
qu.6.8.answer=3@
qu.6.8.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mrow><mi    mathvariant='normal' >cosh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow></mrow></math>@
qu.6.8.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mrow></mrow></mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'     lspace='thickmathspace' rspace='thickmathspace'       >&minus;</mo><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='thickmathspace' rspace='thickmathspace'       >&sdot;</mo><mrow><mi    mathvariant='normal' >cosh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.6.8.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mrow><mi    mathvariant='normal' >cosh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.6.8.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mrow><mi    mathvariant='normal' >cosh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></mrow></math>@
qu.6.8.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mi    mathvariant='normal' >cosh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.6.8.fixed=@

qu.7.topic=archyperbolicgraphs@

qu.7.1.mode=Multiple Choice@
qu.7.1.name=choose archyperbolic graph@
qu.7.1.comment=@
qu.7.1.editing=useHTML@
qu.7.1.solution=@
qu.7.1.algorithm=$z1=rint(3);
$z2=rint(3);
$z3=rint(3);
condition:not(eq($z1,$z2))*not(eq($z3,$z2))*not(eq($z1,$z3));
$f=switch($z1,"arcsinh(x)","arccosh(x)","arctanh(x)");
$B=switch($z2,"arcsinh(x)","arccosh(x)","arctanh(x)");
$C=switch($z3,"arcsinh(x)","arccosh(x)","arctanh(x)");
$pa=plotmaple("plot($f,x=-2..2,y=-2..2,thickness=2),plotdevice='gif', plotoptions='height=250,width=250'");
$pb=plotmaple("plot($B,x=-2..2,y=-2..2,thickness=2),plotdevice='gif', plotoptions='height=250,width=250'");
$pc=plotmaple("plot($C,x=-2..2,y=-2..2,thickness=2),plotdevice='gif', plotoptions='height=250,width=250'");
$pd=plotmaple("plot(arcsinh(-x),x=-2..2,y=-2..2,thickness=2),plotdevice='gif', plotoptions='height=250,width=250'");
$pe=plotmaple("plot(arctanh(-x),x=-2..2,y=-2..2,thickness=2),plotdevice='gif', plotoptions='height=250,width=250'");@
qu.7.1.uid=153ca6c6-6813-4e80-a608-a0ebdeb8c8a7@
qu.7.1.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=archyp graphs;
@
qu.7.1.question=<p>Which of the following is the graph of <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>y</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$f</mi></mrow></mstyle></math>?</p>@
qu.7.1.answer=1@
qu.7.1.choice.1=$pa@
qu.7.1.choice.2=$pb@
qu.7.1.choice.3=$pc@
qu.7.1.choice.4=$pd@
qu.7.1.choice.5=$pe@
qu.7.1.fixed=@

qu.8.topic=archypLN@

qu.8.1.mode=Multiple Choice@
qu.8.1.name=arctanhLN@
qu.8.1.comment=@
qu.8.1.editing=useHTML@
qu.8.1.solution=@
qu.8.1.algorithm=$a=rint(9)+2;@
qu.8.1.uid=6cc344e7-a60b-4872-80e8-cb3a39351e6f@
qu.8.1.info=  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=archyp as ln;
  Difficulty=Easy;
  Author=Jack Weiner, Gord Clement;
@
qu.8.1.question=<p>As a <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>ln</mi></mrow></mstyle></math> funtion, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>arctanh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi></mrow></mfenced></mrow></mstyle></math> equals</p>@
qu.8.1.answer=1@
qu.8.1.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mn    mathvariant='normal' >2</mn></mfrac><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >ln</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mfrac    ><mrow><mn    mathvariant='normal' >1</mn><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mi    mathvariant='italic' >x</mi></mrow><mrow><mn    mathvariant='normal' >1</mn><mo    mathvariant='normal'             >&minus;</mo><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mi    mathvariant='italic' >x</mi></mrow></mfrac></mrow></mfenced></mrow><mrow></mrow></mrow></math>@
qu.8.1.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mn    mathvariant='normal' >2</mn></mfrac><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >ln</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mfrac    ><mrow><mn    mathvariant='normal' >1</mn><mo    mathvariant='normal'             >&minus;</mo><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mi    mathvariant='italic' >x</mi></mrow><mrow><mn    mathvariant='normal' >1</mn><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mi    mathvariant='italic' >x</mi></mrow></mfrac></mrow></mfenced></mrow><mrow></mrow></mrow></math>@
qu.8.1.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mn    mathvariant='normal' >2</mn></mfrac><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >ln</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mfrac    ><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mn    mathvariant='normal' >1</mn></mrow><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mn    mathvariant='normal' >1</mn></mrow></mfrac></mrow></mfenced></mrow><mrow></mrow></mrow></math>@
qu.8.1.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mn    mathvariant='normal' >2</mn></mfrac><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >ln</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mfrac    ><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&minus;</mo><mn    mathvariant='normal' >1</mn></mrow><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mn    mathvariant='normal' >1</mn></mrow></mfrac></mrow></mfenced></mrow><mrow></mrow></mrow></math>@
qu.8.1.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mn    mathvariant='normal' >2</mn></mfrac><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >ln</mi><mo    mathvariant='normal'     lspace='verythinmathspace' rspace='verythinmathspace' stretchy='true'      >&verbar;</mo><mrow><mfrac    ><mrow><mn    mathvariant='normal' >1</mn><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mi    mathvariant='italic' >x</mi></mrow><mrow><mn    mathvariant='normal' >1</mn><mo    mathvariant='normal'             >&minus;</mo><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mi    mathvariant='italic' >x</mi></mrow></mfrac></mrow><mo    mathvariant='normal'     lspace='verythinmathspace' rspace='verythinmathspace' stretchy='true'      >&verbar;</mo></mrow></mrow></math>@
qu.8.1.fixed=@

