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The value of $\lim_{x \to 0} \frac{\cos^{-1}(x - [x^2]) \cdot \sin^{-1}(x - [x^2])}{x - x^3}$, where $[x]$ denotes the greatest integer $\leq x$ is:
(1) $\frac{\pi}{2}$
(2) $0$
(3) $\frac{\pi}{4}$
(4) $\frac{\pi}{2}$
$\lim_{x \to 0} \frac{\cos^{-1}(x - [x^2])}{(1-[x^2])} \times \frac{\sin^{-1}(x-[x^2])}{x} = \frac{\pi}{2} \cdot 1 = \frac{\pi}{2}$.
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