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Differentiating and integrating power series | Ch 9.2 - 37E

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

Solution for problem 37E 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 37E

Differentiating and integrating power series Find the power series representation for g centered at 0 by differentiating or integrating the power series for f (perhaps more than once). Give the interval of convergence for the resulting series.g(x) = In (1 ? 3x) using

Step-by-Step Solution:

Solution 37EStep 1:In this problem we need to find the the power series representation for centered at 0 by differentiating or integrating the power series for We already know a power series for ,namely for Therefore power series representation foris Step 2:Now let us find the interval of convergence of Use Ratio test to determine the interval of convergence.If there exists an N so that for all , and and1. If L<1, converges.2. If L>1, diverges.3. If L=1, the test is inconclusive.We have

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Chapter 9.2, Problem 37E is Solved
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Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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Differentiating and integrating power series | Ch 9.2 - 37E

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