qu.1.topic=CompleteTheSquare@

qu.1.1.mode=Non Permuting Multiple Choice@
qu.1.1.name=CTS(fraction for "a")@
qu.1.1.comment=@
qu.1.1.editing=useHTML@
qu.1.1.solution=@
qu.1.1.algorithm=$a=range(2,4);
$b=range(2,5);
$c=range(1,5);
$M=2*$b;
$C=$a*$b^2+$c;
$B=$a*$b;
condition:eq(gcd($a,$b),1);
condition:eq(gcd($a,$c),1);
$f="1/($a)*x^2+2*$b*x+ $C";
$display=maple("printf(MathML[ExportPresentation]($f))");@
qu.1.1.uid=64fe9eea-76e1-4a2a-a6df-32e73866a121@
qu.1.1.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Review;
  Sub-Topic=Complete the Square;
@
qu.1.1.question=<p>Complete the square: $display</p>@
qu.1.1.answer=1@
qu.1.1.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mo    mathvariant='normal'             >&sdot;</mo><msup ><mfenced><mrow><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$B</mi></mrow></mfenced><mn    mathvariant='normal' >2</mn></msup><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$c</mi></mrow></math>@
qu.1.1.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><msup ><mfenced><mrow><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$B</mi></mrow></mfenced><mn    mathvariant='normal' >2</mn></msup><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$c</mi></mrow></math>@
qu.1.1.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><msup ><mfenced><mrow><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced><mn    mathvariant='normal' >2</mn></msup><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$C</mi></mrow></math>@
qu.1.1.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mo    mathvariant='normal'             >&sdot;</mo><msup ><mfenced><mrow><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced><mn    mathvariant='normal' >2</mn></msup><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$c</mi></mrow></math>@
qu.1.1.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mfenced><mrow><msup ><mrow><mfenced><mrow><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mn    mathvariant='normal' >2</mn></msup><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$c</mi></mrow></mfenced></mrow></math>@
qu.1.1.fixed=@

qu.1.2.mode=Multiple Choice@
qu.1.2.name=CTS(a greater-than 0)@
qu.1.2.comment=@
qu.1.2.editing=useHTML@
qu.1.2.solution=@
qu.1.2.algorithm=$a=range(2,5);
$b=range(2,6);
$c=range(1,9);
$M=2*$a*$b;
$C=$c+$a*$b^2;
$D=$c-$a*$b^2;
$B=2*$b;@
qu.1.2.uid=9364be79-4983-4b73-8eb1-6c0b35516053@
qu.1.2.info=  Author=Jack Weiner, Gord Clement;
  Course=Introduction to Calculus II;
  Difficulty=Easy;
  Topic=Review;
  Sub-Topic=Complete the Square;
@
qu.1.2.question=<p>Complete the square: <math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><msup ><mi    mathvariant='italic' >x</mi><mn    mathvariant='normal' >2</mn></msup><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$M</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$C</mi></mrow></math></p>@
qu.1.2.answer=1@
qu.1.2.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><msup ><mfenced><mrow><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced><mn    mathvariant='normal' >2</mn></msup><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$c</mi></mrow></math>@
qu.1.2.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><msup ><mfenced><mrow><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$B</mi></mrow></mfenced><mn    mathvariant='normal' >2</mn></msup><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$c</mi></mrow></math>@
qu.1.2.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><msup ><mfenced><mrow><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced><mn    mathvariant='normal' >2</mn></msup><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$C</mi></mrow></math>@
qu.1.2.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mo    mathvariant='normal'             >&sdot;</mo><msup ><mfenced><mrow><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced><mn    mathvariant='normal' >2</mn></msup><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$c</mi></mrow></math>@
qu.1.2.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mfenced><mrow><msup ><mrow><mfenced><mrow><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mn    mathvariant='normal' >2</mn></msup><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$c</mi></mrow></mfenced></mrow></math>@
qu.1.2.fixed=@

qu.1.3.mode=Non Permuting Multiple Choice@
qu.1.3.name=CTS(a less-than 0)@
qu.1.3.comment=@
qu.1.3.editing=useHTML@
qu.1.3.solution=@
qu.1.3.algorithm=$a=range(-5,-2);
$Aa=abs($a);
$b=range(2,6);
$c=range(1,9);
$M=2*$a*$b;
$C=$c+$a*$b^2;
$D=$c-$a*$b^2;
$B=2*$b;
$f="($a)*x^2+($M)*x+($C)";
$display=maple("printf(MathML[ExportPresentation]($f))");@
qu.1.3.uid=a3669373-76cd-4b21-9208-c305bcd55950@
qu.1.3.info=  Author=Jack Weiner, Gord Clemet;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=Review;
  Sub-Topic=Complete the Square;
@
qu.1.3.question=<p>Complete the square: $display</p>@
qu.1.3.answer=1@
qu.1.3.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><msup ><mfenced><mrow><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced><mn    mathvariant='normal' >2</mn></msup><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$c</mi></mrow></math>@
qu.1.3.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><msup ><mfenced><mrow><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$B</mi></mrow></mfenced><mn    mathvariant='normal' >2</mn></msup><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$c</mi></mrow></math>@
qu.1.3.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><msup ><mfenced><mrow><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced><mrow><mn    mathvariant='normal' >2</mn></mrow></msup><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mi    mathvariant='normal' >$c</mi></mrow></math>@
qu.1.3.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' >$Aa</mi></mfrac><mo    mathvariant='normal'             >&sdot;</mo><msup ><mfenced><mrow><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced><mn    mathvariant='normal' >2</mn></msup><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$c</mi></mrow></math>@
qu.1.3.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mfenced><mrow><msup ><mrow><mfenced><mrow><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced></mrow><mn    mathvariant='normal' >2</mn></msup><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$c</mi></mrow></mfenced></mrow></math>@
qu.1.3.fixed=@

