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.
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.
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 f uniformly on a set ACR. Assume that |fn(x)| < M for
all x E A. Show that if g is continuous function on [-M, M], then the sequence (go fn) converges
uniformly on A.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71926a0a-b180-40cf-af91-e31ac368073e%2Fe2937f45-58a7-44c5-8599-3a04b2143fcb%2Ft72tlg_processed.png&w=3840&q=75)
Transcribed Image Text:Let (fn) be a sequence that converges to f uniformly on a set ACR. Assume that |fn(x)| < M for
all x E A. Show that if g is continuous function on [-M, M], then the sequence (go fn) converges
uniformly on A.
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