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Solution: Exponential function In Section 9.3, we show that

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

Solution for problem 62E 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 62E

Problem 62E

Exponential function In Section 9.3, we show that the power series for the exponential function centered at 0 is

Use the methods of this section to find the power series for the following functions. Give the interval of convergence for the resulting series.

f(x) = x2ex

Step-by-Step Solution:

Solution 62E

Step 1:

We are given that  for

We have to find the power series for

Therefore  

It is a fact that the x’s outside the series is not going to affect the interval of convergence.

The radius of convergence in the resulting series is

Therefore the interval of convergence is

The power series representation is

Step 2 of 1

Chapter 9.2, Problem 62E is Solved
Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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Solution: Exponential function In Section 9.3, we show that