qu.2.topic=DerArcTrigXchoice@

qu.2.1.mode=Multiple Choice@
qu.2.1.name=derarctanXChoice@
qu.2.1.comment=@
qu.2.1.editing=useHTML@
qu.2.1.solution=@
qu.2.1.algorithm=$a=range(2,9,2);
$b=range(1,10,1);
$X=mathml("$a*x+$b");@
qu.2.1.uid=01ab28db-46c6-487e-97c5-019e75b8fd5c@
qu.2.1.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=arctrig;
  Sub-Topic=Derivatives;
@
qu.2.1.question=<p>Find the derivative: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mfrac><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mfrac></mrow><mrow><mi mathvariant='normal'>arctan</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced></mrow></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math></p>@
qu.2.1.answer=1@
qu.2.1.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mi    mathvariant='normal' >$a</mi><mrow><mn    mathvariant='normal' >1</mn><mo    mathvariant='normal'             >&plus;</mo><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><mn    mathvariant='normal' >2</mn></msup></mrow></mfrac></mrow></math>@
qu.2.1.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mfrac    ><mi    mathvariant='normal' >$a</mi><mrow><mn    mathvariant='normal' >1</mn><mo    mathvariant='normal'             >&plus;</mo><msup ><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced><mn    mathvariant='normal' >2</mn></msup></mrow></mfrac></mrow></math>@
qu.2.1.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mn    mathvariant='normal' >1</mn></mrow><mrow><mn    mathvariant='normal' >1</mn><mo    mathvariant='normal'             >&plus;</mo><msup ><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced><mn    mathvariant='normal' >2</mn></msup></mrow></mfrac></mrow></math>@
qu.2.1.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi mathvariant='normal'>$a</mi><mrow><msqrt><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><msup><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><mn>2</mn></mrow></msup></mrow></msqrt></mrow></mfrac></mrow></mstyle></math>@
qu.2.1.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mrow><mn    mathvariant='normal' >1</mn><mo    mathvariant='normal'             >&plus;</mo><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><mn    mathvariant='normal' >2</mn></msup></mrow></mfrac></mrow></math>@
qu.2.1.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'>$a</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mi mathvariant='normal'>arcsec</mi><mrow><mn>2</mn></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced></mrow></mstyle></math>@
qu.2.1.choice.7=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mi mathvariant='normal'>arcsec</mi><mrow><mn>2</mn></mrow></msup><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></mstyle></math>@
qu.2.1.fixed=@

qu.2.2.mode=Multiple Choice@
qu.2.2.name=derarccsc||XChoice@
qu.2.2.comment=@
qu.2.2.editing=useHTML@
qu.2.2.solution=@
qu.2.2.algorithm=$a=range(2,9,2);
$b=range(1,10,1);
$X=mathml("$a*x+$b");@
qu.2.2.uid=c06fbeb5-bee7-4d98-9a2d-ccda423f0824@
qu.2.2.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=arctrig;
  Sub-Topic=Derivatives;
@
qu.2.2.question=<p>Find the derivative: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mfrac><mi mathvariant='normal'>arccsc</mi><mfenced open='(' close=')' separators=','><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mfenced open='&LeftBracketingBar;' close='&RightBracketingBar;' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mfenced></mrow><mrow></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math></p>@
qu.2.2.answer=5@
qu.2.2.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$a</mi></mrow><mrow><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'>&sdot;</mo><mrow><msqrt><mrow><msup><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><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msqrt></mrow></mrow></mfrac></mrow><mrow></mrow></mstyle></math>@
qu.2.2.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><mrow><mi mathvariant='normal'>$a</mi></mrow><mrow><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mrow><msqrt><mrow><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msqrt></mrow></mrow></mfrac></mrow></mstyle></math>@
qu.2.2.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mn>1</mn><mrow><mfenced open='|' close='|' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mrow><msqrt><mrow><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msqrt></mrow></mrow></mfrac></mrow></mstyle></math>@
qu.2.2.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow><mrow><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mrow><msqrt><mrow><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msqrt></mrow></mrow></mfrac></mrow></mstyle></math>@
qu.2.2.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$a</mi></mrow><mrow><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'>&sdot;</mo><mrow><msqrt><mrow><msup><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><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msqrt></mrow></mrow></mfrac></mrow></mstyle></math>@
qu.2.2.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'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>arccsc</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>arccot</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced></mrow></mstyle></math>@
qu.2.2.choice.7=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>arccsc</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'>&sdot;</mo><mi mathvariant='normal'>arccot</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></mstyle></math>@
qu.2.2.fixed=@

qu.2.3.mode=Multiple Choice@
qu.2.3.name=derarccscXChoice@
qu.2.3.comment=@
qu.2.3.editing=useHTML@
qu.2.3.solution=@
qu.2.3.algorithm=$a=range(2,9,2);
$b=range(1,10,1);
$X=mathml("$a*x+$b");@
qu.2.3.uid=d9be64a5-c8af-41ad-b708-1c5a2394e295@
qu.2.3.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=arctrig;
  Sub-Topic=Derivatives;
@
qu.2.3.question=<p>Find the derivative: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mfrac><mi mathvariant='normal'>arccsc</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math></p>@
qu.2.3.answer=1@
qu.2.3.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$a</mi></mrow><mrow><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'>&sdot;</mo><mrow><msqrt><mrow><msup><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><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msqrt></mrow></mrow></mfrac></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><mfrac><mrow><mi mathvariant='normal'>$a</mi></mrow><mrow><mfenced open='|' close='|' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mrow><msqrt><mrow><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msqrt></mrow></mrow></mfrac></mrow></mstyle></math>@
qu.2.3.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mn>1</mn><mrow><mfenced open='|' close='|' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mrow><msqrt><mrow><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msqrt></mrow></mrow></mfrac></mrow><mrow><mi></mi></mrow></mstyle></math>@
qu.2.3.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow><mrow><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mrow><msqrt><mrow><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msqrt></mrow></mrow></mfrac></mrow></mstyle></math>@
qu.2.3.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mn>1</mn><mrow><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mrow><msqrt><mrow><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msqrt></mrow></mrow></mfrac></mrow></mstyle></math>@
qu.2.3.choice.6=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>arccsc</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'>&sdot;</mo><mi mathvariant='normal'>arccot</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></mi></mrow></mstyle></math>@
qu.2.3.choice.7=<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'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>arccsc</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>arccot</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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></mstyle></math>@
qu.2.3.fixed=@

