Answer
$\lim\limits_{x\to3}(2-[[-x]])$ does not exist.
Work Step by Step
$\lim\limits_{x\to3^+}(2-[[-x]])=2-[[-3^+]]=2-(-4)=6.$
$\lim\limits_{x\to3^-}(2-[[-x]])=2-[[-3^-]]=2-(-3)=5.$
$\lim\limits_{x\to3^+}(2-[[-x]])\ne\lim\limits_{x\to3^-}(2-[[-x]])\to\lim\limits_{x\to3}(2-[[-x]])$ does not exist.
