Question

lim x-> infinity of arctan(lnx) ??? i know the limit of arctan if pi/2 but what about limit of lnx?

Answer 1

\[\lim_{x \rightarrow \infty} \tan^{-1} (\ln x) = \tan^{-1} \left[ \lim_{x \rightarrow \infty} \ln x \right] = \tan^{-1} \left[ \infty \right] = \frac {\pi}{2}\]

Answer 2

\[\lim_{x \rightarrow \infty} \ln x = \infty\]

Answer 3

ok so...