Taylor Series Plots with Animation
Please Click on ANIMATION
to see the Mathematica code for the Taylor Series animation.
Off[General::spell]; Off[General::spell1]; Pagewidth->70;
f[x_]=Sin[x] Sin[x] (* Taylor polynomal of order n=9 near point a=0 *)
1) Generate a polynomial of 10 element
Table[poly[x_,n]=Series[f[x],{x,0,n}]//Normal,{n,0,9}];
2) generate p1,p2,p3 and p9 of order n=1,2,3 and 9
p1=poly[x,1] (* Taylor polynomial of order n=1 *) x p2=poly[x,5] (* Taylor polynomial of order n=5 *) 3 5 x x x - -- + --- 6 120 p3=poly[x,3] (* Taylor polynomial of order n=3 *) 3 x x - -- 6 p9=poly[x,9] (* Taylor polynomial of order n=9 *) 3 5 7 9 x x x x x - -- + --- - ---- + ------ 6 120 5040 362880
3) Plot of y(x)=f(x)=sin(x)
plotf=Plot[f[x],{x,0,Pi/2},ImageSize->200,PlotStyle->RGBColor[1,0,0]];
4) Plots of Taylor Polynomial p1,p2,p3 and p9
plotps=Plot[{p1,p2,p3,p9}, {x,0,Pi/2},ImageSize->200, PlotStyle->RGBColor[0,0,1]];
5) Combine the Plots of f(x)=sin(x) and the polynomial p1,p2,p3,p9
Show[{plotps,plotf},ImageSize->250];
Please Click on ANIMATION
to see the Mathematica code for the Taylor Series animation.