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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{x \rightarrow 0} \frac{\sqrt{3+\cos x}-2}{\sin ^2 x}=$
  • A
    $\frac{1}{8}$
  • B
    $\frac{1}{4}$
  • C
    $-\frac{1}{4}$
  • ✓
    $-\frac{1}{8}$
✓

Answer

Correct option: D.
$-\frac{1}{8}$
(D)
$\lim _{x \rightarrow 0} \frac{\sqrt{3+\cos x}-2}{\sin ^2 x}$
$=\lim _{x \rightarrow 0} \frac{(3+\cos x)-4}{\sin ^2 x(\sqrt{3+\cos x}+2)}$
$=\lim _{x \rightarrow 0} \frac{-(1-\cos x)}{(1-\cos x)(1+\cos x)(\sqrt{3+\cos x}+2)}=-\frac{1}{8}$

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