> with(plots):

> a:=array(0..20):

> f:=x->sin(2*Pi*x):

> for i from 1 to 20 do a[i]:=evalf(subs(x=0,diff(f(x),x$i))) od:

> s:=(x,n1)->sum(a[n]/n!*x^n,n=1..n1):

> an:=animate(s(x,n1),x=-1..1,n1=1..20,frames=60,color=red,thickness=2):

> am:=plot(f(x),x=-1..1,y=-1.2..1.2,color=black,thickness=2):

> display({an,am},title=`Taylor Series for Sine Curve`,titlefont=[TIMES,BOLD,10]);

>