If `lim_(xto1) (2-x+a[x-1]+b[1+x])` exists, then a and b can take the values (where `[.]` denotes the greatest integer function)

Answer

B, C

Explanation

Since the greatest integer function is discountinuous at integral values of x, for a given limit to exist both left-and right-hand limits must be equal.
`L.H.L.=underset(xto1^(-))lim(2-x+a[x-1]+b[1+x])`
`=2-1+a(-1)+b(1)=1-a+b`
`R.H.L.=underset(xto1^(+))lim(2-x+a[x-1]+b[1+x])`
`=2-1+a(0)+b(2)=1+2b`
On comparing, we have `-a=b`.