Let fn(x) := nx/(1 + nx2) for x A := [0, ). Show that each fn

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Let fn(x) := nx/(1 + nx2) for x ∈ A := [0, ∞). Show that each fn is bounded on A, but the point wise limit f of the sequence is not bounded on A. Does (fn) converge uniformly to f on A?

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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 + nx2) for x A := [0, ). Show that each fn

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Since 0 f n x n x n on 0 1 and 0 f n x 1x 1 on 1 ...View the full answer

Introduction to Real Analysis

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