If f and g have power series representations centered at x = 0 of radii R1 and R2, respectively, then the product fg has a power series representation centered at x = 0 of radius R, where R = min{R1, R2}.

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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decide if the given statement is true or false,and give a brief justification for your answer.If true, you can quote a relevant definition or theorem . If false,provide an example,illustration,or brief explanation of why the statement is false.

If f and g have power series representations centered
at x = 0 of radii R1 and R2, respectively, then the
product fg has a power series representation centered
at x = 0 of radius R, where R = min{R1, R2}.
Transcribed Image Text:If f and g have power series representations centered at x = 0 of radii R1 and R2, respectively, then the product fg has a power series representation centered at x = 0 of radius R, where R = min{R1, R2}.
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