Question

Solve
$\underset{x\to 0}{lim}\frac{\sqrt{1+x}-1}{x}$.

Answer 1

Let $L=\underset{x\to 0}{lim}\frac{\sqrt{x+1}-1}{x}$

Using $L^{\prime }$ Hospital Rule, we get

$L=\underset{x\to 0}{lim}\frac{1}{2\sqrt{1+x}}=\frac{1}{2}$