Let's do some calculus! (13)

Calculus Level 3

f(x)={sinxx,forx00,forx=0f(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)f(x) is as defined above, find limx0f(x)\displaystyle \lim_{x \to 0^{-}}{f(x)}.

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


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