Limit Revision

Calculus Level 3

limx0(1sin2x1x2) \displaystyle\lim_{x \rightarrow 0} \left( \dfrac{1}{\sin^2x} - \dfrac{1}{x^2}\right)

If the limit above is equal to ab \dfrac ab, where aa and bb are coprime positive integers, find the value of a+ba+b.

Submit your answer as 0 if you don't think the limit exist.

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