real analysis 1. For x < 1, define fn(x) = ²x.(a) Prove that for x < 1,k=1x(1+x)(1 − x)³(b) Does fn(x) converge uniformly to f(x) on (-1, 1)? Justify your answers.f(x) = lim fn(x) =84x

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Answered: 1. For r < 1, define fn(x) = ²x. (a)…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

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1. For r < 1, define fn(x) = ²x. (a) Prove that for x < 1, k=1 ƒ(x) = lim_ƒn(x) = 84x x(1+x) (1-x)³ - (b) Does fn(x) converge uniformly to f(x) on (-1, 1)? Justify your answers.