Задача №2116

\[ \lim_{n\to\infty}\frac{(n+2)^3+(n-2)^3}{n^4+2n^2-1} =\left[\frac{\infty}{\infty}\right] =\lim_{n\to\infty}\frac{\frac{(n+2)^3+(n-2)^3}{n^4}}{\frac{n^4+2n^2-1}{n^4}} =\lim_{n\to\infty}\frac{\frac{1}{n}\cdot\left(1+\frac{2}{n}\right)^3+\frac{1}{n}\cdot\left(1-\frac{2}{n}\right)^3}{1+\frac{2}{n^2}-\frac{1}{n^4}} =\frac{0}{1} =0 \]