A) \[2\sqrt{2}\]
B) \[4\sqrt{2}\]
C) \[\sqrt{2}\]
D) 4
Correct Answer: B
Solution :
\[\underset{x\to 0}{\mathop{\lim }}\,\frac{\left( \frac{{{\sin }^{2}}x}{{{x}^{2}}} \right)\left( \sqrt{2}+\sqrt{1+\cos x} \right)}{\left( \frac{1-\cos x}{{{x}^{2}}} \right)}\] \[=\frac{{{(1)}^{2}}.\left( 2\sqrt{2} \right)}{\frac{1}{2}}=4\sqrt{2}\]
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