let `f(x)=(sin4pi[x])/(1+[x]^(2))`, where px] is the greatest integer less than or equal to x then

The function f(x)=(tan |pi[x-pi]|)/(1+[x]^(2)) , where [x] denotes the greatest integer less than or equal to x, is

Let f(x) = (x^2-9x+20)/(x-[x]) where [x] denotes greatest integer less than or equal to x ), then

The domain of the function f(x)=sqrt(x^2-[x]^2) , where [x] is the greatest integer less than or equal to x , is (a) R (b) [0,+oo) (c) (-oo,0) (d) none of these

Let f(x)=sgn(cot^(-1)x)+tan(pi/2[x]), where [x] is the greatest integer function less than or equal to x , then which of the following alternatives is/are true? f(x) is many-one but not an even function. f(x) is a periodic function. f(x) is a bounded function. The graph of f(x) remains above the x-axis.

The function f(x)=(sec^(-1)x)/(sqrt(x)-[x]), where [x] denotes the greatest integer less than or equal to x , is defined for all x in R (b) R-{(-1,1)uu{n"|"n in Z}} R^+-(0,1) (d) R^+-{n|n in N}

The value of int_(1)^(2)[x]dx , where [x] is the greatest integer less than or equal to x is

Let f: RvecR be a function defined by f(x)={[x],xlt=2 0,x >2 where [x] is the greatest integer less than or equal to xdot If I=int_(-1)^2(xf(x^2))/(2+f(x+1))dx ,t h e nt h ev a l u eof(4I-1)i s

Let f (x) = [x] , where [x] denotes the greater integer less than or equal to x. if a = sqrt(2011 ^2 +2012 ) then the value of f (a) is equal to

Find all the points of discontinuity of the greatest interger function defined by f(x)= [x] , where [x] denote the greatest integer less than or equal to x.

If f(x)={{:((sin[x])/([x])","" ""for "[x]ne0),(0","" ""for "[x]=0):} where [x] denotes the greatest integer less than or equal to x. Then find lim_(xto0)f(x).