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What is the result of $\displaystyle \lim_{n\to \infty}\left(1+\frac{1}{\tan(n)}\right)^{\tan(n)}$ = ?
The limit does not exist as stated by Adam Rubinson.

Looks like the requested answer is e but then the question is wrong.
What is the correct question to give the answer e?

Did answered correctly. But I think this is some kind of typographical error.
This question appeared on a high school test and the intended question should have a small error.
What is the correct question to give the answer e changing only one value?

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    $\begingroup$ What makes you think that this limit exists? $\endgroup$ – us2012 Aug 8 '13 at 14:15
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    $\begingroup$ Even if we set the domain as R \ {(1/2)n*pi}, the "limit" is not really a limit. It "Oscillates" by "starting" at 1/e, spending a fair amount of it's time near 1, then buzzing off to e. Rinse and repeat this process. So the limit does not exist. $\endgroup$ – Adam Rubinson Aug 8 '13 at 14:26
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    $\begingroup$ Joe Oliver - The correct question would then be "What is limsup...?" $\endgroup$ – Adam Rubinson Aug 8 '13 at 14:35
  • $\begingroup$ "Did answered correctly" Two characters disagree. $\endgroup$ – Did Nov 19 '13 at 15:43
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$$ \lim_{n\to\color{red}{\pi/2}}\left(1+\frac{1}{\tan(n)}\right)^{\tan(n)} = e$$

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What is the correct question to give the answer $\mathrm e$?

$$ \lim_{n\to \infty}\left(1+\tan(1/n)\right)^{1/\tan(1/n)} =\ ? $$

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  • $\begingroup$ This is slightly more likely to be the "correct question" then my proposed question, whatever is meant by "correct question". $\endgroup$ – Adam Rubinson Aug 8 '13 at 14:45

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