## Task Condition

Calculate the limit of the numerical sequence:

$$
\lim _{n \rightarrow \infty} \frac{(3-n)^{2}+(3+n)^{2}}{(3-n)^{2}-(3+n)^{2}}
$$
## Solution

$$
\begin{aligned}
& \lim _{n \rightarrow \infty} \frac{(3-n)^{2}+(3+n)^{2}}{(3-n)^{2}-(3+n)^{2}}=\lim _{n \rightarrow \infty} \frac{9-6 n+n^{2}+9+6 n+n^{2}}{9-6 n+n^{2}-\left(9+6 n+n^{2}\right)}= \\
& =\lim _{n \rightarrow \infty} \frac{2\left(9+n^{2}\right)}{9-6 n+n^{2}-9-6 n-n^{2}}=\lim _{n \rightarrow \infty} \frac{2\left(9+n^{2}\right)}{-12 n}= \\
& =-\frac{2}{12} \lim _{n \rightarrow \infty}\left(\frac{9}{n}+n\right)=-\infty
\end{aligned}
$$

## Problem Kuznetsov Limits 3-1