   Chapter 9.9, Problem 27E 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 ) = 1 4 x 2 + 1

To determine

To calculate: The power series of the function h(x)=14x2+1, centered at 0and determine the interval of convergence.

Explanation

Given:

The function is h(x)=14x2+1

Formula used:

Power series:

11+x=n=0(1)nxn,|x|<1

Calculation:

Since, Power series is

11+x=n=0(1)nxn,|x|<1

So,

h(x)=14x2+1=11+(2x)2<

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