Limit of monotic transformation

  • Thread starter tunaaa
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  • #1
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Main Question or Discussion Point

Hello, I was just wondering if is it true that the limit of a monotonic transformation of a function is the same as the monotonic transformation of its limit? That is, does

[tex]\lim_{n \rightarrow a} f(g(x)) = f(\lim_{n \rightarrow a} g(x))[/tex]

for monotonic [tex]f[/tex], some [tex]a[/tex], and such that if the limit does not exist for one side of the expression, it doesn't exist for both?

Thanks.
 

Answers and Replies

  • #2
mathman
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Your original equation does not describe the dependence on n of anything.
 
  • #3
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Sorry, replace n with x - was very tired!
 
  • #4
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Correction: [tex]\lim_{x \rightarrow a} f(g(x)) = f(\lim_{x \rightarrow a} g(x))[/tex]
 
  • #5
mathman
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I believe you need f to be continuous at g(a). The g(x) may be a red herring. Just look at lim(x->a)f(x)=f(a).
 

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