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