(a) Show that the absolute value function F(x) = |x| is continuous everywhere. (b) Prove that if...
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(b) Prove that if f is a continuous function on an interval, then so is | f |.
(c) Is the converse of the statement in part (b) also true? In other words, if | f | is continuous, does it follow that f is continuous? If so, prove it. If not, find a counterexample.
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a lim Fx 0 and lim Fx 0 so lim Fx 0 which is F0 and he...View the full answer
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Related Book For
Introduction to Real Analysis
ISBN: 978-0471433316
4th edition
Authors: Robert G. Bartle, Donald R. Sherbert
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