Mathematics - Statistics Question with Solution | TestHub

$\begin{array}{rl}& \underset{x\to 0}{\lim }\frac{\sqrt{1+x^2}-\sqrt{1-x^2}}{x^2}\cdot \frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}+\sqrt{1-x^2}}\\ \Rightarrow & \underset{x\to 0}{\lim }\frac{1+x^2-1+x^2}{x^2\left(\sqrt{1+x^2}+\sqrt{1-x^2}\right)}\\ \Rightarrow & \underset{x\to 0}{\lim }\frac{2x^2}{x^2\left(\sqrt{1+x^2}+\sqrt{1-x^2}\right)}=\frac{2}{\sqrt{1}+\sqrt{1}}=\frac{2}{2}=1\end{array}$