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I am having a problem with the calculation of the following limit.

I need to find: $\lim_{x \to 0^{+}} (\ln \frac{1}{x})^x$

Thank you in advance

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    Coming from the right suggests that $x$ stays positive, so the $\ln$ will be well-defined. The power suggests we use logarithmic differentiation, which says something to the effect of $\lim f(x) = \exp(\lim \ln f(x))$. Do you see why that's useful?2012-11-14
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    That is what I did. But I am having trouble calculating the limit of ln(ln(1/x))2012-11-14
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    Naively, as $x\to 0$, for positive $x$, $1/x \to \infty$, and as $u\to\infty$, $\ln u \to \infty$ as well. Taking another $\ln$ only compounds the problem. But, that's not the only term in the limit; having infinities involved generally means L'Hôpital is afoot.2012-11-14

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