Giải thích các bước giải:
$\lim _{x\to 1}\dfrac{x^3-\sqrt{3x-2}}{x-1}$
$=\lim _{x\to 1}\dfrac{x^3-1-(\sqrt{3x-2}-1)}{x-1}$
$=\lim _{x\to 1}\dfrac{(x-1)(x^2+x+1)-\dfrac{3(x-1)}{\sqrt{3x-2}+1}}{x-1}$
$=\lim _{x\to 1} (x^2+x+1)-\dfrac{3}{\sqrt{3x-2}+1}$
$= (1^2+1+1)-\dfrac{3}{\sqrt{3.1-2}+1}$
$= \dfrac{3}{2}$