Let's do some calculus! (13)

Calculus Level 3

\[f(x) = \begin{cases} \dfrac{\sin \left \lfloor x \right \rfloor}{\left \lfloor x \right \rfloor}, & \text{for} & \left \lfloor x \right \rfloor \neq 0 \\ \\ 0, & \text{for} & \left \lfloor x \right \rfloor = 0 \end{cases}\]

If \(f(x)\) is as defined above, find \(\displaystyle \lim_{x \to 0^{-}}{f(x)}\).

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


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