Calculus Examples

$lim_{x \to 0} \arctan (\frac{1}{x^{2}})$

Step 1

Since the numerator is a constant and the denominator approaches $0$ when $x$ approaches $0$ , the fraction $\frac{1}{x^{2}}$ approaches infinity.

$\infty$

Step 2

Substitute $t$ for $\frac{1}{x^{2}}$ and let $t$ approach $\infty$ since $lim_{x \to 0} \frac{1}{x^{2}} = \infty$ .

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

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:

$1.57079632 \dots$