Question

$\underset{x\to 2}{lim}\frac{\sqrt{x-2}+\sqrt{x}-\sqrt{2}}{\sqrt{x^2-4}}\text{is equal to}$

• A. 1/2
• B. 1
• C. 2
• D. -1

Answer 1

The correct option is A

1/2

$=\underset{x\to 2}{lim}\{\frac{1}{\sqrt{x+2}}+\frac{\sqrt{x}-\sqrt{2}}{\sqrt{x^2-4}}\}\text{Limit}=\frac{1}{2}+\underset{x\to 2}{lim}\frac{x-2}{\sqrt{x}+\sqrt{2}}\frac{1}{\sqrt{(x+2)(x-2)}}=\frac{1}{2}+\underset{x\to 2}{lim}\frac{1}{\sqrt{x}+\sqrt{2}}\sqrt{\frac{x-2}{x+2}}=\frac{1}{2}$