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Babyslapmafro
 2 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{x \rightarrow 0^+}\frac{ cotx }{ lnx } \]

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