`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

lim_(x rarr0^(+))(((pi)/(2)-cot^(-1){x})x)/(sgn backslash x-cos x) (where {.} and sgn(.) denotes fractional part function and signum function respectively) is equal to

lim_(x rarr1)({x})^((1)/(n pi x)) ,where {.} denotes the fractional part function

If x in[2,3) ,then {x} equals, where {.} denotes fractional part function.

underset( x rarr0 ) ("lim") (sin [cos x ])/( 1+[cos x ] ) ( where {x} denotes fractional part function )

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}, and sgn(x) are greatest integer function,fractional part function and signum function respectively.

Let function f(x) is defined in [-2,2] as f(x)={{:({x}",",-2lexle-1),(|sgnx|",",-1lexle1),({-x}",",1ltxle2):} where {x} and sgn x denotes fractional part and signum functions, respectively. Then the area bounded by the graph of f(x) and x-axis is

Evaluate int _(-1) ^(15) Sgn ({x})dx, (where {**} denotes the fractional part function)

The number of integral values of x satisfying the equation sgn([(19)/(2+x^(2))])=[1+{5x}] (where [x],{x} and sgn(x) denote the greatest integer,the fractional part and the signum functions 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.