qu.8.2.mode=Multiple Choice@
qu.8.2.name=arcsinhLN@
qu.8.2.comment=@
qu.8.2.editing=useHTML@
qu.8.2.solution=@
qu.8.2.algorithm=$a=rint(9)+2;
$b=$a^2;@
qu.8.2.uid=83688cd6-4ef6-46c4-ab0d-9b6e333c4fad@
qu.8.2.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=archyp as ln;
@
qu.8.2.question=<p>As a <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>ln</mi></mrow></mstyle></math> funtion, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>arcsinh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi></mrow></mfenced></mrow></mstyle></math> equals</p>@
qu.8.2.answer=1@
qu.8.2.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mi    mathvariant='normal' >ln</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><msqrt><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mrow><msup ><mi    mathvariant='italic' >x</mi><mrow><mn    mathvariant='normal' >2</mn></mrow></msup><mo    mathvariant='normal'             >&plus;</mo><mn    mathvariant='normal' >1</mn></mrow></mrow></msqrt></mrow></mfenced></mrow><mrow></mrow></mrow></math>@
qu.8.2.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mi    mathvariant='normal' >ln</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><msqrt><mrow><mrow><mrow><mrow><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><msup ><mi    mathvariant='italic' >x</mi><mn    mathvariant='normal' >2</mn></msup></mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mn    mathvariant='normal' >1</mn></mrow></mrow></mrow></mrow></msqrt></mrow></mfenced></mrow><mrow></mrow></mrow></math>@
qu.8.2.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mi    mathvariant='normal' >ln</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><msqrt><mrow><mrow><mrow><mn    mathvariant='normal' >1</mn><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><msup ><mi    mathvariant='italic' >x</mi><mn    mathvariant='normal' >2</mn></msup></mrow></mrow></mrow></mrow></msqrt></mrow></mfenced></mrow><mrow></mrow></mrow></math>@
qu.8.2.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mi    mathvariant='normal' >ln</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&minus;</mo><msqrt><mrow><mrow><mrow><mn    mathvariant='normal' >1</mn><mo    mathvariant='normal'             >&plus;</mo><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><msup ><mi    mathvariant='italic' >x</mi><mn    mathvariant='normal' >2</mn></msup></mrow></mrow></mrow></mrow></msqrt></mrow></mfenced></mrow><mrow></mrow></mrow></math>@
qu.8.2.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mi    mathvariant='normal' >ln</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><msqrt><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mrow><mrow><mrow><msup ><mi    mathvariant='italic' >x</mi><mn    mathvariant='normal' >2</mn></msup><mo    mathvariant='normal'             >&minus;</mo><mn    mathvariant='normal' >1</mn></mrow></mrow></mrow></mrow></msqrt></mrow></mfenced></mrow><mrow></mrow></mrow></math>@
qu.8.2.fixed=@

