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Differentiating and integrating power series Find the

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

Solution for problem 33E 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 33E

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.

 using

Step-by-Step Solution:

Solution 33E 

Step 1:

In this  problem  we need to find the power series representation  for g(x) =  centered at ‘0’  by differentiating or integrating the power series for f(x) =

We already know a power series for f(x) =  =  for

                        

                

                 , since , and  =

                 

Therefore , power series representation  for g(x) =

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 and

If L<1, converges.If L>1, diverges.If L=1, the test is inconclusive.

We have

 

              , since

           

           

        , since  as n , then

Step 3:

The series  converges for L < 1

Therefore  solve |x| < 1

By using , “ if |f(x)| < a  then -a < f(x) < a “  we get  -1 < x < 1

Step 4 of 5

Chapter 9.2, Problem 33E is Solved
Step 5 of 5

Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

The full step-by-step solution to problem: 33E from chapter: 9.2 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Since the solution to 33E from 9.2 chapter was answered, more than 251 students have viewed the full step-by-step answer. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. The answer to “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. using” is broken down into a number of easy to follow steps, and 38 words. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. This full solution covers the following key subjects: differentiating, Series, power, Integrating, once. This expansive textbook survival guide covers 85 chapters, and 5218 solutions.

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