Задача №2108

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