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

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BabyslapmafroBest ResponseYou've already chosen the best response.0
\[\lim_{x \rightarrow 0^+}\frac{ cotx }{ lnx } \]
 one year ago

LolWolfBest ResponseYou've already chosen the best response.1
There's no nice elementary method, other than l'Hospital's. At least, not that I can come up with: \[\begin{align} \lim_{x\to0^+}\left(\frac{\cot x}{\ln x}\right) &= \lim_{x\to0^+}\left(\frac{\frac{d}{dx}\cot x}{\frac{d}{dx}\ln x}\right)=\\\lim_{x\to0^+}\left(\frac{\csc^2 x}{\frac{1}{x}}\right)&=\lim_{x\to0^+}\left(x\csc x\right)=\infty \end{align}\]
 one year ago
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