4. Show that the sequence {fn}, where fn(x) = xER 1+n°x*' is point-wise convergent but is not uniformly convergent in any interval containing zero.

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Sequences And Series
Section8.1: Sequences And Summation Notation
Problem 1E: A sequence is a function whose domain is ____________.
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4. Show that the sequence {fn}, where
nx
=(x)"f
1+n°x
xER
is point-wise convergent but is not uniformly convergent in any interval
containing zero.
Transcribed Image Text:4. Show that the sequence {fn}, where nx =(x)"f 1+n°x xER is point-wise convergent but is not uniformly convergent in any interval containing zero.
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