Tính lim từ x đến 3 căn bậc hai (x+1)-2/căn bậc hai 3x -3 bằng? A.2/3 B.1/3 C.1/2 D.1

* Hướng dẫn giải

$\begin{array}{l}\underset{x\to 3}{\lim }\frac{\sqrt{x+1}-2}{\sqrt{3x}-3}\\ =\underset{x\to 3}{\lim }\frac{\left(\sqrt{x+1}-2\right)\left(\sqrt{x+1}+2\right)\left(\sqrt{3x}+3\right)}{\left(\sqrt{3x}-3\right)\left(\sqrt{3x}+3\right)\left(\sqrt{x+1}+2\right)}\\ =\underset{x\to 3}{\lim }\frac{(x+1-4)\left(\sqrt{3x}+3\right)}{(3x-9)\left(\sqrt{x+1}+2\right)}\\ =\underset{x\to 3}{\lim }\frac{(x-3)\left(\sqrt{3x}+3\right)}{3(x-3)\left(\sqrt{x+1}+2\right)}\\ =\underset{x\to 3}{\lim }\frac{\sqrt{3x}+3}{3\left(\sqrt{x+1}+2\right)}\\ =\frac{\sqrt{3.3}+3}{3\left(\sqrt{3+1}+2\right)}=\frac{1}{2}\end{array}$