Задача №2092

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