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STD 11 - 12. limits — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 12. limits1 Mark
MCQ
$\mathop {Limit}\limits_{x \to \frac{\pi }{2}} \,\frac{{\sin x}}{{{{\cos }^{ - 1}}\left[ {\frac{1}{4}\,(3\sin x\, - \,\sin 3x)} \right]}}\,$ where [ ] denotes greatest integer function , is
  • ✓
    $\frac{2}{\pi }\,$
  • B
    $1$
  • C
    $\frac{4}{\pi }\,$
  • D
    does not exist
✓

Answer

Correct option: A.
$\frac{2}{\pi }\,$
a
$\mathop {Limit}\limits_{x \to \frac{\pi }{2}} \,\frac{{\sin x}}{{{{\cos }^{ - 1}}[{{\sin }^3}x]}}\,$

at  $x \to \pi /2 , [sin^3x] \to 0$ and $sinx \to 1$
$\therefore \,\,l =$ $\frac{2}{\pi }\,$

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