Question

lim x > 0 (√(1+x^2)-1)/x^2

Answer 1

$limlimits _{x to 0} frac{sqrt{1+x^2}-1}{x^2} = limlimits _{x to 0} frac{(sqrt{1+x^2}-1)(sqrt{1+x^2}+1)}{x^2(sqrt{1+x^2}+1)} = limlimits _{x to 0} frac{1+x^2-1}{x^2(sqrt{1+x^2}+1)} =\\= limlimits _{x to 0} frac{1}{sqrt{1+x^2}+1} = frac{1}{sqrt1+1} = frac{1}{2}$