Calculus Examples

$lim_{x \to \infty} \arctan (e^{x})$

Change the two-sided limit into a left sided limit.

$lim_{x \to \infty^{-}} \arctan (e^{x})$

Since the exponent $x$ approaches $\infty$ , the quantity $e^{x}$ approaches $\infty$ .

$\infty$

Substitute $t$ for $e^{x}$ and let $t$ approach $\infty$ since $lim_{x \to \infty^{-}} e^{x} = \infty$ .

$lim_{t \to \infty^{-}} \arctan (t)$

The limit as $t$ approaches $\infty$ is $\frac{π}{2}$ .

$\frac{π}{2}$