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

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

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.

Evaluate: int_0^2[x^2-x+1]dx ,w h e r e[dot] denotos the greatest integer function.

lim_(x->0)[(1-e^x)(sinx)/(|x|)]i s(w h e r e[dot] represents the greatest integer function). (a) -1 (b) 1 (c) 0 (d) does not exist

Find the domain and range of f(x)=sin^(-1)[x]w h e r[] represents the greatest function).

Discuss the differentiability of f(x)=[x]+|1-x|, x in (-1,3),w h e r e[dot] represents greatest integer function.

Evaluate: int_(-5)^5x^2[x+1/2]dx(w h e r e[dot] denotes the greatest integer function).