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For number 51, can you show why -1/2  and 1/2 diverge and are not included.?

For number 51, can you show why -1/2  and 1/2 diverge and are not included.?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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For number 51, can you show why -1/2  and 1/2 diverge and are not included.?

11.2.51 The power series for f(x) is > (2x)*, which is convergent for -1 < 2x < 1, so for -1/2 <z<1/2. k=0 The power series for g(r) = f'(x) is >k(2x)*-1. 2= 2 *(2x)*=1, also convergent on r| < 1/2. At the %3D k=1 k=1 1 1 endpoints the series diverges by the Divergence Test. The interval of convergence is 22
Transcribed Image Text:11.2.51 The power series for f(x) is > (2x)*, which is convergent for -1 < 2x < 1, so for -1/2 <z<1/2. k=0 The power series for g(r) = f'(x) is >k(2x)*-1. 2= 2 *(2x)*=1, also convergent on r| < 1/2. At the %3D k=1 k=1 1 1 endpoints the series diverges by the Divergence Test. The interval of convergence is 22
50. f(x*) = In(1-x²) 51-56. Differentiating and integrating power series Find the power series representation for g centered at 0 by differentiating or integrating the power series for f (perhaps more than once). Give the interval of convergence for the resulting series. Power beries Representantion by differentiatian 2. 51. g(x) using f(x) = %3D %3D (1–2 x)² 1-2x
Transcribed Image Text:50. f(x*) = In(1-x²) 51-56. Differentiating and integrating power series Find the power series representation for g centered at 0 by differentiating or integrating the power series for f (perhaps more than once). Give the interval of convergence for the resulting series. Power beries Representantion by differentiatian 2. 51. g(x) using f(x) = %3D %3D (1–2 x)² 1-2x
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