## Problem Statement

Calculate the limit of the function:

$\lim _{x \rightarrow 1} \frac{2 x^{2}-x-1}{x^{3}+2 x^{2}-x-2}$
## Solution

$$
\begin{aligned}
& \lim _{x \rightarrow 1} \frac{2 x^{2}-x-1}{x^{3}+2 x^{2}-x-2}=\left\{\frac{0}{0}\right\}=\lim _{x \rightarrow 1} \frac{(x-1)(2 x+1)}{(x-1)\left(x^{2}+3 x+2\right)}= \\
& =\lim _{x \rightarrow 1} \frac{2 x+1}{x^{2}+3 x+2}=\frac{2 \cdot 1+1}{1^{2}+3 \cdot 1+2}=\frac{3}{6}=\frac{1}{2}
\end{aligned}
$$

## Problem Kuznetsov Limits 10-25