art-maths

As the degree of the Taylor polynomial rises, it approaches the correct function. This image shows sinx (in black) and Taylor approximations, polynomials of degree 1, 3, 5, 7, 9, 11 and 13.
An 8th degree approximation of the cosine function in the complex plane.
The Taylor polynomials for log(1+x) only provide accurate approximations in the range −1 < x ≤ 1. Note that, for x > 1, the Taylor polynomials of higher degree are worse approximations
The sine function (blue) is closely approximated by its Taylor polynomial of degree 7 (pink) for a full period centered at the origin.The Golden Curve

Java Applet to see how Taylor approximation works

http://stud3.tuwien.ac.at/~e0004876/taylor/Taylor_en.html

Maths With Java
http://www.ies.co.jp/math/java/
http://www.ies.co.jp/math/java/misc/SimpleGraph3D/SimpleGraph3D.html