qu.2.4.mode=Multiple Choice@
qu.2.4.name=derarccosXChoice@
qu.2.4.comment=@
qu.2.4.editing=useHTML@
qu.2.4.solution=@
qu.2.4.algorithm=$a=range(2,9,2);
$b=range(1,10,1);
$X=mathml("$a*x+$b");@
qu.2.4.uid=c060ac40-a1fb-4e04-bcf6-0c77d92a8b45@
qu.2.4.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=arctrig;
  Sub-Topic=Derivatives;
@
qu.2.4.question=<p>Find the derivative: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mfrac><mi mathvariant='normal'>arccos</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math></p>@
qu.2.4.answer=2@
qu.2.4.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi mathvariant='normal'>$a</mi><mrow><msqrt><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msup><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><mn>2</mn></mrow></msup></mrow></msqrt></mrow></mfrac></mrow></mstyle></math>@
qu.2.4.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><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mfrac><mi mathvariant='normal'>$a</mi><mrow><msqrt><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup></mrow></msqrt></mrow></mfrac></mrow></mstyle></math>@
qu.2.4.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mn>1</mn><mrow><msqrt><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup></mrow></msqrt></mrow></mfrac></mrow></mstyle></math>@
qu.2.4.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mfrac><mn>1</mn><mrow><msqrt><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup></mrow></msqrt></mrow></mfrac></mrow></mstyle></math>@
qu.2.4.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$a</mi></mrow><mrow><msqrt><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$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></mrow></mstyle></math>@
qu.2.4.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'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>arcsin</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced></mrow></mstyle></math>@
qu.2.4.choice.7=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>arcsin</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></mstyle></math>@
qu.2.4.fixed=@

qu.2.5.mode=Multiple Choice@
qu.2.5.name=derarcsinXChoice@
qu.2.5.comment=@
qu.2.5.editing=useHTML@
qu.2.5.solution=@
qu.2.5.algorithm=$a=range(2,9,2);
$b=range(1,10,1);
$X=mathml("$a*x+$b");@
qu.2.5.uid=4019bec5-1879-463f-821f-932af9c6d95a@
qu.2.5.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=arctrig;
  Sub-Topic=Derivatives;
@
qu.2.5.question=<p>Find the derivative: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mfrac><mi mathvariant='normal'>arcsin</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math></p>@
qu.2.5.answer=1@
qu.2.5.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi mathvariant='normal'>$a</mi><mrow><msqrt><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msup><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><mn>2</mn></mrow></msup></mrow></msqrt></mrow></mfrac></mrow></mstyle></math>@
qu.2.5.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><mfrac><mi mathvariant='normal'>$a</mi><mrow><msqrt><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup></mrow></msqrt></mrow></mfrac></mrow></mstyle></math>@
qu.2.5.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mn>1</mn><mrow><msqrt><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup></mrow></msqrt></mrow></mfrac></mrow></mstyle></math>@
qu.2.5.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mfrac><mn>1</mn><mrow><msqrt><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup></mrow></msqrt></mrow></mfrac></mrow></mstyle></math>@
qu.2.5.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi mathvariant='normal'>$a</mi><mrow><msqrt><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$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></mrow></mstyle></math>@
qu.2.5.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'>$a</mi><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>arccos</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced></mrow></mstyle></math>@
qu.2.5.choice.7=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>arccos</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></mstyle></math>@
qu.2.5.fixed=@

qu.2.6.mode=Multiple Choice@
qu.2.6.name=derarcsecXChoice@
qu.2.6.comment=@
qu.2.6.editing=useHTML@
qu.2.6.solution=@
qu.2.6.algorithm=$a=range(2,9,2);
$b=range(1,10,1);
$X=mathml("$a*x+$b");@
qu.2.6.uid=1aa91212-241a-47aa-9f7a-02256de61c3a@
qu.2.6.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=arctrig;
  Sub-Topic=Derivatives;
@
qu.2.6.question=<p>Find the derivative: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mfrac><mi mathvariant='normal'>arcsec</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math></p>@
qu.2.6.answer=1@
qu.2.6.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi mathvariant='normal'>$a</mi><mrow><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'>&sdot;</mo><mrow><msqrt><mrow><msup><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><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msqrt></mrow></mrow></mfrac></mrow></mstyle></math>@
qu.2.6.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><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$a</mi></mrow><mrow><mfenced open='|' close='|' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mrow><msqrt><mrow><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msqrt></mrow></mrow></mfrac></mrow></mstyle></math>@
qu.2.6.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mn>1</mn><mrow><mfenced open='|' close='|' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mrow><msqrt><mrow><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msqrt></mrow></mrow></mfrac></mrow></mstyle></math>@
qu.2.6.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi mathvariant='normal'>$a</mi><mrow><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'>&sdot;</mo><mrow><msqrt><mrow><msup><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><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msqrt></mrow></mrow></mfrac></mrow></mstyle></math>@
qu.2.6.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><mrow><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'>&sdot;</mo><mrow><msqrt><mrow><msup><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><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msqrt></mrow></mrow></mfrac></mrow></mstyle></math>@
qu.2.6.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'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>arcsec</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>arctan</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced></mrow></mstyle></math>@
qu.2.6.choice.7=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>arcsec</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'>&sdot;</mo><mi mathvariant='normal'>arctan</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></mstyle></math>@
qu.2.6.fixed=@

