   Chapter 9.9, Problem 24E Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Solutions

Chapter
Section Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

Using a Power Series In Exercises 19-28, use the power series 1 1 + x = ∑ n = 0 ∞ ( − 1 ) n x n ,     | x |   < 1 to find a power series for the function, centered at 0, and determine the Interval of convergence. f ( x ) = ln ( 1 − x 2 ) = ∫ 1 1 + x d x − ∫ 1 1 − x d x

To determine
Find the power series of the function, centered at 0and determine theinterval of convergence.

Explanation

Given: f(x)=ln(1x2)=11+xdx11xdx

Explanation:

11+xdx=[n=0(1)nxn]dx=n=0(1)n.xn1n+111xdx=(n=0xn)dx=n=0xn1n+1  ln

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