If f(x)=(|x|)/(|x|), x ≠ 0 , where [.] denotes the greatest integer...

$f(x)=\frac{[x]}{|x|}=$\begin{cases}\frac{[x]}{-x}, & x < 0 \\ \frac{[x]}{x} & , x \geq 0\end{cases}$$Right hand limit of$f(x)$at$x=1$,$\mathrm{RHL}=\lim _{x \rightarrow 1} \frac{[x]}{x}=\lim _{h \rightarrow 0} \frac{[1+h]}{1+h}=1$