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Under which conditions

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

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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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It's always true. You can take exponentials on both sides, and then pull the $\lim$ outside on the left-hand side since the exponential function is continuous.

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    Now I got it. Thank you very much! No need for a calculus textbook.;)2012-10-21