A) \[\frac{\pi }{2}\]
B) 1
C) \[-\pi \]
D) \[\pi \]
Correct Answer: D
Solution :
\[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin (\pi co{{s}^{2}}x)}{{{x}^{2}}}=\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin \left\{ \pi -\pi {{\sin }^{2}}x \right\}}{{{x}^{2}}}\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin \left( \pi co{{s}^{2}}x \right)}{\pi \,{{\sin }^{2}}x}\cdot \frac{\pi {{\sin }^{2}}x}{{{x}^{2}}}=\pi \]
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