#13 Measure your Calibre

Calculus Level 4

\[\large \lim_{x \to 0} \frac{\sqrt{\cos x} - \sqrt[3]{\cos x}}{\sin^2x} = \frac{A}{B}\]

The limit above holds true for coprime integers \(A\) and \(B\), where \(A\) is negative and \(B\) is positive. Find \(A+B\).

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Bonus: Evaluate this limit without applying L'Hôpital's rule.


Other problems: Check your Calibre
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