If `[x]` and `{x}` represetnt the integral and fractional parts of `x ,` respectively, then the value of `sum_(r=1)^(2000)({x+r})/(2000)` is (a)`x` (b) `[x]` (c) `{x}` (d) `x+2001`

In the questions, [x]a n d{x} represent the greatest integer function and the fractional part function, respectively. If y=3[x]+1=4[x-1]-10 , then find the value of [x+2y]dot

Which of the following is/are not functions ([.]) and {.} denote the greatest integer and fractional part functions, respectively? (a) 1/(1n(1-|x|)) (b) (x !)/({x}) (c) x !{x} (d) (1n(x-1))/(sqrt((1-x^2)))

Solve 2[x]=x+{x},w h r e[]a n d{} denote the greatest integer function and the fractional part function, respectively.

If f(x) = min({x}, {-x}) x in R , where {x} denotes the fractional part of x, then int_(-100)^(100)f(x)dx is

Find the value of int_(-1)^1[x^2+{x}]dx ,w h e r e[dot]a n d{dot} denote the greatest function and fractional parts of x , respectively.