# How do I find the limit as x approaches infinity of x^7/(7x)?

Aug 20, 2014

We start by plugging in $\infty$ for x.

We get ${\infty}^{7} / \left(7 \left(\infty\right)\right)$

That is not able to be evaluated. In this situation, we can use L'Hôpital's Rule. The key here is to use the rule only when the limit is not able to be determined.

Taking the derivative of the top and bottom where $f \left(x\right) = {x}^{7}$ and $g \left(x\right) = 7 x$, we have:

$f ' \left(x\right) = 7 {x}^{6}$
$g ' \left(x\right) = 7$

We have $7 {x}^{6} / 7$ which simplifies to ${x}^{6}$

Since this is able to be evaluated, we have our limit as ${\infty}^{6} = \infty$

Therfore, as $x \to \infty$, the limit is $\infty$