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lim_(x→1⁻) (√π − √(2 sin⁻¹ x)) / √(1−x) is equal to:

1. √(2/π)
2. 1/√(2π)
3. √(π/2)
4. √π

Correct answer: √(2/π)

Solution

As x approaches 1 from the left, the expression inside the limit simplifies, and applying L'Hôpital's rule helps resolve the indeterminate form. The limit evaluates to √(2/π) by analyzing the behavior of the numerator and denominator near the point.

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