qu.8.3.mode=Multiple Choice@
qu.8.3.name=arccoshLN@
qu.8.3.comment=@
qu.8.3.editing=useHTML@
qu.8.3.solution=@
qu.8.3.algorithm=$a=rint(9)+2;
$b=$a^2;@
qu.8.3.uid=a9e8ffa0-ec03-42c0-8970-350adbb0f3fd@
qu.8.3.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=archyp as l;
@
qu.8.3.question=<p>As a <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>ln</mi></mrow></mstyle></math> function, <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>arccosh</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi></mrow></mfenced></mrow></mstyle></math> equals</p>@
qu.8.3.answer=2@
qu.8.3.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mi    mathvariant='normal' >ln</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><msqrt><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mrow><msup ><mi    mathvariant='italic' >x</mi><mrow><mn    mathvariant='normal' >2</mn></mrow></msup><mo    mathvariant='normal'             >&plus;</mo><mn    mathvariant='normal' >1</mn></mrow></mrow></msqrt></mrow></mfenced></mrow><mrow></mrow></mrow></math>@
qu.8.3.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mi    mathvariant='normal' >ln</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><msqrt><mrow><mrow><mrow><mrow><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><msup ><mi    mathvariant='italic' >x</mi><mn    mathvariant='normal' >2</mn></msup></mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mn    mathvariant='normal' >1</mn></mrow></mrow></mrow></mrow></msqrt></mrow></mfenced></mrow><mrow></mrow></mrow></math>@
qu.8.3.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mi    mathvariant='normal' >ln</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><msqrt><mrow><mrow><mrow><mn    mathvariant='normal' >1</mn><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><msup ><mi    mathvariant='italic' >x</mi><mn    mathvariant='normal' >2</mn></msup></mrow></mrow></mrow></mrow></msqrt></mrow></mfenced></mrow><mrow></mrow></mrow></math>@
qu.8.3.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mi    mathvariant='normal' >ln</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&minus;</mo><msqrt><mrow><mrow><mrow><mn    mathvariant='normal' >1</mn><mo    mathvariant='normal'             >&plus;</mo><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><msup ><mi    mathvariant='italic' >x</mi><mn    mathvariant='normal' >2</mn></msup></mrow></mrow></mrow></mrow></msqrt></mrow></mfenced></mrow><mrow></mrow></mrow></math>@
qu.8.3.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mi    mathvariant='normal' >ln</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><msqrt><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mrow><mrow><mrow><msup ><mi    mathvariant='italic' >x</mi><mn    mathvariant='normal' >2</mn></msup><mo    mathvariant='normal'             >&minus;</mo><mn    mathvariant='normal' >1</mn></mrow></mrow></mrow></mrow></msqrt></mrow></mfenced></mrow><mrow></mrow></mrow></math>@
qu.8.3.fixed=@

qu.9.topic=ARCHYPBABA@

qu.9.1.mode=Non Permuting Multiple Choice@
qu.9.1.name=arcsinh@
qu.9.1.comment=<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.0em' rspace='0.0em' stretchy='true' largeop='true'>&Integral;</mo><mfrac><mn>1</mn><mrow><msqrt><mrow><msup><mi>a</mi><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><msup><mi>b</mi><mrow><mn>2</mn></mrow></msup><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mi>x</mi><mrow><mn>2</mn></mrow></msup></mrow></msqrt></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mn>1</mn><mrow><mi>b</mi></mrow></mfrac><mi mathvariant='normal'>arcsinh</mi><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mi>b</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi></mrow><mrow><mi>a</mi></mrow></mfrac></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mstyle></math></p>@
qu.9.1.editing=useHTML@
qu.9.1.solution=@
qu.9.1.algorithm=$a=range(2,12);
$b=range(2,12);
condition:eq(gcd($a,$b),1);
$A=$a^2;
$B=$b^2;
$P=$a*$b;@
qu.9.1.uid=8c995e52-9490-4184-849f-e845c4410c34@
qu.9.1.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=Integration;
@
qu.9.1.question=<p>BABA works for archyperbolics!</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.0em' rspace='0.0em' stretchy='true' largeop='true'>&Integral;</mo><mfrac><mn>1</mn><mrow><msqrt><mrow><mi mathvariant='normal'>$A</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$B</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mi>x</mi><mrow><mn>2</mn></mrow></msup></mrow></msqrt></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mstyle></math></p>@
qu.9.1.answer=5@
qu.9.1.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$P</mi></mfrac><mrow><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >arctanh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mfrac    ><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi></mrow><mi    mathvariant='normal' >$a</mi></mfrac></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.9.1.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$b</mi></mfrac><mrow><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >arctanh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mfrac    ><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi></mrow><mi    mathvariant='normal' >$a</mi></mfrac></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.9.1.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mrow><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >arctanh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mfrac    ><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi></mrow><mi    mathvariant='normal' >$a</mi></mfrac></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.9.1.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$P</mi></mfrac><mrow><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >arcsinh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mfrac    ><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi></mrow><mi    mathvariant='normal' >$a</mi></mfrac></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.9.1.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$b</mi></mfrac><mrow><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >arcsinh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mfrac    ><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi></mrow><mi    mathvariant='normal' >$a</mi></mfrac></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.9.1.choice.6=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mrow><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >arcsinh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mfrac    ><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi></mrow><mi    mathvariant='normal' >$a</mi></mfrac></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.9.1.choice.7=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mrow><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >arcsec</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mfrac    ><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'             >&sdot;</mo><mo    mathvariant='normal'     lspace='verythinmathspace' rspace='verythinmathspace' stretchy='true'      >&verbar;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'     lspace='verythinmathspace' rspace='verythinmathspace' stretchy='true'      >&verbar;</mo></mrow><mi    mathvariant='normal' >$a</mi></mfrac></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.9.1.choice.8=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mrow><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >arcsech</mi><mfenced><mrow><mfrac    ><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi></mrow><mi    mathvariant='normal' >$a</mi></mfrac></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.9.1.fixed=@

