If a>0 .[ ] denotes greatest integer function and _ x a⁻ ( |x|^3 a - [ x a ]^3 )=k, _ x a⁺ ( |x|^3 a - [ x a ]^3 )=l , then

Step-by-step solution

For x a⁻ x a 1 [ x a ]=1 _ x a⁺ |x|^3 a = a^3 a =a^2 aligned & k=a^2-0=a^2 & l= (a^2-1 ) & k-l=a^2- (a^2-1 ) & =1 aligned Note: In question, for l also limit is x a⁻ which should x a⁺