6.53. $\lim _{x \rightarrow \infty} \frac{x}{e^{x}}$.
Solution.

$$
\lim _{x \rightarrow \infty} \frac{x}{e^{x}}=(\infty / \infty)=\lim _{x \rightarrow \infty} \frac{(x)^{\prime}}{\left(e^{x}\right)^{\prime}}=\lim _{x \rightarrow \infty} \frac{1}{e^{x}}=0
$$

## INDETERMINACY OF THE FORM «0 $\cdot$