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Let f : R → R be a function such that |f (x) – f(y)| < k|r – y|2, Vr, y E R, for some k > 0. Write the e-d definition of continuous function on R, and prove that f is continuous on R.

Let f : R → R be a function such that |f (x) – f(y)| < k|r – y|2, Vr, y E R, for some k > 0. Write the e-d definition of continuous function on R, and prove that f is continuous on R.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.2: Mappings
Problem 27E: 27. Let , where and are nonempty. Prove that has the property that for every subset of if and...
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Let f : R → R be a function such that |f (x) – f(y)| < k|r – y|2, Vx, y E R, for some k > 0. Write the e-d definition of continuous function on R, and prove that f is continuous on R.
Transcribed Image Text:Let f : R → R be a function such that |f (x) – f(y)| < k|r – y|2, Vx, y E R, for some k > 0. Write the e-d definition of continuous function on R, and prove that f is continuous on R.
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