$I=\lim\dfrac{1}{\sqrt{n^2+2}-\sqrt{n^2+4}}$
$=\lim\dfrac{ \sqrt{n^2+2}+\sqrt{n^2+4} }{n^2+2-n^2-4}$
$=\lim\dfrac{ \sqrt{n^2+2}+\sqrt{n^2+4} }{-2}$
$=\lim n.\dfrac{ \sqrt{1+\dfrac{2}{n^2}}+\sqrt{1+\dfrac{4}{n^2} }}{-2}$
Ta có:
$\lim n=+\infty$
$\lim\dfrac{ \sqrt{1+\dfrac{2}{n^2}}+\sqrt{1+\dfrac{4}{n^2}} }{-2}=\dfrac{1+1}{-2}=-1<0$
$\to I=-\infty$