Limit of the product of these two functions

  • #1
LagrangeEuler
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If we have two functions ##f(x)## such that ##\lim_{x \to \infty}f(x)=0## and ##g(x)=\sin x## for which ##\lim_{x \to \infty}g(x)## does not exist. Can you send me the Theorem and book where it is clearly written that
[tex]\lim_{x \to \infty}f(x)g(x)=0[/tex]
I found that only for sequences, but it should be correct for functions also.
 

Answers and Replies

  • #2
PeroK
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If we have two functions ##f(x)## such that ##\lim_{x \to \infty}f(x)=0## and ##g(x)=\sin x## for which ##\lim_{x \to \infty}g(x)## does not exist. Can you send me the Theorem and book where it is clearly written that
[tex]\lim_{x \to \infty}f(x)g(x)=0[/tex]
I found that only for sequences, but it should be correct for functions also.
If ##g## is any bounded function then there is a straightforward epsilon-delta proof.
 
  • #3
mathman
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|f(x)g(x)| is bounded by |f(x)| goes to 0
 

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