6.52. $\lim _{x \rightarrow+\infty} \frac{\ln x}{x}$.
Solution.

$$
\lim _{x \rightarrow+\infty} \frac{\ln x}{x}=(\infty / \infty)=\lim _{x \rightarrow+\infty} \frac{(\ln x)^{\prime}}{(x)^{\prime}}=\lim _{x \rightarrow+\infty} \frac{1 / x}{1}=\lim _{x \rightarrow+\infty} \frac{1}{x}=0
$$