Let (fn) be a sequence that converges to f uniformly on a set ACR. Assume that |fn(x)| < M forall x E A. Show that if g is continuous function on [-M, M], then the sequence (go fn) convergesuniformly on A.

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Answered: Let (fn) be a sequence that converges…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

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Let (fn) be a sequence that converges to ƒ uniformly on a set A CR. Assume that |fn(x)| < M for all x € A. Show that if g is continuous function on [-M, M], then the sequence (go fn) converges uniformly on A.