a) Prove that x/n 0 uniformly, as n , on any closed interval [a, b]

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a) Prove that x/n → 0 uniformly, as n → ∞, on any closed interval [a, b]
b) Prove that 1/(nx) → 0 pointwise but not uniformly on (0, 1) as n → ∞.

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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 04:08 AM

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a) Prove that x/n 0 uniformly, as n , on any closed interval [a, b]

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a Given 0 choose N so large that N maxa b Then n N and x a b impl...View the full answer

An Introduction to Analysis

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