Question

〖lim〗┬(x→0) (√(1+x)-1)/x

Answer 1

$\lim_{x \to 0} \frac{\sqrt{1+x} -1}{x} = \lim_{x \to 0} \frac{\sqrt{1+x} -1}{(1+x)-1} = \\\\ =\lim_{x \to 0} \frac{\sqrt{1+x} -1}{(\sqrt{1+x} -1)(\sqrt{1+x} +1)} =\lim_{x \to 0} \frac{1}{\sqrt{1+x} +1}=\frac{1}{2}$