Answer
$\lim\limits_{x\to4}[[x-1]]$ does not exist.
Work Step by Step
$\lim\limits_{x\to4^-}[[x-1]]=[[4^--1]]=[[3^-]]=2.$
$\lim\limits_{x\to4^+}[[x-1]]=[[4^+-1]]=[[3^+]]=3.$
Since $\lim\limits_{x\to4^-}[[x-1]]\ne\lim\limits_{x\to4^+}[[x-1]]\to\lim\limits_{x\to4}[[x-1]]$ does not exist.
