## Problem Statement

Calculate the limit of the function:

$\lim _{x \rightarrow 1} \frac{x^{4}-1}{2 x^{4}-x^{2}-1}$
## Solution

$$
\begin{aligned}
& \lim _{x \rightarrow 1} \frac{x^{4}-1}{2 x^{4}-x^{2}-1}=\left\{\frac{0}{0}\right\}=\lim _{x \rightarrow 1} \frac{(x-1)\left(x^{3}+x^{2}+x+1\right)}{(x-1)\left(2 x^{3}+2 x^{2}+x+1\right)}= \\
& =\lim _{x \rightarrow 1} \frac{x^{3}+x^{2}+x+1}{2 x^{3}+2 x^{2}+x+1}=\frac{1^{3}+1^{2}+1+1}{2 \cdot 1^{3}+2 \cdot 1^{2}+1+1}=\frac{4}{6}=\frac{2}{3}
\end{aligned}
$$

## Problem Kuznetsov Limits 10-23