#13 Measure your Calibre

Calculus Level 4

limx0cosxcosx3sin2x=AB\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 AA and BB, where AA is negative and BB is positive. Find A+BA+B.

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

Other problems: Check your Calibre

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