Determine whether the following statements are true and give an explanation or counterexample. a. The function f(x)

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Determine whether the following statements are true and give an explanation or counterexample.

a. The function f(x) = √x has a Taylor series centered at 0.

b. The function f(x) = csc x has a Taylor series centered at π/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(x - 1) 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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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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