Example 1. (a) Find the Taylor polynomial of degree n = 5 for , expanded about .

First, find the derivatives of f(x).

Second, evaluate the derivatives of f(x) at x = -1, and obtain a sequence of constants .

Third, substitute the constants in Taylor's formula.

Example 1. (b) Find the Taylor polynomial of degree n = 8.

(c) John H. Mathews, 1998