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Evaluate the limit as x approaches π/2: (cot x - cos x) / (π - 2x)³.

1. 1/4
2. 1/24
3. 1/16
4. 1/8

Correct answer: 1/16

Solution

The limit evaluates to 1/16 because as x approaches π/2, both the numerator and denominator approach 0, allowing us to apply L'Hôpital's Rule. After differentiating the numerator and denominator appropriately, the limit simplifies to 1/16.

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