Answer
$\infty $
Work Step by Step
\begin{align*}
\lim _{x \rightarrow \infty} \frac{x^{-1}+x^{-4}}{x^{-2}-x^{-3}} \cdot \frac{x^{2}}{x^{2}}&=\lim _{x \rightarrow \infty} \frac{x+x^{-2}}{1-x^{-1}}\\
&= \frac{\lim _{x \rightarrow \infty}x+\lim _{x \rightarrow \infty}x^{-2}}{\lim _{x \rightarrow \infty}(1)-\lim _{x \rightarrow \infty}x^{-1}}\\
&=\frac{\infty+0}{1-0}\\
&=\infty
\end{align*}