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Evaluate the limit as x approaches 0 of (√(1-cos(x²)))/(1-cos x).

1. (1)/(2)
2. 2
3. √(2)
4. None of these

Correct answer: √(2)

Solution

The limit evaluates to sqrt{2} because as x approaches 0, both the numerator and denominator approach 0, allowing us to apply L'Hôpital's rule or use trigonometric identities to simplify the expression, ultimately leading to the result of sqrt{2}.

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