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47-50. Combining power series Use the power series representation 00 f(x) = In(1-x) = - for -1sx<1, k=1 to find the power series for the following functions (centered at 0). Give the interval of convergence of the new series. 47. f(3 x) = In (1-3 x) 48. g(x) = x³ In (1-x)

47-50. Combining power series Use the power series representation 00 f(x) = In(1-x) = - for -1sx<1, k=1 to find the power series for the following functions (centered at 0). Give the interval of convergence of the new series. 47. f(3 x) = In (1-3 x) 48. g(x) = x³ In (1-x)

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 48, how did they get the answer in the answer key? 

11.2.48 g(x) = x° In(1 – x) = xk+3 for -1 < x < 1, so the radius of convergence is 1. The series k k=1 diverges at 1 and converges at -1. The interval of convergence is [-1,1). Copyright 2019 Pearson Education, Inc.
Transcribed Image Text:11.2.48 g(x) = x° In(1 – x) = xk+3 for -1 < x < 1, so the radius of convergence is 1. The series k k=1 diverges at 1 and converges at -1. The interval of convergence is [-1,1). Copyright 2019 Pearson Education, Inc.
47-50. Combining power series Use the power series representation f(x) = In(1-x) = -Z , for -1sx<1, k %D k=1 to find the power series for the following functions (centered at 0). Give the interval of convergence of the new series. 47. f(3 x) = In (1-3 x) %3D 48. g(x) = x³ In (1– x) %3D
Transcribed Image Text:47-50. Combining power series Use the power series representation f(x) = In(1-x) = -Z , for -1sx<1, k %D k=1 to find the power series for the following functions (centered at 0). Give the interval of convergence of the new series. 47. f(3 x) = In (1-3 x) %3D 48. g(x) = x³ In (1– x) %3D
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