qu.2.7.mode=Multiple Choice@
qu.2.7.name=derarccotXChoice@
qu.2.7.comment=@
qu.2.7.editing=useHTML@
qu.2.7.solution=@
qu.2.7.algorithm=$a=range(2,9,2);
$b=range(1,10,1);
$X=mathml("$a*x+$b");@
qu.2.7.uid=dd9b3ee2-b958-45d1-bf5b-3242e84a90b0@
qu.2.7.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=arctrig;
  Sub-Topic=Derivatives;
@
qu.2.7.question=<p>Find the derivative: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mfrac><mi mathvariant='normal'>arccot</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math></p>@
qu.2.7.answer=2@
qu.2.7.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mi    mathvariant='normal' >$a</mi><mrow><mn    mathvariant='normal' >1</mn><mo    mathvariant='normal'             >&plus;</mo><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><mn    mathvariant='normal' >2</mn></msup></mrow></mfrac></mrow></math>@
qu.2.7.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mfrac    ><mi    mathvariant='normal' >$a</mi><mrow><mn    mathvariant='normal' >1</mn><mo    mathvariant='normal'             >&plus;</mo><msup ><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced><mn    mathvariant='normal' >2</mn></msup></mrow></mfrac></mrow></math>@
qu.2.7.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mn    mathvariant='normal' >1</mn></mrow><mrow><mn    mathvariant='normal' >1</mn><mo    mathvariant='normal'             >&plus;</mo><msup ><mfenced><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$b</mi></mrow></mfenced><mn    mathvariant='normal' >2</mn></msup></mrow></mfrac></mrow></math>@
qu.2.7.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi mathvariant='normal'>$a</mi><mrow><msqrt><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><msup><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><mn>2</mn></mrow></msup></mrow></msqrt></mrow></mfrac></mrow></mstyle></math>@
qu.2.7.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mrow><mn    mathvariant='normal' >1</mn><mo    mathvariant='normal'             >&plus;</mo><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><mn    mathvariant='normal' >2</mn></msup></mrow></mfrac></mrow></math>@
qu.2.7.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'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mi mathvariant='normal'>arccsc</mi><mrow><mn>2</mn></mrow></msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced></mrow></mstyle></math>@
qu.2.7.choice.7=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mi mathvariant='normal'>arccsc</mi><mrow><mn>2</mn></mrow></msup><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></mstyle></math>@
qu.2.7.fixed=@

qu.2.8.mode=Multiple Choice@
qu.2.8.name=derarcsec||XChoice@
qu.2.8.comment=@
qu.2.8.editing=useHTML@
qu.2.8.solution=@
qu.2.8.algorithm=$a=range(2,9,2);
$b=range(1,10,1);
$X=mathml("$a*x+$b");@
qu.2.8.uid=c05fedec-16a0-44b2-989a-b99e479ced17@
qu.2.8.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=arctrig;
  Sub-Topic=Derivatives;
@
qu.2.8.question=<p>Find the derivative: <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mfrac><mi mathvariant='normal'>arcsec</mi><mfenced open='(' close=')' separators=','><mrow><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mfenced open='&LeftBracketingBar;' close='&RightBracketingBar;' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow></mfenced></mrow></mstyle></math><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow></mrow></math></p>@
qu.2.8.answer=4@
qu.2.8.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi mathvariant='normal'>$a</mi><mrow><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'>&sdot;</mo><mrow><msqrt><mrow><msup><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><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msqrt></mrow></mrow></mfrac></mrow></mstyle></math>@
qu.2.8.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><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$a</mi></mrow><mrow><mfenced open='|' close='|' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mrow><msqrt><mrow><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msqrt></mrow></mrow></mfrac></mrow></mstyle></math>@
qu.2.8.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mn>1</mn><mrow><mfenced open='|' close='|' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mrow><msqrt><mrow><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msqrt></mrow></mrow></mfrac></mrow></mstyle></math>@
qu.2.8.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mi mathvariant='normal'>$a</mi><mrow><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'>&sdot;</mo><mrow><msqrt><mrow><msup><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><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msqrt></mrow></mrow></mfrac></mrow></mstyle></math>@
qu.2.8.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><mrow><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'>&sdot;</mo><mrow><msqrt><mrow><msup><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><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mn>1</mn></mrow></msqrt></mrow></mrow></mfrac></mrow></mstyle></math>@
qu.2.8.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'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>arcsec</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>arctan</mi><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$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'>$b</mi></mrow></mfenced></mrow></mstyle></math>@
qu.2.8.choice.7=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>arcsec</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'>&sdot;</mo><mi mathvariant='normal'>arctan</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></mstyle></math>@
qu.2.8.fixed=@

qu.3.topic=DerArcTrigMapleGraded@

qu.3.1.question=<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mfrac    ><mo    mathvariant='normal'   fence='unset' separator='unset' lspace='' rspace='' stretchy='unset' symmetric='unset' maxsize='' minsize='' largeop='unset' movablelimits='unset' accent='unset'>&DifferentialD;</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></mfrac></mrow></mrow></math> $display</p>@
qu.3.1.maple=is(simplify(($RESPONSE)-($ANSWER))=0)@
qu.3.1.allow2d=1@
qu.3.1.maple_answer=diff($f,x)@
qu.3.1.type=formula@
qu.3.1.mode=Maple@
qu.3.1.name=derivative of arctrig@
qu.3.1.comment=@
qu.3.1.editing=useHTML@
qu.3.1.solution=@
qu.3.1.algorithm=$a=range(1,9,2);
$b=range(-10,10,1);
$f=switch(rint(6), "arcsin(($a)*x+($b))","arccos(($a)*
x+($b))","arctan(($a)*x+($b))","arccsc(($a)*x+($b))","arcsec(($a)*x+($b))","arccot(($a)*x+($b))");
$display=maple("printf(MathML[ExportPresentation]($f))");@
qu.3.1.uid=bfb1e465-847a-49c3-9a7d-e1c7902ba9aa@
qu.3.1.info=  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=arctrig;
  Sub-Topic=Derivatives;
  Author=Jack Weiner, Gord Clement;
@

