when is it justified to do something like this(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \lim_{n\to\infty} e^{lnx^{1/n}} = e^{\displaystyle\lim_{n\to\infty}lnx^{1/n}}[/tex]

or something like this

[tex] \lim_{n\to\infty} 2^{f(n)} = 2^{\displaystyle\lim_{n\to\infty}f(n)}}[/tex] ?

I am assuming that I can do something like this in both cases, but why?

thank you.

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# When is it OK to pass the limit to the exponent

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