Question

lim_(x--->2) {[2-x] + [x-2] -x},  where [.] denotes greatest integer function

Answer 1

lim_(x--->2) {[2-x] + [x-2] -x}

RHL 
lim_(x--->2⁺) {[2 - 2⁺] + [2⁺ - 2] - 2⁺} = {-1 + 0 - 2} = -3

LHL
lim_(x--->2^-){[2 - 2^-] + [2^- - 2] - 2^-} = {0 + -1 - 2} = -3

At 2
lim_(x--->2) {[2-x] + [x-2] -x} = -2