Answer
$$0$$
Work Step by Step
Since
$$
\lim _{x \rightarrow \infty} \frac{ x }{e^x}=\frac{\infty}{\infty}
$$
is an intermediate form, then we can apply L’Hôpital’s Rule as follows
$$
\lim _{x \rightarrow \infty} \frac{ x }{e^x}=\lim _{x \rightarrow \infty} \frac{ 1 }{e^x}=\frac{1}{\infty}=0.
$$