qu.4.topic=SimpleBABA@

qu.4.1.mode=Multiple Choice@
qu.4.1.name=arcsec@
qu.4.1.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><mi>x</mi><mrow><msqrt><mrow><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><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msup><mi>a</mi><mrow><mn>2</mn></mrow></msup></mrow></msqrt></mrow></mrow></mfrac><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></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>arcsec</mi><mo fence='true' lspace='0.1666667em' rspace='0.1666667em' stretchy='true'>&lpar;</mo><mfrac><mrow><mi>b</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mfenced open='|' close='|' separators=','><mrow><mi>x</mi></mrow></mfenced></mrow><mrow><mi>a</mi></mrow></mfrac><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.4.1.editing=useHTML@
qu.4.1.solution=@
qu.4.1.algorithm=$a=range(2,12);
$b=range(2,12);
condition:eq(gcd($a,$b),1);
$A=$a^2;
$B=$b^2;
$P=$a*$b;@
qu.4.1.uid=5b19f74c-f6f4-4941-9c66-edbf826c044e@
qu.4.1.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=arctrig;
  Sub-Topc=Integration;
@
qu.4.1.question=<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.0em' rspace='0.0em'>&Integral;</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mrow><msqrt><mrow><mi mathvariant='normal'>$B</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mi>x</mi><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$A</mi></mrow></msqrt></mrow></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mrow><mrow><mi></mi></mrow></mstyle></math></p>@
qu.4.1.answer=1@
qu.4.1.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mn>1</mn><mi mathvariant='normal'>$a</mi></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi mathvariant='normal'>arcsec</mi><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mi mathvariant='normal'>$b</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mrow><mfenced open='&LeftBracketingBar;' close='&RightBracketingBar;' separators=','><mi>x</mi></mfenced></mrow></mrow><mi mathvariant='normal'>$a</mi></mfrac></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mstyle></math>@
qu.4.1.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><mfrac><mn>1</mn><mi mathvariant='normal'>$a</mi></mfrac><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi mathvariant='normal'>arcsec</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mi mathvariant='normal'>$b</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi></mrow><mi mathvariant='normal'>$a</mi></mfrac></mrow></mfenced></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mstyle></math>@
qu.4.1.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mn>1</mn><mi mathvariant='normal'>$b</mi></mfrac><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi mathvariant='normal'>arcsec</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.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><mfrac><mn>1</mn><mi mathvariant='normal'>$b</mi></mfrac><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi mathvariant='normal'>arcsec</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mi mathvariant='normal'>$b</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mrow><mfenced open='&LeftBracketingBar;' close='&RightBracketingBar;' separators=','><mrow><mi>x</mi></mrow></mfenced></mrow></mrow><mi mathvariant='normal'>$a</mi></mfrac></mrow></mfenced></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mstyle></math>@
qu.4.1.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle    veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mfrac><mn>1</mn><mi mathvariant='normal'>$a</mi></mfrac><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi mathvariant='normal'>arcsec</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mi mathvariant='normal'>$b</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mrow><mfenced open='&LeftBracketingBar;' close='&RightBracketingBar;' separators=','><mi>x</mi></mfenced></mrow></mrow><mi mathvariant='normal'>$a</mi></mfrac></mrow></mfenced></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mstyle></math>@
qu.4.1.fixed=@

qu.4.2.mode=Multiple Choice@
qu.4.2.name=arcsin@
qu.4.2.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'>&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'>&minus;</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><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>arcsin</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><mrow><mi></mi></mrow></mstyle></math></p>@
qu.4.2.editing=useHTML@
qu.4.2.solution=@
qu.4.2.algorithm=$a=range(2,12);
$b=range(2,12);
condition:eq(gcd($a,$b),1);
$A=$a^2;
$B=$b^2;
$P=$a*$b;@
qu.4.2.uid=5a9bd02a-2ef6-431b-b5fa-ed91e90d3f27@
qu.4.2.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=arctrig;
  Sub-Topic=Integration;
@
qu.4.2.question=<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.0em' rspace='0.0em'>&Integral;</mo><mfrac><mn>1</mn><mrow><msqrt><mrow><mi mathvariant='normal'>$A</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$B</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mi>x</mi><mrow><mn>2</mn></mrow></msup></mrow></msqrt></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mrow></mstyle></math></p>@
qu.4.2.answer=1@
qu.4.2.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$b</mi></mfrac><mrow><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >arcsin</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.4.2.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><mrow><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >arcsin</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mfrac    ><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi></mrow><mi    mathvariant='normal' >$a</mi></mfrac></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.4.2.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$P</mi></mfrac><mrow><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >arcsin</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.4.2.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$b</mi></mfrac><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mrow><mi    mathvariant='normal' >arcsin</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mfrac    ><mrow><mi    mathvariant='normal' >$B</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi></mrow><mi    mathvariant='normal' >$A</mi></mfrac></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.4.2.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$b</mi></mfrac><mrow><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >arcsin</mi><mfenced><mrow><mfrac    ><mrow><mi    mathvariant='normal' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi></mrow><mi    mathvariant='normal' >$b</mi></mfrac></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.4.2.fixed=@

