Y`=6+3x²>0
при любом х, значит функция монотонно возрастает на (-∞;+∞) и не имеет экстремумов.
При х=0 у=0- единственная точка пересечения с осями координат
2x²+3x-5=2x²-2x+5x-5=2x(x-1)+5(x-1)=(2x+5)(x-1)
№3
х - в 1 ведре
х+3 - во 2-м ведре
х-4 - в 3-м ведре
Х + (Х+3) + (Х-4) = Х+Х+3+Х-4 = 3Х-1 - всего в трех ведрах
В решении расписывать не буду
![\lim_{n \to +\infty} \frac{1}{n}=0](https://tex.z-dn.net/?f=%5Clim_%7Bn+%5Cto+%2B%5Cinfty%7D+%5Cfrac%7B1%7D%7Bn%7D%3D0)
;
![\lim_{n \to +\infty} \frac{2}{n}=0](https://tex.z-dn.net/?f=%5Clim_%7Bn+%5Cto+%2B%5Cinfty%7D+%5Cfrac%7B2%7D%7Bn%7D%3D0)
; и т.д.
![\lim_{n \to +\infty} \frac{1}{n^2}=0](https://tex.z-dn.net/?f=%5Clim_%7Bn+%5Cto+%2B%5Cinfty%7D+%5Cfrac%7B1%7D%7Bn%5E2%7D%3D0)
;
![\lim_{n \to +\infty} \frac{2}{n^2}=0](https://tex.z-dn.net/?f=%5Clim_%7Bn+%5Cto+%2B%5Cinfty%7D+%5Cfrac%7B2%7D%7Bn%5E2%7D%3D0)
и т.д.
а)
![\lim_{n \to +\infty} \frac{2n+5}{n}= \lim_{n \to +\infty} \frac{ \frac{2n+5}{n} }{ \frac{n}{n}} = \lim_{n \to +\infty} \frac{ \frac{2n}{n}+\frac{5}{n} }{ \frac{n}{n}}](https://tex.z-dn.net/?f=+%5Clim_%7Bn+%5Cto+%2B%5Cinfty%7D++%5Cfrac%7B2n%2B5%7D%7Bn%7D%3D+%5Clim_%7Bn+%5Cto+%2B%5Cinfty%7D++%5Cfrac%7B+%5Cfrac%7B2n%2B5%7D%7Bn%7D+%7D%7B+%5Cfrac%7Bn%7D%7Bn%7D%7D+%3D+%5Clim_%7Bn+%5Cto+%2B%5Cinfty%7D++%5Cfrac%7B++%5Cfrac%7B2n%7D%7Bn%7D%2B%5Cfrac%7B5%7D%7Bn%7D+%7D%7B+%5Cfrac%7Bn%7D%7Bn%7D%7D)
=
![\lim_{n \to +\infty} \frac{ 2+\frac{5}{n} }{1}=2](https://tex.z-dn.net/?f=%5Clim_%7Bn+%5Cto+%2B%5Cinfty%7D+%5Cfrac%7B+2%2B%5Cfrac%7B5%7D%7Bn%7D+%7D%7B1%7D%3D2)
б)
![\lim_{n \to +\infty} \frac{2n^3+n-1}{n^2+4n+2}=\lim_{n \to +\infty} \frac{ \frac{2n^3+n-1}{n^3} }{ \frac{n^2+4n+2}{n^3}}](https://tex.z-dn.net/?f=%5Clim_%7Bn+%5Cto+%2B%5Cinfty%7D+%5Cfrac%7B2n%5E3%2Bn-1%7D%7Bn%5E2%2B4n%2B2%7D%3D%5Clim_%7Bn+%5Cto+%2B%5Cinfty%7D+%5Cfrac%7B+%5Cfrac%7B2n%5E3%2Bn-1%7D%7Bn%5E3%7D+%7D%7B+%5Cfrac%7Bn%5E2%2B4n%2B2%7D%7Bn%5E3%7D%7D++)
=
![\lim_{n \to +\infty} \frac{ \frac{2n^3}{n^3}+ \frac{n}{n^3}- \frac{1}{n^3} }{ \frac{n^2}{n^3}+ \frac{4n}{n^3}+\frac{2}{n^3} }=\lim_{n \to +\infty} \frac{2+ \frac{1}{n^2}- \frac{1}{n^3} }{ \frac{1}{n}+ \frac{4}{n^2}+\frac{2}{n^3} }](https://tex.z-dn.net/?f=%5Clim_%7Bn+%5Cto+%2B%5Cinfty%7D+%5Cfrac%7B+%5Cfrac%7B2n%5E3%7D%7Bn%5E3%7D%2B+%5Cfrac%7Bn%7D%7Bn%5E3%7D-+%5Cfrac%7B1%7D%7Bn%5E3%7D+%7D%7B++%5Cfrac%7Bn%5E2%7D%7Bn%5E3%7D%2B+%5Cfrac%7B4n%7D%7Bn%5E3%7D%2B%5Cfrac%7B2%7D%7Bn%5E3%7D+%7D%3D%5Clim_%7Bn+%5Cto+%2B%5Cinfty%7D+%5Cfrac%7B2%2B+%5Cfrac%7B1%7D%7Bn%5E2%7D-+%5Cfrac%7B1%7D%7Bn%5E3%7D+%7D%7B++%5Cfrac%7B1%7D%7Bn%7D%2B+%5Cfrac%7B4%7D%7Bn%5E2%7D%2B%5Cfrac%7B2%7D%7Bn%5E3%7D+%7D++)
=
![\lim_{n \to +\infty}\frac{2+\frac{1}{n^2}-\frac{1}{n^3} }{\frac{1}{n}+\frac{4}{n^2}+\frac{2}{n^3} }=+\infty](https://tex.z-dn.net/?f=%5Clim_%7Bn+%5Cto+%2B%5Cinfty%7D%5Cfrac%7B2%2B%5Cfrac%7B1%7D%7Bn%5E2%7D-%5Cfrac%7B1%7D%7Bn%5E3%7D+%7D%7B%5Cfrac%7B1%7D%7Bn%7D%2B%5Cfrac%7B4%7D%7Bn%5E2%7D%2B%5Cfrac%7B2%7D%7Bn%5E3%7D+%7D%3D%2B%5Cinfty++++)