Greatest Limit

Calculus Level 3

\[\lim_{x\rightarrow 0} \left( \left \lfloor \dfrac{100 x}{\sin x}\right \rfloor + \left \lfloor \dfrac{99 \sin x}{x}\right \rfloor \right) = \ ?\]

Notation: \(\lfloor \cdot \rfloor\) denotes the floor function.

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