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.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 72E
icon
Related questions
Question
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.
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.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax