A) 0
B) 1/2
C) ¼
D) 1
Correct Answer: D
Solution :
[d] \[\underset{x\to 0}{\mathop{\lim }}\,\frac{2(1-\cos \,x)}{{{x}^{2}}}=\underset{x\to 0}{\mathop{\lim }}\,\frac{2.2\,\,{{\sin }^{2}}\frac{x}{2}}{{{x}^{2}}}\] \[=4\,\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin \frac{x}{2}}{\frac{x}{2}\times 2}.\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin \frac{x}{2}}{\frac{x}{2}\times 2}\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin \frac{x}{2}}{\frac{x}{2}}.\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin \frac{x}{2}}{\frac{x}{2}}=1\times 1=1\]
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