L’Hôpital’s rule practice question 9

What do $1 - \cos(3x)$ and $x^{2}$ each tend to as $x \to 0$? Check the form again before every application, not only the first.

After one application the form is still $\tfrac{0}{0}$: $\dfrac{3\sin(3x)}{2x}$. Apply the rule again, or recognise $\dfrac{\sin(3x)}{3x} \to 1$.