For each nЄ Z+ let fn : R → R be the function пх fn(2) n|x| +1° (a) Prove that (fn) converges pointwise to some function ƒ : R → R. (b) Prove that (fn) does not converge uniformly.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
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For each n = Z+ let fn : R → R be the function
пх
fn (2)
=
n|x| +1
(a) Prove that (fn) converges pointwise to some function f : R→ R.
(b) Prove that (fn) does not converge uniformly.
Transcribed Image Text:For each n = Z+ let fn : R → R be the function пх fn (2) = n|x| +1 (a) Prove that (fn) converges pointwise to some function f : R→ R. (b) Prove that (fn) does not converge uniformly.
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