Answer
$$\lim _{x \rightarrow \infty} \frac{e^{x}}{x^{2}}=\infty$$
Work Step by Step
Given $$\lim _{x \rightarrow \infty} \frac{e^{x}}{x^{2}}$$
using the Limit Rules and replacement, leads to the indeterminate form $$\lim _{x \rightarrow \infty} \frac{e^{x}}{x^{2}}=\frac{\infty}{\infty}$$
Applying L'Hôpital's Rule
\begin{align*}
\lim _{x \rightarrow \infty} \frac{e^{x}}{x^{2}}&=\lim _{x \rightarrow \infty} \frac{e^{x}}{2x }\\
&=\frac{\infty}{\infty}
\end{align*}
Applying L'Hôpital's Rule again
\begin{align*}
\lim _{x \rightarrow \infty} \frac{e^{x}}{2x }&=\lim _{x \rightarrow \infty} \frac{e^{x}}{2 }\\
&= \infty
\end{align*}
