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

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).

If f: R rarr R is a function defined by: f(x) = [x] cos((2x-1)/2)pi , where [x] denotes the greatest integer function, then 'f' is

If 0 lt x lt pi and cos x + sin x = 1/2 , then tan x 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 continutity and diffrentiability of f(x)

If f(x) = {{:("sin"(pix)/(2)",",x lt 1),([x]",",x ge 1):} , where [x] denotes the greatest integer function, then

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 a. f'(1^(-)) = 2 b. f'(1^(+)) = 2 c. f'(1^(-)) = -2 d. f'(1^(+)) = 0

If f(x) = |sinx| + | cos x| , find f'((3pi)/(4))