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# Differentiating and integrating power series | Ch 9.2 - 37E ISBN: 9780321570567 2

## Solution for problem 37E Chapter 9.2

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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##### ISBN: 9780321570567

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