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# Explain why or why not Determine whether the | Ch 9.3 - 51E

ISBN: 9780321570567 2

## Solution for problem 51E Chapter 9.3

Calculus: Early Transcendentals | 1st Edition

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Problem 51E

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.a. The function has a Taylor series centered at 0.b. The function f(x) = csc x has a Taylor series centered at ?/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 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.

Step-by-Step Solution:

Solution 51EStep 1:(a). The function has a Taylor series centered at 0.The general equation of a taylor series centered at 0 is Here and the differentiation of at 0 is always 0.Thus this is a false statement .Step 2:(b).The function has a Taylor series centered at /2.The general equation of a taylor series centered at is Here This continues.Thus the taylor expansion of Thus the given statement is true.Step 3:(c). . If f has a Taylor series that converges only on (2, 2), then has a Taylor series that also converges only on (2, 2).f has a Taylor series that converges only on (2, 2), implies that is the radius of convergence.Therefore the radius of convergence of will be Thus has a Taylor series that converge on .

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##### ISBN: 9780321570567

The full step-by-step solution to problem: 51E from chapter: 9.3 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Since the solution to 51E from 9.3 chapter was answered, more than 244 students have viewed the full step-by-step answer. This full solution covers the following key subjects: Series, Taylor, Centered, function, converges. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. The answer to “Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.a. The function has a Taylor series centered at 0.b. The function f(x) = csc x has a Taylor series centered at ?/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 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.” is broken down into a number of easy to follow steps, and 103 words. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1.

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