# What is the limit of arctan(e^x) as x goes to infinity?

We know that ${\lim}_{x \to + \infty} {e}^{x} = + \infty$ and ${\lim}_{x \to + \infty} \arctan x = \frac{\pi}{2}$ from the stuy of ${e}^{x}$ and of $\arctan x$.
So, as $x \to \infty$, ${e}^{x} \to \infty$ so that, letting $t = {e}^{x}$ we have
${\lim}_{x \to \infty} \arctan \left({e}^{x}\right) = {\lim}_{t \to \infty} \arctan \left(t\right) = \setminus \frac{\pi}{2}$.