limx→3([x−3]+[3−x]−x),where[.]denote the greatest integer function, is equal to:
-4
R.H.L=limh→0([(3+h)−3]+[3−(3+h)−(3+h)) =limh→0([h]+[−h]−3−h) =limh→0(0−1−3−h)=−4L.H.L=limh→0([(3−h)−3]+[3−(3−h)−(3−h)) =limh→0([−h]+[h]−3+h) =limh→0(−1+0−3+h)=−4L.H.L=R.H.L∴limx→3([x−3]+[3−x]−x)=−4