Question

If the function f(x) = $\frac{\sqrt{4+x}-2}{x},x\ne 0$ , is continuous at x = 0, the f(0) =

• A. 1/2
• B. 1/3
• C. 1/4
• D. 1/5

Answer 1

The correct option is C

1/4

$f\left(0\right)=\underset{x\to 0}{lt}\frac{\sqrt{4+x}-2}{x}=\underset{x\to 0}{lt}\frac{1}{\sqrt{4+x}+2}=\frac{1}{4}$