1 1-x Use the geometric series f(x)= = Σx, for |x|<1, to find the power series representation for the following function (centered at 0). Give the interval of k=0 convergence of the new series. f(3x)= 1 1-3x Which of the following is the power series representation for f(3x)? 3k Ο Α.Σ x Ο Β. Σ 3xk k=0 k=0 1 Oc. Σ k=0 1-(3x)* OD.Σ (3x)* k=0 The interval of convergence is (Simplify your answer. Type your answer in interval notation.)

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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1
1-x
Use the geometric series f(x)=
=
Σx, for |x|<1, to find the power series representation for the following function (centered at 0). Give the interval of
k=0
convergence of the new series.
f(3x)=
1
1-3x
Which of the following is the power series representation for f(3x)?
3k
Ο Α.Σ x
Ο Β. Σ 3xk
k=0
k=0
1
Oc. Σ
k=0 1-(3x)*
OD.Σ (3x)*
k=0
The interval of convergence is
(Simplify your answer. Type your answer in interval notation.)
Transcribed Image Text:1 1-x Use the geometric series f(x)= = Σx, for |x|<1, to find the power series representation for the following function (centered at 0). Give the interval of k=0 convergence of the new series. f(3x)= 1 1-3x Which of the following is the power series representation for f(3x)? 3k Ο Α.Σ x Ο Β. Σ 3xk k=0 k=0 1 Oc. Σ k=0 1-(3x)* OD.Σ (3x)* k=0 The interval of convergence is (Simplify your answer. Type your answer in interval notation.)
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