Giải thích các bước giải:
$f.\lim_{x\to -\infty}(\sqrt[3]{3x^3-1}+\sqrt{x^2+2})$
$=\lim_{x\to -\infty}x.(\sqrt[3]{3-\dfrac{1}{x^3}}\pm\sqrt{1+\dfrac{2}{x^2}})$
$=\lim_{x\to -\infty}x.(\sqrt[3]{3-0}\pm\sqrt{1+0})$
$=-\infty$
$g.\lim_{x\to 1}(\dfrac{1}{1-x}-\dfrac{3}{1-x^3})$
$=\lim_{x\to 1}(\dfrac{1}{1-x}-\dfrac{3}{(1-x)(1+x+x^2)})$
$=\lim_{x\to 1}.\dfrac{1}{1-x}(1-\dfrac{3}{1+x+x^2})$
$=\infty.(1-\dfrac{3}{1+1+1^2})$
$=\infty$