Question

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

Answer 1

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

Answer 2

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

Answer 3

thank you

Answer 4

Sure thing.