qu.4.3.mode=Multiple Choice@
qu.4.3.name=arcsec||@
qu.4.3.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><mo lspace='0.0em' rspace='0.0em' stretchy='true' largeop='true'>&Integral;</mo><mfrac><mrow><mn>1</mn><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow><mrow><mfenced open='|' close='|' separators=','><mrow><mi>x</mi></mrow></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mrow><msqrt><mrow><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><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msup><mi>a</mi><mrow><mn>2</mn></mrow></msup></mrow></msqrt></mrow></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&#32;</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></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>arcsec</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.4.3.editing=useHTML@
qu.4.3.solution=@
qu.4.3.algorithm=$a=range(2,12);
$b=range(2,12);
condition:eq(gcd($a,$b),1);
$A=$a^2;
$B=$b^2;
$P=$a*$b;@
qu.4.3.uid=e1b490ec-1a72-411b-93e5-c9d34a15f81a@
qu.4.3.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=arctrig;
  Sub-Topic=Integration;
@
qu.4.3.question=<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.0em' rspace='0.0em'>&Integral;</mo><mfrac><mn>1</mn><mrow><mfenced open='&LeftBracketingBar;' close='&RightBracketingBar;' separators=','><mi>x</mi></mfenced><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mrow><msqrt><mrow><mi mathvariant='normal'>$B</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mi>x</mi><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$A</mi></mrow></msqrt></mrow></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mrow></mstyle></math></p>@
qu.4.3.answer=1@
qu.4.3.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$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' >$b</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi></mrow><mi    mathvariant='normal' >$a</mi></mfrac></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.4.3.choice.2=<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><mrow><mfenced open='&LeftBracketingBar;' close='&RightBracketingBar;'><mi    mathvariant='italic' >x</mi></mfenced></mrow></mrow><mi    mathvariant='normal' >$a</mi></mfrac></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.4.3.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$b</mi></mfrac><mrow><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >arcsec</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mfrac    ><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi></mrow><mi    mathvariant='normal' >$a</mi></mfrac></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.4.3.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$b</mi></mfrac><mrow><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >arcsec</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mfrac    ><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'             >&sdot;</mo><mrow><mfenced open='&LeftBracketingBar;' close='&RightBracketingBar;'><mrow><mi    mathvariant='italic' >x</mi></mrow></mfenced></mrow></mrow><mi    mathvariant='normal' >$a</mi></mfrac></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.4.3.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&minus;</mo><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$a</mi></mfrac><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' >$b</mi><mo    mathvariant='normal'             >&sdot;</mo><mrow><mfenced open='&LeftBracketingBar;' close='&RightBracketingBar;'><mi    mathvariant='italic' >x</mi></mfenced></mrow></mrow><mi    mathvariant='normal' >$a</mi></mfrac></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=arctan@
qu.4.4.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><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'>&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></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><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>arctan</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.4.4.editing=useHTML@
qu.4.4.solution=@
qu.4.4.algorithm=$a=range(2,12);
$b=range(2,12);
condition:eq(gcd($a,$b),1);
$A=$a^2;
$B=$b^2;
$P=$a*$b;@
qu.4.4.uid=e3f906c4-9c0b-40ec-ad4e-0b086dfdf64a@
qu.4.4.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=arctrig;
  Sub-Topic=Integration;
@
qu.4.4.question=<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mrow><mo    mathvariant='normal'   fence='unset' separator='unset' lspace='' rspace='' stretchy='unset' symmetric='unset' maxsize='' minsize='' largeop='unset' movablelimits='unset' accent='unset'>&Integral;</mo><mfrac    ><mn    mathvariant='normal' >1</mn><mrow><mi    mathvariant='normal' >$B</mi><mo    mathvariant='normal'             >&sdot;</mo><msup ><mi    mathvariant='italic' >x</mi><mn    mathvariant='normal' >2</mn></msup><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$A</mi></mrow></mfrac><mo    mathvariant='normal'   fence='unset' separator='unset' lspace='0em' rspace='0em' stretchy='unset' symmetric='unset' maxsize='' minsize='' largeop='unset' movablelimits='unset' accent='unset'>&InvisibleTimes;</mo><mrow><mo    mathvariant='normal'   fence='unset' separator='unset' lspace='' rspace='' stretchy='unset' symmetric='unset' maxsize='' minsize='' largeop='unset' movablelimits='unset' accent='unset'>&DifferentialD;</mo><mi    mathvariant='italic' >x</mi></mrow></mrow></mrow></math></p>@
qu.4.4.answer=1@
qu.4.4.choice.1=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$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.4.4.choice.2=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$b</mi></mfrac><mrow><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='normal' >arctan</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mfrac    ><mrow><mi    mathvariant='normal' >$b</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi></mrow><mi    mathvariant='normal' >$a</mi></mfrac></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.4.4.choice.3=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$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.4.4.choice.4=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$P</mi></mfrac><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&sdot;</mo><mrow><mi    mathvariant='normal' >arctan</mi><mo    mathvariant='normal'     lspace='0em' rspace='0em'       >&ApplyFunction;</mo><mfenced><mrow><mfrac    ><mrow><mi    mathvariant='normal' >$B</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi></mrow><mi    mathvariant='normal' >$A</mi></mfrac></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.4.4.choice.5=<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mfrac    ><mn    mathvariant='normal' >1</mn><mi    mathvariant='normal' >$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' >$a</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi></mrow><mi    mathvariant='normal' >$b</mi></mfrac></mrow></mfenced></mrow><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='italic' >C</mi></mrow></math>@
qu.4.4.fixed=@

