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Do the interval and radius of convergence of a power

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 5E Chapter 9.2

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 5E

Do the interval and radius of convergence of a power series change when the series is differentiated or integrated? Explain.

Step-by-Step Solution:

Solution 5E

Step 1:

Consider the function ,

which is the derivative of the function

This has the power series representation of the form

This series converges when .

The power series representation of is obtained by differentiating the series term by term.thus we get

 

This also converges when .

Thus the interval and radius of convergence of a power series does not change on differentiating.

Step 2 of 2

Chapter 9.2, Problem 5E is Solved
Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

Since the solution to 5E from 9.2 chapter was answered, more than 247 students have viewed the full step-by-step answer. The answer to “Do the interval and radius of convergence of a power series change when the series is differentiated or integrated? Explain.” is broken down into a number of easy to follow steps, and 20 words. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This full solution covers the following key subjects: Series, integrated, differentiated, explain, Convergence. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The full step-by-step solution to problem: 5E from chapter: 9.2 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM.

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Do the interval and radius of convergence of a power

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