Giải thích các bước giải:
$\lim (1+n^2-\sqrt{n^4+3n+1})$
$=\lim \dfrac{(1+n^2)^2-(n^4+3n+1)}{1+n^2+\sqrt{n^4+3n+1}}$
$=\lim \dfrac{2n^2-3n}{1+n^2+\sqrt{n^4+3n+1}}$
$=\lim \dfrac{2-\dfrac{3}{n}}{\dfrac{1}{n^2}+1+\sqrt{1+\dfrac{3}{n^3}+\dfrac{1}{n^4}}}$
$= \dfrac{2-0}{0+1+\sqrt{1+0+0}}$
$=1$