Задача №1080

\[ \lim_{x\to\infty}\left(\frac{3x^2}{2x+1}-\frac{(2x-1)\left(3x^2+x+2\right)}{4x^2}\right) =\lim_{x\to\infty}\frac{-4x^3-5x^2+x+2}{4x^2\cdot(2x+1)} =\left[\frac{\infty}{\infty}\right]=\\ =\lim_{x\to\infty}\frac{\frac{-4x^3-5x^2+x+2}{x^3}}{\frac{4x^2\cdot(2x+1)}{x^3}} =\lim_{x\to\infty}\frac{-4-\frac{5}{x}+\frac{1}{x^2}+\frac{2}{x^3}}{4\cdot(2+\frac{1}{x})} =-\frac{1}{2}. \]