Calculus Examples

$lim_{x \to 0^{+}} \arctan (\ln (x))$

Step 1

As $x$ approaches $0$ from the right side, $\ln (x)$ decreases without bound.

$- \infty$

Step 2

Substitute $t$ for $\ln (x)$ and let $t$ approach $- \infty$ since $lim_{x \to 0^{+}} \ln (x) = - \infty$ .

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

Step 3

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

$- \frac{π}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{π}{2}$

Decimal Form:

$- 1.57079632 \dots$