$\lim (2n^3-3n+7)$
$=\lim n^3\Big(2-\dfrac{3}{n^2}+\dfrac{7}{n^3}\Big)$
$=+\infty$
$\lim(\sqrt{n^4-4n^2+6}-n^2)$
$=\lim\dfrac{-4n^2+6}{\sqrt{n^4-4n^2+6}+n^2}$
$=\lim\dfrac{-4+\dfrac{6}{n^2}}{\sqrt{1-\dfrac{4}{n^2}+\dfrac{6}{n^4}}+1}$
$=\dfrac{-4}{2}=-2$