Suppose we have the sequence of functions $f_n(x)=x^n$ defined on $[0,1],$ and suppose $f_n\to f$ pointwise where $f(x)=0$ if $x\in(0,1]$ and $f(x)=1$ if $x=1.$ Prove that Uniform Convergence fails.
Suppose we have the sequence of functions $f_n(x)=x^n$ defined on $[0,1],$ and suppose $f_n\to f$ pointwise where $f(x)=0$ if $x\in(0,1]$ and $f(x)=1$ if $x=1.$ Prove that Uniform Convergence fails.
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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Suppose we have the sequence of functions $f_n(x)=x^n$ defined on $[0,1],$ and suppose $f_n\to f$ pointwise where $f(x)=0$ if $x\in(0,1]$ and $f(x)=1$ if $x=1.$ Prove that Uniform Convergence fails.
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