$a)\lim\frac{5+2n-3n^3}{n^3+n^2}$
$=\lim\frac{\frac{5}{n^3}+\frac{2}{n^2}-3}{1+\frac{1}{n}}$
$=\frac{0+0-3}{1+0}$
$=-3$
$b)\lim\frac{2n^3-5n+4}{n^2+3}$
$=\lim\frac{2-\frac{5}{n^2}+\frac{4}{n^3}}{\frac{1}{n}+\frac{3}{n^3}}$
$=\frac{2-0+0}{0+0}$
$=+\infty$$\text{(Vì 2>0)}$
$c)\lim\frac{3n\sqrt{n}+2}{n^2+2n+1}$
$=\lim\frac{\frac{3\sqrt{n}}{n}+\frac{2}{n^2}}{1+\frac{2}{n}+\frac{1}{n^2}}$
$=\lim\frac{\frac{3}{\sqrt{n}}+\frac{2}{n^2}}{1+\frac{2}{n}+\frac{1}{n^2}}$
$=\frac{0+0}{1+0+0}$
$=0$
$d)\lim\frac{\sqrt{4n^2+2n-1}-\sqrt{n^2-2}}{3n+3}$
$=\lim\frac{4n^2+2n-1-(n^2-2)}{(3n+3)(\sqrt{4n^2+2n-1}+\sqrt{n^2-2})}$
$=\lim\frac{3n^2+2n+1}{(3n+3)\Big[n\Big(\sqrt{4+\frac{2}{n}-\frac{1}{n^2}}+\sqrt{1-\frac{2}{n^2}}\Big)\Big]}$
$=\lim\frac{3n^2+2n+1}{(3n+3).3n}$
$=\lim\frac{3n^2+2n+1}{9n^2+9n}$
$=\lim\frac{3+\frac{2}{n}+\frac{1}{n^2}}{9+\frac{9}{n}}$
$=\frac{3+0+0}{9+0}$
$=\frac{1}{3}$
