1)
$\,\,\,\,\lim \dfrac{3{{n}^{2}}+1}{{{n}^{2}}-2}$
$=\lim \dfrac{3+\dfrac{1}{{{n}^{2}}}}{1-\dfrac{2}{{{n}^{2}}}}$
$=\dfrac{3}{1}$
$=3$
2)
$\lim \dfrac{8{{n}^{2}}+3n-1}{4+5n+2{{n}^{2}}}$
$=\lim \dfrac{8{{n}^{2}}+3n-1}{2{{n}^{2}}+5n+4}$
$=\lim \dfrac{8+\frac{3}{n}-\dfrac{1}{{{n}^{2}}}}{2+\dfrac{5}{n}+\dfrac{4}{{{n}^{2}}}}$
$=\dfrac{8}{2}$
$=4$