Explain why or why not Determine whether the

Chapter 9, Problem 73

(choose chapter or problem)

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. a. Only even powers of x appear in the Taylor polynomials for f 1x2 = e-2x centered at 0. b. Let f 1x2 = x5 - 1. The Taylor polynomial for f of order 10 centered at 0 is f itself. c. Only even powers of x appear in the nth-order Taylor polynomial for f 1x2 = 21 + x2 centered at 0. d. Suppose f _ is continuous on an interval that contains a, where f has an inflection point at a. Then the second-order Taylor polynomial for f at a is linear.