Let [P] denote the greatest integer P , If 0 a 2 , then the number of integral values of ' a ' such that _ x a ( [x^2 ]-[x]^2 ) does not exist is

Step-by-step solution

0 a 2 . Integral values of a are 0,1,2 aligned & For a=0 ; _ x 0 ( [x^2 ]-[x]^2 )= _ x 0 ( [x^2 ]-[x]^2 ) & L.H.L. = _ h 0 ( [(0-h)^2 ]-[0-h]^2 )=0-(-1)^2=-1 aligned R.H.L. = _ h 0 ( [(0+h)^2 ]-[0+h]^2 )=0 Limit doesn't exist for a=0 For a=1: L.H.L. = _ h 0 ( [(1-h)^2 ]-[1-h]^2 )=0 R.H.L. = _ h 0 ( [(1+h)^2 ]-[1+h]^2 )=1-1=0 Limit exist for a=1 For a=2 : L.H.L. = _ h 0 ( [(2-h)^2 ]-[2-h]^2 )=3-1=2 R.H.L. = _ h 0 ( [(2+h)^2 ]-[2+h]^2 )=4-4=0 Limit doesn't exist for a=2 Hence, for 2 values of ' a ' limit doesn't exis