Задача №2091

\[ \lim_{n\to\infty}\frac{(3-n)^4-(2-n)^4}{(1-n)^4-(1+n)^4} =\lim_{n\to\infty}\frac{81-108n+54n^2-12n^3+n^4-\left(16-31n+24n^2-8n^3+n^4\right)}{1-4n+6n^2-4n^3+n^4-\left(1+4n+6n^2+4n^3+n^4\right)}=\\ =\lim_{n\to\infty}\frac{65-76n+30n^2-4n^3}{-8n-8n^3} =\left[\frac{\infty}{\infty}\right] =\lim_{n\to\infty}\frac{\frac{65}{n^3}-\frac{76}{n^2}+\frac{30}{n}-4}{-\frac{8}{n^2}-8} =\frac{-4}{-8}=\frac{1}{2} \]