   Chapter 9.9, Problem 20E 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. h ( x ) = x x 2 − 1 = 1 2 ( 1 + x ) + 1 2 ( 1 − x )

To determine
Find the power series of the function, centered at c and determine the interval of convergence.

Explanation

Given: h(x)=xx21=12(1+x)12(1x)

Explanation:

12(1+x)=12n=0(1)nxn   and  12(1+x)=12n=0xnThen       xx21=12(

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