Example 3. (a) Find the Taylor polynomial of degree n = 3 for , expanded about .

First, find the derivatives of f(x).

Second, evaluate the derivatives of f(x) at x = 4, and obtain a sequence of constants .

Third, substitute the constants in Taylor's formula.

Example 3. (b) Find the Taylor polynomial of degree n = 6.

(c) John H. Mathews, 1998