Chapter 11.1, Problem 4QC

Write out the next two Taylor polynomials p₄ and p₅ for f(x) = e^x in Example 3.

Example 3 Taylor Polynomials for e^x

1. a. Find the Taylor polynomials of order n = 0, 1, 2, and 3 for f(x) = e^x centered at 0. Graph f and the polynomials.
2. b. Use the polynomials in part (a) to approximate e^0.1 and e^−0.25. Find the absolute errors, |f(x) − p_n(x)|, in the approximations. Use calculator values for the exact values of f.