Question

Find the limit of (lnx)^(1/x) as x approaches to infinity.

Answer 1

\[\lim_{x\to\infty}\left(\ln x\right)^{1/x}\]
\[\exp\left(\ln\lim_{x\to\infty}\left(\ln x\right)^{1/x}\right)\]
\[\exp\left(\lim_{x\to\infty}\ln \left(\ln x\right)^{1/x}\right)\]
\[\exp\left(\lim_{x\to\infty}\frac{\ln \left(\ln x\right)}{x}\right)\]
A good candidate for L'hopital's rule