A) 1
B) ?1
C) 0
D) None of these
Correct Answer: D
Solution :
\[\underset{x\to 0}{\mathop{\lim }}\,\,\frac{\sqrt{\tfrac{1}{2}(1-\cos 2x)}}{x}=\underset{x\to 0}{\mathop{\lim }}\,\,\frac{|\,\,\sin x\,\,|}{x}\] So, \[\underset{x\to 0+}{\mathop{\lim }}\,\,\frac{|\,\sin x\,|}{x}=1\] and \[\underset{x\to 0-}{\mathop{\lim }}\,\,\frac{|\,\sin x\,|}{x}=-1\] Hence limit does not exist.
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