The period of `x-[x]` where `[x]` represents the integral part of `x` is

The period of x-[x] where [x] represents the intergral part of x is

Statement -I : Period of [x] where [.] represents the integral part of x is 1, Statement -II : Period of x-[x] where [.] represents the integral part x is 1. Statement -III : A real function f : A to B is such that f(a+x) = f(x ) AA a E R then F is called periodic function .Which of the above state ments is correct.

lim_(x to 2) (([x]^(3))/(3) - [(x)/(3)]^(-3)) is where [x] represents the integral part of x

lim_(x to 2^+) (([x]^(3))/(3) - [(x)/(3)]^(3)) is where [x] represents the integral part of x

Prove that f (x) =x-[x], where [x] denotes the integral part of x not exceeding and is periodic and find its period.

The period of f(x) = sin x + [x] , where [x] is fractional part of x is

If f(x)=(x^(3)+x+1)tan(pi[x]) (where, [x] represents the greatest integer part of x), then

If f(x)=(x^(3)+x+1)tan(pi[x]) (where, [x] represents the greatest integer part of x), then

Points of discontinuities of the function f(x)=4x+7[x]+2log(1+x) , where [x] denotes the integral part of x, is