## Problem Statement

Calculate the limit of the function:

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

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

## Problem Kuznetsov Limits 10-22