   Chapter 9.9, Problem 22E 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 ) = 2 ( x + 1 ) 3 = d 2 d x 2 [ 1 x + 1 ]

To determine
Find the power series of the function f(x)=2(x+1)3=d2dx2(11+x), centered at 0and determine theinterval of convergence.

Explanation

Given: f(x)=2(x+1)3=d2dx2(11+x)

Explanation:

f(x)=d2dx2(11+x) =d2dx2(n=0(1)nxn)       =ddxn=1(1)nn

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