qu.5.topic=SimpleBABA +LNorRTMG@

qu.5.1.question=<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'>&Integral;</mo><mfrac><mrow><mi mathvariant='normal'>$M</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$n</mi></mrow><mrow><mrow><msqrt><mrow><mi mathvariant='normal'>$A</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$B</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mi>x</mi><mrow><mn>2</mn></mrow></msup></mrow></msqrt></mrow><mrow></mrow></mrow></mfrac><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>&nbsp;</p>@
qu.5.1.maple=if not(simplify(diff(($ANSWER)-($RESPONSE),x))=0) then
grade:=0:
else
if (type(simplify(($ANSWER)-($RESPONSE)-C), numeric)) then
grade:=0.75:
else
grade:=1:
end if: 
end if:
grade@
qu.5.1.allow2d=1@
qu.5.1.maple_answer=simplify(int(($M*x+$n)/sqrt($A-$B*x^2),x))+C@
qu.5.1.type=formula@
qu.5.1.mode=Maple@
qu.5.1.name=arcsinMG@
qu.5.1.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><mrow><mi mathvariant='normal'>$M</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$n</mi></mrow><mrow><msqrt><mrow><mi mathvariant='normal'>$A</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$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><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><mrow><mi mathvariant='normal'></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><mi mathvariant='normal'>$num2</mi><mo lspace='0.0em' rspace='0.0em' stretchy='true' largeop='true'>&Integral;</mo><mi mathvariant='normal'>$num1</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mfenced open='(' close=')' separators=','><mrow><mi mathvariant='normal'>$A</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$B</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mi>x</mi><mrow><mn>2</mn></mrow></msup></mrow></mfenced><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mrow><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac></mrow></mrow></msup><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$n</mi><mo lspace='0.0em' rspace='0.0em' stretchy='true' largeop='true'>&Integral;</mo><mfrac><mn>1</mn><mrow><msqrt><mrow><mi mathvariant='normal'>$A</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$B</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mi>x</mi><mrow><mn>2</mn></mrow></msup></mrow></msqrt></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow><mrow><mi mathvariant='normal'></mi></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$num3</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msqrt><mrow><mi mathvariant='normal'>$A</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$B</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mi>x</mi><mrow><mn>2</mn></mrow></msup></mrow></msqrt><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mfrac><mrow><mi mathvariant='normal'>$n</mi></mrow><mrow><mi mathvariant='normal'>$b</mi></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>arcsin</mi><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mi mathvariant='normal'>$b</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi></mrow><mrow><mi mathvariant='normal'>$a</mi></mrow></mfrac></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow><mrow><mi mathvariant='normal'></mi></mrow></mstyle></math></p>@
qu.5.1.editing=useHTML@
qu.5.1.solution=@
qu.5.1.algorithm=$a=range(2,12);
$b=range(2,5);
condition:eq(gcd($a,$b),1);
$A=$a^2;
$B=$b^2;
$P=$a*$b;
$m=range(1,5);
$n=range(1,5);
$M=(-1)^$n*$b^2*$n;
$num1=-2*$b^2;
$maple=maple("
convert((-1)^($n+1)*$n/2,string),
convert((-1)^($n+1)*$n,string)
");
$num2=switch(0,$maple);
$num3=switch(1,$maple);@
qu.5.1.uid=f161f44c-0e1e-4cab-a7bf-171d9fed3d38@
qu.5.1.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Easy;
  Course=Introduction to Calculus II;
  Topic=arctrig;
  Sub-Topic=Integration;
@

qu.5.2.question=<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    ><mrow><mi    mathvariant='normal' >$M</mi><mo    mathvariant='normal'             >&sdot;</mo><mi    mathvariant='italic' >x</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$n</mi></mrow><mrow><mi    mathvariant='normal' >$A</mi><mo    mathvariant='normal'             >&plus;</mo><mi    mathvariant='normal' >$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></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>&nbsp;</p>@
qu.5.2.maple=if not(simplify(diff(($ANSWER)-($RESPONSE),x))=0) then
grade:=0:
else
if (type(simplify(($ANSWER)-($RESPONSE)-C), numeric)) then
grade:=0.75:
else
grade:=1:
end if: 
end if:
grade@
qu.5.2.allow2d=1@
qu.5.2.maple_answer=simplify(int(($M*x+$n)/($A+$B*x^2),x)) + C@
qu.5.2.type=formula@
qu.5.2.mode=Maple@
qu.5.2.name=arctanMG@
qu.5.2.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><mrow><mi mathvariant='normal'>$M</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mrow><mi mathvariant='normal'>$n</mi></mrow></mrow><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></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><mi mathvariant='normal'>$num2</mi><mo lspace='0.0em' rspace='0.0em' stretchy='true' largeop='true'>&Integral;</mo><mfrac><mrow><mi mathvariant='normal'>$num1</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi></mrow><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></mfrac><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$n</mi><mo lspace='0.0em' rspace='0.0em' stretchy='true' largeop='true'>&Integral;</mo><mfrac><mn>1</mn><mrow><mi mathvariant='normal'>$A</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$B</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mi>x</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mstyle></math></p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle     veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$num2</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>ln</mi><mfenced open='(' close=')' separators=','><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></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mfrac><mi mathvariant='normal'>$n</mi><mrow><mi mathvariant='normal'>$a</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi mathvariant='normal'>$b</mi></mrow></mfrac><mi mathvariant='normal'>arctan</mi><mfenced open='(' close=')' separators=','><mrow><mfrac><mrow><mi mathvariant='normal'>$b</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi></mrow><mrow><mi mathvariant='normal'>$a</mi></mrow></mfrac></mrow></mfenced><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>C</mi></mrow></mstyle></math></p>
<p>&nbsp;</p>@
qu.5.2.editing=useHTML@
qu.5.2.solution=@
qu.5.2.algorithm=$a=range(2,12);
$b=range(2,5);
condition:eq(gcd($a,$b),1);
$A=$a^2;
$B=$b^2;
$P=$a*$b;
$m=range(1,5);
$n=range(1,5);
$M=(-1)^$n*$b^2*$n;
$num1=2*$b^2;
$num2=maple("(-1)^($n)*$n/2");@
qu.5.2.uid=f61f3b1a-9f79-4e13-a855-2cef16b1fe3f@
qu.5.2.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Medium;
  Course=Introduction to Calculus II;
  Topic=arctrig;
  Sub-Topic=Integration;
@

