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Find the pointwise limit f(x) for {nxe-nx} for x ∈ (0, +inf)). Does the sequence converge uniformly for x ∈ (0, +inf))? If yes, what is the uniform norm of fn(x)-f(x) on (0, +inf)?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.1: Infinite Sequences And Summation Notation

Problem 72E

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Find the pointwise limit f(x) for {nxe-^nx} for x ∈ (0, +inf)). Does the sequence converge uniformly for x ∈ (0, +inf))?

If yes, what is the uniform norm of fn(x)-f(x) on (0, +inf)?

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