`Lim_(x rarr 0^+) ((pi/2-cot^(-1){x})x)/("sgn"x-cosx)` (where {.} and sgn(.) denotes fractional part function and signum function respectively) is equal to

In which of the following function, range is not singleton set f(x)=[x]+[-x] (b) f(x)={x}+{-x} f(x)=|sgn(x)| (d) f(x)=[sqrt(x-[x]) where [x],{x},a n dsgn(x) are greatest integer function, fractional part function and signum function respectively.

lim_(xrarroo) {(e^(x)+pi^(x))^((1)/(x))} = (where {.} denotes the fractional part of x ) is equal to

f(x)=[x^(2)]-{x}^(2), where [.] and {.} denote the greatest integer function and the fractional part function , respectively , is

int_0^((9pi)/4) [|sinx|-|cosx|)dx+int_-1^5 {-x}dx] , where [.] and {.} denote the integer function and fractional part functions, respectively is equal to …

The value of int_(0)^(|x|){x} dx (where [*] and {*} denotes greatest integer and fraction part function respectively) is

Let a function f(x) be defined in [-2, 2] as f(x) = {{:({x}",",, -2 le xlt -1), (|"sgn "x|",",,-1le x le 1),({-x}",",, 1 lt xle 2):} where {x} and sgn x denote fractional part and signum functions, respectively. Then find the area bounded by the graph of f(x) an the x-axis.

The value of lim_(xto0)((tan({x}-1))sin{x})/({x}({x}-1) is where {x} denotes the fractional part function

lim_(x->1) (x-1){x}. where {.) denotes the fractional part, is equal to:

lim_(x rarr0)(sin^2x)/(1-cosx)

Draw the graph of y =(1)/({x}) , where {*} denotes the fractional part function.