`f:(2,3)vec(0,1)d efin e db yf(x)=x-[x],w h e r e[dot]` represents the greatest integer function.

Find the range of f(x)=(x-[x])/(1-[x]+x '),w h e r e[] represents the greatest integer function.

Find the range of f(x)=(x-[x])/(1-[x]+x '),w h e r e[] represents the greatest integer function.

Evaluate: int_0^(100)(x-[x]dx(w h e r e[dot] represents the greatest integer function).

Find the points of discontinuity of the function: f(x)=[[x]]-[x-1],w h e r e[dot] represents the greatest integer function

Evaluate: ("lim")_(xvec0)(sinx)/x,w h e r e[dot] represents the greatest integer function.

Let f:(4,6)vec(6,8) be a function defined by f(x)=x+[x/2]dotw h e r e[dot] denotes the greatest integer function, then f^(-1)(x) is equal to (A) x-2 (B) x-[x//2] (C) -x-2 (D) none of these

Evaluate: int_0^oo[2e^(-x)]dx ,w h e r e[x] represents greatest integer function.

Evaluate: int_0^oo[2e^(-x)]dx ,w h e r e[x] represents greatest integer function.

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

The population of a country increases by 2% every year. If it increases k times in a century, then prove that [k]=7,w h e r e[dot] represents the greatest integer function.