1. For each n € Z let fn: R→ R be the function nx nx + 1 In(x) = (a) Prove that (fn) converges pointwise to some function f: R→ R. (b) Prove that (n) does not converge uniformly.
1. For each n € Z let fn: R→ R be the function nx nx + 1 In(x) = (a) Prove that (fn) converges pointwise to some function f: R→ R. (b) Prove that (n) does not converge uniformly.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. For each n€ Z let fn: R→ R be the function
nx
nx + 1
In(x) =
(a) Prove that (fn) converges pointwise to some function f: R→ R.
(b) Prove that (n) does not converge uniformly.
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