If `f(x)=cos{(pi)/(2)[x]-x^(3)},1 lt x lt 2and[x]=` the greatest integer `lex`, then find `f'(root(3)((pi)/(2)))`

If f(x)=cos{(pi)/(2)[x]-x^(3)},1ltxlt2 , and [x] denotes the greatest integer less than or equal to x, then the value of f'(root(3)((pi)/(2))) , is

If f (x) = cos (x ^(2) -4[x]), 0 lt x lt 1, (whre [.] denotes greatest integer function) then f '((sqrtpi)/(2)) is equal to:

If f(x)=sin{(pi)/(3)[x]-x^(2)}" for "2ltxlt3 and [x] denotes the greatest integer less than or equal to x, then f'"("sqrt(pi//3)")" is equal to

If f(x)=sin{(pi)/(3)[x]-x^(2)}" for "2ltxlt3 and [x] denotes the greatest integer less than or equal to x, then f'"("sqrt(pi//3)")" is equal to

If f(x)=cos[pi^2]x +cos[-pi^2]x , where [x] stands for the greatest integer function, then

If f(x)=cos[pi^2]x , where [x] stands for the greatest integer function, then (a) f(pi/2)=-1 (b) f(pi)=1 (c) f(-pi)=0 (d) f(pi/4)=1/sqrt(2)

If f(x)= cos [(pi^(2))/(2)] x + sin[(-pi^(2))/(2)]x,[x] denoting the greatest integer function,then

If f(x)=(x^(3)+x+1)tan(pi[x]) (where, [x] represents the greatest integer part of x), then

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 :

Consider a function f (x) in [0,2pi] defined as : f(x)=[{:([sinx]+ [cos x],,, 0 le x le pi),( [sin x] -[cos x],,, pi lt x le 2pi):} where [.] denotes greatest integer function then. lim _(x to ((3pi)/(2))^+), f (x) equals