## Task Condition

Calculate the limit of the numerical sequence:

$$
(6-n)^{2}-(6+n)^{2}
$$
## Solution

$$
\begin{aligned}
& \lim _{n \rightarrow \infty} \frac{(6-n)^{2}-(6+n)^{2}}{(6+n)^{2}-(1-n)^{2}}=\lim _{n \rightarrow \infty} \frac{36-12 n+n^{2}-36-12 n-n^{2}}{36+12 n+n^{2}-1+2 n-n^{2}}= \\
& =\lim _{n \rightarrow \infty} \frac{-24 n}{35+14 n}=\lim _{n \rightarrow \infty} \frac{-24}{\frac{35}{n}+14}=\frac{-24}{0+14}=-\frac{12}{7}=-1 \frac{5}{7}
\end{aligned}
$$

## Problem Kuznetsov Limits 3-5

This problem may have a different condition (possibly due to different editions or errors). See below for more details.