MCQ
$\mathop {\lim }\limits_{x \to 0} \frac{{\sqrt {1 + \sin x} - \sqrt {1 - \sin x} }}{x} = $
- A$-1$
- ✓$1$
- C$2$
- D$-2$
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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