This worksheet illustrates successive Taylor series approximations (about [math]x=0[/math]) to the function [math]f(x) = 1/(1+x)[/math].

[list=1] [*] Vary [math]n[/math] and observe how the graph of the polynomial [color=#ff0000][math]T_n(x)[/math][/color] gets closer and closer to the graph of the function [color=#0000ff][math]1/(1+x)[/math][/color]. [*] Notice, however, that the approximation resolutely fails to converge to [math]1/(1+x)[/math] outside the interval [math](-1,1)[/math]. [/list]