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lim x→0 (sin(π cos² x) / x²) is equal to

1. π
2. π/2
3. 1
4. −π

Correct answer: π

Solution

As x approaches 0, cos²(x) approaches 1, making sin(π cos²(x)) approach sin(π), which is 0. Applying L'Hôpital's rule to the limit of the form 0/0, we differentiate the numerator and denominator, ultimately leading to the limit equating to π.

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