Question

〖lim〗┬(x→0) (√(1+x)-1)/x

Answer 1

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