17) Prove that uniform continuity implies continuity, and give a counterexample to show that continuity does not always imply uniform continuity. Under what conditions continuity implies uniform continuity?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
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17) Prove that uniform continuity implies continuity,
and give a counterexample to show that
continuity does not always imply uniform
continuity. Under what conditions continuity
implies uniform continuity?
Transcribed Image Text:17) Prove that uniform continuity implies continuity, and give a counterexample to show that continuity does not always imply uniform continuity. Under what conditions continuity implies uniform continuity?
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