# 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.