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

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 12. limits1 Mark
MCQ
$\mathop {\lim }\limits_{x \to 0} \frac{{\sqrt {1 + \sin x} - \sqrt {1 - \sin x} }}{x} = $
  • A
    $-1$
  • ✓
    $1$
  • C
    $2$
  • D
    $-2$
✓

Answer

Correct option: B.
$1$
b
(b) $\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}+\sqrt{1-\sin x}}$

Apply $L-$ Hospital‘s rule, 

$\mathop {\lim }\limits_{x \to 0} \frac{{\sqrt {1 + \sin x} - \sqrt {1 - \sin x} }}{x}$

$ = \mathop {\lim }\limits_{x \to 0} \,\,\frac{{\cos x}}{{2\sqrt {1 + \sin x} }} + \frac{{\cos x}}{{2\sqrt {1 - \sin x} }} = \frac{1}{2} + \frac{1}{2} = 1.$

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