Calculus Examples

$lim_{x \to \infty} \arctan (x^{5} - x^{9})$

Step 1

The limit at infinity of a polynomial whose leading coefficient is negative is negative infinity.

$- \infty$

Step 2

Substitute $t$ for $x^{5} - x^{9}$ and let $t$ approach $- \infty$ since $lim_{x \to \infty} x^{5} - x^{9} = - \infty$ .

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

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:

$- 1.57079632 \dots$