Find the value of `{3^(2003)//28}, w h e r e{dot}` denotes the fractional part.

Find the domain and range of f(x)=log{x},w h e r e{} represents the fractional part function).

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.

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

lim_(x->-1)1/(sqrt(|x|-{-x}))(w h e r e{x} denotes the fractional part of (x) ) is equal to (a)does not exist (b) 1 (c) oo (d) 1/2

If the domain of y=f(x)i s[-3,2], then find the domain of g(x)=f(|[x]|),w h e re[] denotes the greatest integer function.

The domain of f(x)=sin^(-1)[2x^2-3],w h e r e[dot] denotes the greatest integer function, is (a) (-sqrt(3/2),sqrt(3/2)) (b) (-sqrt(3/2),-1)uu(-sqrt(5/2),sqrt(5/2)) (c) (-sqrt(5/2),sqrt(5/2)) (d) (-sqrt(5/2),-1)uu(1,sqrt(5/2))

int_0^x(2^t)/(2^([t]))dt ,w h e r e[dot] denotes the greatest integer function and x in R^+ , is equal to

The integral int_0^(1. 5)[x^2]dx ,w h e r e[dot] denotoes the greatest integer function, equals ...........

Evaluate: int_1^(e^6)[(logx)/3]dx ,w h e r e[dot] denotes the greatest integer function.

Prove that int_0^oo[cot^(-1)x]dx ,w h e r e[dot] denotes the greatest integer function.