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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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.
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