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given the following limit:

$$ \lim _ {x \to 0 } \left (\frac{\tan x } {x} \right ) ^{1/x^2}\;, $$

is there any simple way to calculate it ?

I have tried writing it as $e^ {\ln (\dots)} $ , but it doesn't give me anything [ and I did l'Hospital on the limit I received... ]

can someone help me with this?

thanks a lot !

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    Rewriting as $e^{\ln ...}$ is a good idea. Maybe you should apply l'Hospital it twice.2012-12-31
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    applying it twice also doesn't help ... So my guess is that there is some other way to do it .2012-12-31
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    There is some other way to do it. Do you know Taylor expansion?2012-12-31
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    Yes, but I am pretty sure we need to do it with l'Hospital Is there any trick to solve it with l'Hospital ? Thanks !2012-12-31

5 Answers 5