find the limit of $\mathop {\lim }\limits_{x \to 0 } \frac{a}{x}\left[ {\frac{x}{b}} \right]$ $$a,b \gt 0$$
$$\mathop {\lim }\limits_{x \to 0 } \frac{a}{x}\left[ {\frac{x}{b}} \right]$$
So, I know that if x is $x \in \mathbb{Z}$ then the limit is $a\over [b]$
I couldn't figure out the solution for $x \notin \mathbb{Z}$
By the way, $[x]$ notation is equal to floor(x).  
I'll be glad for a direction here

Hint
Assume that $b>0$, prove that
$$\mathop {\lim }\limits_{x \to 0^+ } \frac{a}{x}\left[ {\frac{x}{b}} \right]=0$$
and 
$$\mathop {\lim }\limits_{x \to 0^{-} } \frac{a}{x}\left[ {\frac{x}{b}} \right]=\infty$$
