40. if `f(x) = tan(pi[(2x-3pi)^3])/(1+[2x-3pi]^2) ` ([.] denotes the greatest integer function), then (A) f(x) is continuous in R (B) f(x) is continuous in R but not differentiable in R (C) f (x) exists everywhere but f'(x) does not exist at some x eposilon R (D) None of these

Let f(x) = (sin {pi[x-pi]})/(1+[x^(2)]) , where [.] stands for the greatest integer function. Then, f(x) is continuous or not?

f(x)= [x] + sqrt(x -[x]) , where [.] is a greatest integer function then …….. (a) f(x) is continuous in R+ (b) f(x) is continuous in R (C) f(x) is continuous in R - 1 (d) None of these

If f(x)=cos[(pi)/(x)]cos((pi)/(2)(x-1)); where [x] is the greatest integer function of x, then f(x) is continuous at :

The function f(x)=(sin(pi[x-pi]))/(4+[x]^2) , where [] denotes the greatest integer function,(a) is continuous as well as differentiable for all x in R (b) continuous for all x but not differentiable at some x (c) differentiable for all x but not continuous at some x . (d) none of these

The function f(x)=(sin(pi[x-pi]))/(4+[x]^2) , where [] denotes the greatest integer function, (a) is continuous as well as differentiable for all x in R (b) continuous for all x but not differentiable at some x (c) differentiable for all x but not continuous at some x . (d) none of these

If f(x)=cos[pi/x] cos(pi/2(x-1)) ; where [x] is the greatest integer function of x ,then f(x) is continuous at :

If f(x)=cos[pi/x] cos(pi/2(x-1)) ; where [x] is the greatest integer function of x ,then f(x) is continuous at :

If f(x)=cos[pi/x] cos(pi/2(x-1)) ; where [x] is the greatest integer function of x ,then f(x) is continuous at :

The function f(x)=(sin(pi[x-pi]))/(4+[x]^2) , where [] denotes the greatest integer function, is continuous as well as differentiable for all x in R (b) continuous for all x but not differentiable at some x (c) differentiable for all x but not continuous at some x . (d) none of these

If f : R to [-1, 1] , where f(x)=sin(pi/2[x]) (where [.] denotes the greatest integer function), then the range of f(x) is