Question:
The value of $\lim _{x \rightarrow 0^{+}} \frac{\cos ^{-1}\left(x-[x]^{2}\right) \cdot \sin ^{-1}\left(x-[x]^{2}\right)}{x-x^{3}}$, where $[x]$ denotes the greatest integer $\leq x$ is :
Correct Option: , 4
Solution:
$\left.\lim _{x \rightarrow 0^{+}} \frac{\cos ^{-1} x}{\left(1-x^{2}\right)} \times \frac{\sin ^{-1} x}{x}=\frac{\pi}{2}\right\}$