qu.6.topic=integralArctanln@

qu.6.1.question=<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'>&Integral;</mo><mfrac><mrow><mi mathvariant='normal'>$A</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$B</mi></mrow><mrow><mi mathvariant='normal'>$b</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><msup><mi>x</mi><mn>2</mn></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$m</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'>$p</mi></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mstyle></math>&nbsp;&nbsp;</p>@
qu.6.1.maple=if not(simplify(diff(($ANSWER)-($RESPONSE),x))=0) then
grade:=0:
else
if (type(simplify(($ANSWER)-($RESPONSE)-C), numeric)) then
grade:=0.75:
else
grade:=1:
end if: 
end if:
grade@
qu.6.1.allow2d=1@
qu.6.1.maple_answer=simplify(int(($A*x-$B)/($b*x^2+$m*x+$p),x)) + C@
qu.6.1.type=formula@
qu.6.1.mode=Maple@
qu.6.1.name=BABAlnArctan@
qu.6.1.comment=@
qu.6.1.editing=useHTML@
qu.6.1.solution=@
qu.6.1.algorithm=$A=range(1,4,1);
$B=range(1,4,1);
$a=range(1,4,1);
$b=rint(3)+2;
$c=range(1,4,1);
$p=$c^2+$b*$a^2;
$m=2*$a*$b;
condition:eq(gcd($p,$m),1);@
qu.6.1.uid=00751508-5107-460d-89cf-3d61baa6ca38@
qu.6.1.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Hard;
  Course=Introduction to Calculus II;
  Topic=arctrig;
  Sub-Topic=Integration;
@

qu.6.2.question=<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'>&Integral;</mo><mfrac><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><mrow><mi mathvariant='normal'>$b</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&sdot;</mo><msup><mi>x</mi><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$m</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'>$p</mi></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mi>dx</mi></mrow></mstyle></math>&nbsp;</p>@
qu.6.2.maple=if not(simplify(diff(($ANSWER)-($RESPONSE),x))=0) then
grade:=0:
else
if (type(simplify(($ANSWER)-($RESPONSE)-C), numeric)) then
grade:=0.75:
else
grade:=1:
end if: 
end if:
grade@
qu.6.2.allow2d=1@
qu.6.2.maple_answer=simplify(int(($A*x+$B)/($b*x^2-$m*x+$p),x)) + C@
qu.6.2.type=formula@
qu.6.2.mode=Maple@
qu.6.2.name=BABAlnArctan(-x)@
qu.6.2.comment=@
qu.6.2.editing=useHTML@
qu.6.2.solution=@
qu.6.2.algorithm=$A=range(1,4,1);
$B=range(1,4,1);
$a=range(1,4,1);
$b=rint(3)+2;
$c=range(1,4,1);
$p=$c^2+$b*$a^2;
$m=2*$a*$b;
condition:eq(gcd($p,$m),1);@
qu.6.2.uid=89b16385-1af0-4453-b697-2120cd42f355@
qu.6.2.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Hard;
  Course=Introduction to Calculus II;
  Topic=arctrig;
  Sub-Topic=Integration;
@

qu.7.topic=IntegralArcsinRt@

qu.7.1.question=<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'>&Integral;</mo><mfrac><mrow><mi mathvariant='normal'>$A</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$B</mi></mrow><mrow><msqrt><mrow><mi mathvariant='normal'>$p</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$b</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mi>x</mi><mn>2</mn></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$m</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi></mrow></msqrt></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mrow><mo lspace='0.0em' rspace='0.0em'>&DifferentialD;</mo><mi>x</mi></mrow></mrow><mrow></mrow></mstyle></math>&nbsp;</p>@
qu.7.1.maple=if not(simplify(diff(($ANSWER)-($RESPONSE),x))=0) then
grade:=0:
else
if (type(simplify(($ANSWER)-($RESPONSE)-C), numeric)) then
grade:=0.75:
else
grade:=1:
end if: 
end if:
grade@
qu.7.1.allow2d=1@
qu.7.1.maple_answer=simplify(int(($A*x-$B)/sqrt($p-$b*x^2-$m*x),x)) + C@
qu.7.1.type=formula@
qu.7.1.mode=Maple@
qu.7.1.name=BABARtArcsin@
qu.7.1.comment=@
qu.7.1.editing=useHTML@
qu.7.1.solution=@
qu.7.1.algorithm=$A=range(1,4,1);
$B=range(1,4,1);
$a=range(1,4,1);
$b=rint(2)+2;
$c=range(1,4,1);
$p=$c^2-$b*$a^2;
$m=2*$a*$b;
condition:not(eq($p,0));
condition:eq(gcd($p,$m),1);@
qu.7.1.uid=1a9fd714-f56c-4394-bb02-cf9f05e8027e@
qu.7.1.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Hard;
  Course=Introduction to Calculus II;
  Topic=arctrig;
  Sub-Topic=Integration;
  Note=Designed to be a two mark question;
@

qu.7.2.question=<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'>&Integral;</mo><mfrac><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><mrow><msqrt><mrow><mi mathvariant='normal'>$p</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi mathvariant='normal'>$b</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msup><mi>x</mi><mrow><mn>2</mn></mrow></msup><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$m</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><mi>x</mi></mrow></msqrt></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mi>dx</mi></mrow><mrow></mrow></mstyle></math>&nbsp;</p>@
qu.7.2.maple=if not(simplify(diff(($ANSWER)-($RESPONSE),x))=0) then
grade:=0:
else
if (type(simplify(($ANSWER)-($RESPONSE)-C), numeric)) then
grade:=0.75:
else
grade:=1:
end if: 
end if:
grade@
qu.7.2.allow2d=1@
qu.7.2.maple_answer=simplify(int(($A*x+$B)/sqrt($p-$b*x^2+$m*x),x)) + C@
qu.7.2.type=formula@
qu.7.2.mode=Maple@
qu.7.2.name=BABARtArcsin(-x)@
qu.7.2.comment=@
qu.7.2.editing=useHTML@
qu.7.2.solution=@
qu.7.2.algorithm=$A=range(1,4,1);
$B=range(1,4,1);
$a=range(1,4,1);
$b=rint(3)+2;
$c=range(1,4,1);
$p=$c^2-$b*$a^2;
$m=2*$a*$b;
condition:not(eq($p,0));
condition:eq(gcd($p,$m),1);@
qu.7.2.uid=83e62100-ee16-48a6-b6c5-181b4dd7e26e@
qu.7.2.info=  Author=Jack Weiner, Gord Clement;
  Difficulty=Hard;
  Course=Introduction to Calculus II;
  Topic=arctrig;
  Sub-Topic=Integration;
  Note=Designed to be a 2 mark question;
@

