# Thread: Limit problem (maybe L'Hopital's Rule)

1. ## Limit problem (maybe L'Hopital's Rule)

$\lim x \rightarrow \infty \sqrt[3]{x^3 - 9x^2} - x$

If it weren't for that -x at the end, I'd just use Ln and L'Hopital's Rule if I needed to, but that -x throws me off. Not really sure how to get started...

2. $\sqrt[3]{x^3 - 9x^2} - x = x\left( \sqrt[3]{1 - \frac{9}{x}} -1\right)$

At this point I would make the variable substitution $t = \frac{1}{x}$ and use L'Hospital's Rule.