A) \[1\]
B) \[\frac{1}{16}\]
C) \[16\]
D) None of these
Correct Answer: B
Solution :
\[\underset{x\to \pi /2}{\mathop{\lim }}\,\frac{\cot \,x-\,\cos \,x}{{{(\pi -2x)}^{3}}}\] \[=\underset{h\to 0}{\mathop{\lim }}\,\frac{-\tan \,h+\sin \,h}{{{(-2h)}^{3}}}\] \[=\underset{h\to 0}{\mathop{\lim }}\,\frac{\sin \,h(1-\cos \,h)}{\cos \,h\times 8{{h}^{3}}}\] \[=\frac{1}{8}\underset{h\to 0}{\mathop{\lim }}\,\frac{\sin \,h}{h}\times \frac{2\,{{\sin }^{2}}\,h/2}{4{{(h/2)}^{2}}}\times \frac{1}{\cos \,h}\] \[=\frac{1}{16}\]
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