Question

[Nguyễn Trọng Hiếu]

Tìm giới hạn sau :

\(\lim\limits_{x\rightarrow2}\frac{x-\sqrt{3x-2}}{x^2-4}\)

Answer 1

[Nguyễn Thái Bình]

\(L=\lim\limits_{x\rightarrow2}\frac{x-\sqrt{3x-2}}{x^2-4}\)

   \(=\lim\limits_{x\rightarrow2}\frac{x^2-3x+2}{\left(x-4\right)\left(x+\sqrt{3x-2}\right)}=\lim\limits_{x\rightarrow2}\frac{\left(x-2\right)\left(x-1\right)}{\left(x-2\right)\left(x+2\right)\left(x+\sqrt{3x-2}\right)}\)

   \(=\lim\limits_{x\rightarrow2}\frac{x-1}{\left(x+2\right)\left(x+\sqrt{3x-2}\right)}=\frac{1}{16}\)