calculus - Find $lim_{xrightarrow0}frac{x}{[x]}$

Find $\lim_{x\rightarrow0}\frac{x}{[x]}$

$[x]$ represent greatest integer less than or equal to x.

Right hand limit is not defined as [0+]=0, left hand limit is zero as [0-]=-1.
I want to know whether we can say limit exist or not. Because Left Hand Limit $\ne$Right Hand Limit

Answer

For $x\to 0$ the expression $\frac{x}{[x]}$ is not well defined since for $0

As you noticed, we can only consider

$$\lim_{x\rightarrow0^-}\frac{x}{[x]}=0$$