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Under which conditions

$$\lim_{a\to+\infty}\ln(f(a,x)) = \ln(z(x))\Longrightarrow \underset{a\to+\infty}{\lim}f(a,x) = z(x)\;?$$

  • 1
    Was the switching of the parameters $a,x$ in $f$ in the second limit intentional?2012-10-21
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    No, it should read as $f(a,x)$ or $f(x,a)$ in both cases.2012-10-21
  • 0
    Put it simpler I just want to know if I find a limit of log of something is equal to the log. Can I infer that limit of the expressions under logs are equal.2012-10-21
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    Or it would be simpler if the following is true $\lim_{a\to+\infty}\ln(f(a,x)) = \ln(\lim_{a\to+\infty} f(a,x))$. Is it always true and why?2012-10-21

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