Limit Revision

Calculus Level 3

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

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

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

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