If limx→12-x+ax-1+b1+x exists, then a and b can take the values (where t.] denotes the greatest integer function)

Since the greatest integer function is discontinuous at integral values of x, for a given limit to exist both left- and right-hand limits must be equal.L.H.L.  =   limx→1-  2-x+ax-1+b1+x              =  2-1+a-1+b1=1-a+bR.H.L.   limx→1+    2-x+ax-1+b1+x                  =2-1+a0+b2=1+2bOn   comparing,  we  have   -a=b.