Prove that each of the following functions is uniformly continuous on (0, 1). (You may use l'Hopital's

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Prove that each of the following functions is uniformly continuous on (0, 1). (You may use l'Hopital's Rule and assume that sin x and log x are continuous on their domains.)
a)

c) f(x) = x log x
d) f(x) = (1 - x2)1/x

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An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

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Question Posted: Mar 29, 2016 03:58 AM

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Prove that each of the following functions is uniformly continuous on (0, 1). (You may use l'Hopital's

Question:

f(x) = sinx f(x) = x cos x2

Step by Step Answer:

a By LHpitals Rule sin xx 1 as x 0 Therefore f is uniformly continuous on 0 1 by ...View the full answer

An Introduction to Analysis

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