116. Find $\lim _{x \rightarrow \infty} \frac{3}{x+5}$.
Solution. When $x \rightarrow \infty$, the denominator $x+5$ also tends to infinity, and its reciprocal $\frac{1}{x+5} \rightarrow 0$. Therefore, the product $\frac{1}{x+5} \cdot 3=\frac{3}{x+5}$ tends to zero if $x \rightarrow \infty$. Thus, $\lim _{x \rightarrow \infty} \frac{3}{x+5}=0$.

Identical transformations under the limit sign are applicable not only when the argument tends to a finite limit, but also when $x \rightarrow \infty$.