Let fn(x) := nx/(1 + nx) for x (0, 1). Show that (fn) converges non uniformly

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Let fn(x) := nx/(1 + nx) for x ∈ (0, 1). Show that (fn) converges non uniformly to an integrable function f and that ∫10 f(x)dx = lim ∫10 fn(x)dx.

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Introduction to Real Analysis

ISBN: 978-0471433316

4th edition

Authors: Robert G. Bartle, Donald R. Sherbert

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Question Posted: Apr 07, 2016 11:07 AM

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Let fn(x) := nx/(1 + nx) for x (0, 1). Show that (fn) converges non uniformly

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The limit function is f0 0 ...View the full answer

Introduction to Real Analysis

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