qu.9.2.mode=Multiple Choice@
qu.9.2.name=arctanh@
qu.9.2.comment=<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.0em' rspace='0.0em' stretchy='true' largeop='true'>&Integral;</mo><mfrac><mn>1</mn><mrow><msup><mi>a</mi><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msup><mi>b</mi><mrow><mn>2</mn></mrow></msup><msup><mi>x</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mn>1</mn><mrow><mi>a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>b</mi></mrow></mfrac><mi mathvariant='normal'>arctanh</mi><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mi>b</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi></mrow><mrow><mi>a</mi></mrow></mfrac></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mstyle></math></p>@
qu.9.2.editing=useHTML@
qu.9.2.solution=@
qu.9.2.algorithm=$a=range(2,12);
$b=range(2,12);
condition:eq(gcd($a,$b),1);
$A=$a^2;
$B=$b^2;
$P=$a*$b;@
qu.9.2.uid=67b092b1-16d5-45a2-af8c-fe0c85af9909@
qu.9.2.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Hyperbolic Trig;
  Sub-Topic=Integration;
@
qu.9.2.question=<p>BABA works for archyperbolics!</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mo    mathvariant='normal'   fence='unset' separator='unset' lspace='' rspace='' stretchy='unset' symmetric='unset' maxsize='' minsize='' largeop='unset' movablelimits='unset' accent='unset'>&Integral;</mo><mfrac    ><mn    mathvariant='normal' >1</mn><mrow><mi    mathvariant='normal' >$A</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mi    mathvariant='normal' >$B</mi><mo    mathvariant='normal'             >&sdot;</mo><msup ><mi    mathvariant='italic' >x</mi><mn    mathvariant='normal' >2</mn></msup></mrow></mfrac><mo    mathvariant='normal'   fence='unset' separator='unset' lspace='0em' rspace='0em' stretchy='unset' symmetric='unset' maxsize='' minsize='' largeop='unset' movablelimits='unset' accent='unset'>&InvisibleTimes;</mo><mrow><mo    mathvariant='normal'   fence='unset' separator='unset' lspace='' rspace='' stretchy='unset' symmetric='unset' maxsize='' minsize='' largeop='unset' movablelimits='unset' accent='unset'>&DifferentialD;</mo><mi    mathvariant='italic' >x</mi></mrow></mrow></mrow></math></p>@
qu.9.2.answer=2@
qu.9.2.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$P</mi></mfrac><mrow><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >arctan</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mfrac    ><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi></mrow><mi    mathvariant='normal' >$a</mi></mfrac></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.9.2.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mn>1</mn><mrow><mi mathvariant='normal'>$P</mi></mrow></mfrac><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi mathvariant='normal'>arctanh</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mi mathvariant='normal'>$b</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi></mrow><mi mathvariant='normal'>$a</mi></mfrac></mrow></mfenced></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mstyle></math>@
qu.9.2.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mrow><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >arctan</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mfrac    ><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi></mrow><mi    mathvariant='normal' >$a</mi></mfrac></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.9.2.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$P</mi></mfrac><mrow><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >arcsinh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mfrac    ><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi></mrow><mi    mathvariant='normal' >$a</mi></mfrac></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.9.2.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$b</mi></mfrac><mrow><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >arcsinh</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mfrac    ><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi></mrow><mi    mathvariant='normal' >$a</mi></mfrac></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.9.2.choice.6=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mn>1</mn><mi mathvariant='normal'>$a</mi></mfrac><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>arctanh</mi><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mi mathvariant='normal'>$b</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi></mrow><mi mathvariant='normal'>$a</mi></mfrac></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mstyle></math>@
qu.9.2.choice.7=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mrow><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >arcsech</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mfrac    ><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'             >&sdot;</mo><mo    mathvariant='normal'     lspace='verythinmathspace' rspace='verythinmathspace' stretchy='true'      >&verbar;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'     lspace='verythinmathspace' rspace='verythinmathspace' stretchy='true'      >&verbar;</mo></mrow><mi    mathvariant='normal' >$a</mi></mfrac></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.9.2.choice.8=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mrow><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >arcsech</mi><mfenced><mrow><mfrac    ><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi></mrow><mi    mathvariant='normal' >$a</mi></mfrac></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.9.2.fixed=@

