A) ?1
B) 1
C) 2
D) ?2
Correct Answer: B
Solution :
Apply L-Hospital?s rule, \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sqrt{1+\sin x}-\sqrt{1-\sin x}}{x}\] \[=\underset{x\to 0}{\mathop{\lim }}\,\,\,\frac{\cos x}{2\sqrt{1+\sin x}}+\frac{\cos x}{2\sqrt{1-\sin x}}=\frac{1}{2}+\frac{1}{2}=1.\]
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