A function f E R is called Lipschitz (or more precisely M-Lipschitz) if there exists an...
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A function f E→ R is called Lipschitz (or more precisely M-Lipschitz) if there exists an M >0 such that for all x, y € E, f(x)-f(y)| ≤ Mx - y. 1. Show that any Lipschitz function is uniformly continuous. 2. Show that if f: (a, b)→ R is a differentiable function such that f'(t)| ≤ M for all t€ (a, b), then f is M-Lipschitz. A function f E→ R is called Lipschitz (or more precisely M-Lipschitz) if there exists an M >0 such that for all x, y € E, f(x)-f(y)| ≤ Mx - y. 1. Show that any Lipschitz function is uniformly continuous. 2. Show that if f: (a, b)→ R is a differentiable function such that f'(t)| ≤ M for all t€ (a, b), then f is M-Lipschitz.
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Related Book For
Introduction to Real Analysis
ISBN: 978-0471433316
4th edition
Authors: Robert G. Bartle, Donald R. Sherbert
Posted Date:
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