## Problem Statement

Calculate the limit of the function:

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

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

## Problem Kuznetsov Limits 10-4