67. Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. a. The function f (a ) = vac has a Taylor series centered at 0. b. The function f (a) = csc x has a Taylor series centered at 7 / 2. c. If f has a Taylor series that converges only on (-2, 2), then f(x2) has a Taylor series that also converges only on (-2, 2). d. If p(x) is the Taylor series for f centered at 0, then p(a - 1) is the Taylor series for f centered at 1. e. The Taylor series for an even function centered at 0 has only even powers of x