Задача №2099

\[ \lim_{n\to\infty}\frac{(n+1)^2+(n-1)^2-(n+2)^3}{(4-n)^3} =\lim_{n\to\infty}\frac{\frac{(n+1)^2}{n^3}+\frac{(n-1)^2}{n^3}-\frac{(n+2)^3}{n^3}}{\frac{(4-n)^3}{n^3}}=\\ =\lim_{n\to\infty}\frac{\frac{1}{n}\cdot\left(1+\frac{1}{n}\right)^2+\frac{1}{n}\cdot\left(1-\frac{1}{n}\right)^2-\left(1+\frac{2}{n}\right)^3}{\left(\frac{4}{n}-1\right)^3} =\frac{-1}{-1} =1 \]