real analysis - Is there a form $lim_{xtoinfty}left[frac{infty}{infty}right] $ of l'Hôpital's rule?

In course of learning L'Hospital rule I've learned both $\displaystyle\lim_{x\to\infty}\left[\dfrac{0}{0}\right]$ and $\displaystyle\lim_{x\to0}\left[\dfrac{\infty}{\infty}\right]$ form. But is there a form $\displaystyle\lim_{x\to\infty}\left[\dfrac{\infty}{\infty}\right]?$

For example can I evaluate $\displaystyle\lim_{x\to\infty}\dfrac{x}{e^x}$ as follows:

$$\displaystyle\lim_{x\to\infty}\dfrac{x}{e^x}=\displaystyle\lim_{x\to\infty}\dfrac{1}{e^x}=0?$$