I have f₁=x, and f_n=x+sin(f_n-1).

I would like to write a procedure that would allow me to find the first derivative of f_n. Thanks.

 

I want to plot my function f(x)=sin(e^x +1) and its third order taylor polynomial on the same graph. My code so far (which is giving me an error when I try to define i) is:

f:=x->sin(exp(x)+1);

with(Student[NumericalAnalysis]):

g:=TaylorPolynomial(f(x),x,order=3);

unapply(g,x);

h:=plot(f,0..3,-2..2,color=blue);

i:=plot(g,0..3,-2..2,color=red);

with(plots):

display({h,i},axes=boxed,title=`The function f and its Third Order Taylor Polynomial`);

 

Thanks.

 

Solve the following initial value problem for y(t), z(t).

 

dy/dt + dz/dt =t

dy/dt-2 dz/dt=t^2

 

with initial condition y(0)=1, z(0)=2.

 

Thanks.

I wish to find the slope of the tangent line to the graph of y=(3x)/(x-2) at the point x=3, y=9. Then I want to plot both the tangent line and the graph on the same plot with the tangent line with a green solid line, and the original graph with a blue dashed line. So far I've gotten: v := proc (x) options operator, arrow; 3*x/(x-2) end proc; vprime := D(v); eval(diff(3*x/(x-2), x), {x = 3, y = 9}); plotv:=plot(v); plotvprime:=plot(D(v)); Then I'm not sure how to add the colors in the plot. I can get both graphs on the same set of axes by using: plots[display](plotv,plotvprime); Anyone know how to add the appropriate colors? (Also is what I have done correct?) Thanks.

I have an equation x²y-3y³x=0. I want to find the slope of the graph at the point (3,1) , that is the derivative at that point. I was told it was possible to do this in one line of command, so I was just wondering if anyone knoew how to do this. Any ideas would be helpful. Thanks in advance.