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)=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([x]pi))/(x^2+x+1) , where [dot] denotes the greatest integer function, then

Let [x] be the greatest integer function f(x)=(sin(1/4(pi[x]))/([x])) is

3x-2 lt 2x+1

If f(x) = |cos x- sin x| then find f'((pi)/(6))

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 :

f(x)=sin^(-1)[2x^(2)-3] , where [*] denotes the greatest integer function. Find the domain of f(x).

The function f(x) = [x] cos((2x-1)/2) pi where [ ] denotes the greatest integer function, is

If f(x)={{:(,x[x], 0 le x lt 2),(,(x-1)[x], 2 le x lt 3):} where [.] denotes the greatest integer function, then (x) is continuous at x=2

If f(x) = {{:([cos pi x]",",x le 1),(2{x}-1",",x gt 1):} , where [.] and {.} denotes greatest integer and fractional part of x, then