JEE Mains · Maths · STD 11 - 12. limits
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
- A \(\pi\)
- B \(0\)
- C \(\frac{\pi}{4}\)
- D \(\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow 0^{+}} \frac{\cos ^{-1} x}{\left(1-x^{2}\right)} \times \frac{\sin ^{-1} x}{x}=\frac{\pi}{2}\)
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