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## Babyslapmafro Group Title Please help me find the limit of the following function (click to see). one year ago one year ago

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1. Babyslapmafro

$\lim_{x \rightarrow 0^+}\frac{ cotx }{ lnx }$

2. LolWolf

There's no nice elementary method, other than l'Hospital's. At least, not that I can come up with: \begin{align} \lim_{x\to0^+}\left(\frac{\cot x}{\ln x}\right) &= \lim_{x\to0^+}\left(\frac{\frac{d}{dx}\cot x}{\frac{d}{dx}\ln x}\right)=\\\lim_{x\to0^+}\left(\frac{-\csc^2 x}{\frac{1}{x}}\right)&=\lim_{x\to0^+}\left(-x\csc x\right)=-\infty \end{align}

3. Babyslapmafro

thank you

4. LolWolf

Sure thing.