Question

Tính:

\(a.\lim\limits_{x\rightarrow-1}\dfrac{\sqrt{3x^2+2}-x}{x-1}\)

\(b.\lim\limits_{x\rightarrow-2}\dfrac{\sqrt[]{3x^2+1}-x}{x-2}\)

Answer 1

\(\lim\limits_{x\rightarrow-1}\dfrac{\sqrt{3x^2+2}-x}{x-1}=\dfrac{\sqrt{3.\left(-1\right)^2+2}-\left(-1\right)}{-1-1}=-3\)

\(\lim\limits_{x\rightarrow-2}\dfrac{\sqrt{3x^2+1}-x}{x-2}=\dfrac{\sqrt{3.\left(-1\right)^2+1}-\left(-2\right)}{-2-2}=-\dfrac{2+\sqrt{13}}{4}\)