## Problem Statement

Calculate the limit of the function:

$$
\lim _{x \rightarrow-2} \frac{x^{3}+5 x^{2}+8 x+4}{x^{3}+3 x^{2}-4}
$$
## Solution

$$
\begin{aligned}
& \lim _{x \rightarrow-2} \frac{x^{3}+5 x^{2}+8 x+4}{x^{3}+3 x^{2}-4}=\left\{\frac{0}{0}\right\}=\lim _{x \rightarrow-2} \frac{(x+2)\left(x^{2}+3 x+2\right)}{(x+2)\left(x^{2}+x-2\right)}= \\
& =\lim _{x \rightarrow-2} \frac{x^{2}+3 x+2}{x^{2}+x-2}=\left\{\frac{0}{0}\right\}=\lim _{x \rightarrow-2} \frac{(x+2)(x+1)}{(x+2)(x-1)}= \\
& =\lim _{x \rightarrow-2} \frac{x+1}{x-1}=\frac{-2+1}{-2-1}=\frac{-1}{-3}=\frac{1}{3}
\end{aligned}
$$

## Problem Kuznetsov Limits 10-15