Limit $\lim_{x\rightarrow \infty} x^3 e^{-x^2}$ using L'Hôpital's rule I am trying to solve a Limit using L'Hôpital's rule with $e^x$
So my question is how to find $$\lim_{x\rightarrow \infty} x^3 e^{-x^2}$$
I know to get upto this part here, but I'm lost after that
$$\lim_{x\rightarrow \infty} \frac{x^3}{e^{x^2}}$$

$$\begin{align}
\lim_{x\rightarrow \infty} \dfrac{x^3}{e^{x^2}}
&=\lim_{x\rightarrow \infty} \dfrac{3x^2}{e^{x^2}2x}\\
&=\lim_{x\rightarrow \infty} \dfrac{3x}{e^{x^2}2}\\
&=\lim_{x\rightarrow \infty} \dfrac{3}{e^{x^2}.2.2x}\\
&=0
\end{align}$$
