Задача №2106

\[ \lim_{n\to\infty}\frac{(2n-3)^3-(n+5)^3}{(3n-1)^3+(2n+3)^3} =\lim_{n\to\infty}\frac{\frac{(2n-3)^3}{n^3}-\frac{(n+5)^3}{n^3}}{\frac{(3n-1)^3}{n^3}+\frac{(2n+3)^3}{n^3}} =\lim_{n\to\infty}\frac{\left(2-\frac{3}{n}\right)^3-\left(1+\frac{5}{n}\right)^3}{\left(3-\frac{1}{n}\right)^3+\left(2+\frac{3}{n}\right)^3} =\frac{7}{35} =\frac{1}{5}. \]