Question

$\underset{x\to 0}{lim}\frac{\sqrt{1+x}-1}{x}$ is equal to

• A. $\frac{1}{2}$
• B. $2$
• C. $0$
• D. $1$

Answer 1

The correct option is A $\frac{1}{2}$

We have,
$\underset{x\to 0}{lim}\frac{\sqrt{1+x}-1}{x}$
$=\underset{x\to 0}{lim}\frac{(\sqrt{1+x}-1)(\sqrt{1+x}+1)}{x(\sqrt{1+x}+1)}$
$=\underset{x\to 0}{lim}\frac{x}{x(\sqrt{1+x}+1)}$
$=\underset{x\to 0}{lim}\frac{1}{\sqrt{1+x}+1}=\frac{1}{2}$