6. PROVE: Let f be defined on an interval I. Suppose that there exists M > 0 and a > 0 such that |f(x) – f(y)| < M|æ – y/ª for all x, y E I. Then f is uniformly continuous.
6. PROVE: Let f be defined on an interval I. Suppose that there exists M > 0 and a > 0 such that |f(x) – f(y)| < M|æ – y/ª for all x, y E I. Then f is uniformly continuous.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.2: Mappings
Problem 19E
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![6.
PROVE: Let f be defined on an interval I. Suppose that there exists M > 0 and a >0 such that
\f (x) – f(y)| < M\x – y|ª
for all x, y E I. Then f is uniformly continuous.
Answer:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F187d6ce3-f16e-4919-9795-1c801fb3fce4%2Fca87ced0-4afe-451d-966d-9706a4243e18%2Fbt5gv5g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6.
PROVE: Let f be defined on an interval I. Suppose that there exists M > 0 and a >0 such that
\f (x) – f(y)| < M\x – y|ª
for all x, y E I. Then f is uniformly continuous.
Answer:
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