http://www.adeptscience.co.uk/products/mathsim/maple/powertool
s/calcII/html/L20-taylorIntro.html
Taylor
restart; with(plots):
> f := x -> sin(x);
> on := x -> piecewise( x <0, 0, x <
1, 1,1);
> a := -6: b := 6: c := -3: d:= 4:
> g := (x,k) -> convert(series(f(x),
x, k), polynom):
> display( plot( f(x), x = a..b, y =
c..d, thickness = 3, color = blue),
animate( on(t-1)*g(x,2) , x = a..b, t
= 0..7, view = c..d, color = cyan),
animate( on(t-2)*g(x,4) , x = a..b, t
= 0..7, view = c..d, color =
coral),animate( on(t-3)*g(x,6) , x =
a..b, t = 0..7, view = c..d, color =
green), animate( on(t-4)*g(x,8) , x
= a..b, t = 0..7, view = c..d, color =
violet), animate( on(t-5)*g(x,10) ,
x = a..b, t = 0..7, view = c..d, color
= red), animate( on(t-6)*g(x,12) , x
= a..b, t = 0..7, view = c..d, color =
coral) );
Taylor Polynomials--A Visual
Approach to Approximations
http://mathdemos.gcsu.edu/TaylorPolynomials/
Approximation to f(x) = cos(x) by Maclaurin Polynomials and the error.
http://mathdemos.gcsu.edu/TaylorPolynomials/
Approximation to f(x) = log(x+1) by Maclaurin Polynomials and the error.
http://mathdemos.gcsu.edu/TaylorPolynomials/gallery/index.html
http://mathdemos.gcsu.edu/TaylorPolynomials/gallery/index.html