Question

Lim x > 0 (√(1+x^2)-1)/x^2

Answer 1

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