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Evaluate the limit as x approaches 0: (sin(π cos² x))/(x²).

1. -π
2. π
3. π/2
4. 1

Correct answer: π

Solution

As x approaches 0, Bcos² x approaches 1, making Bsin(Bpi Bcos² x) approach Bsin(Bpi). Using L'Hôpital's rule or the small angle approximation, the limit simplifies to Bpi, confirming that the correct answer is Bpi.

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