Answer
\[\frac{π}{2}\]
Work Step by Step
Let \[l=\lim_{x\rightarrow \infty}arc\tan (e^x)\]
\[l=arc\tan (e^{\infty})\]
Since $e^x$ is strictly increasing function in its domain of definition
\[l=arc\tan (\infty)\]
\[l=arc\tan (\tan\frac{π}{2})\]
\[l=\frac{π}{2}\]
Hence \[l=\frac{π}{2}\]
