Explain why or why not Determine whether the

Chapter 9, Problem 61

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Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. a. The function f 1x2 = 1x has a Taylor series centered at 0. b. The function f 1x2 = csc x has a Taylor series centered at p>2. c. If f has a Taylor series that converges only on 1-2, 22, then f 1x22 has a Taylor series that also converges only on 1-2, 22. d. If p 1x2 is the Taylor series for f centered at 0, then p 1x - 12 is the Taylor series for f centered at 1. e. The Taylor series for an even function about 0 has only even powers of x.

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