If `f(x)=[x]tan(πx)` then `f ′(k ^+ ) `is equal to (where k is some integer and [.] denotes greatest integer function)

If f (x) =[x] tan (pix ) then f '(k') is equal to (k in and [.] denotes greatest integer function):

Period of f(x) = sgn([x] +[-x]) is equal to (where [.] denotes greatest integer function

Period of f(x) = sgn([x] +[-x]) is equal to (where [.] denotes greatest integer function

draw the graph of f(x)=x+[x] , [.] denotes greatest integer function.

If f(x)=[sin^(2) x] ([.] denotes the greatest integer function), then

Draw the graph of f(x)=x+[x], [.] denotes greatest integer function.

The value of int_(0)^(100)[ tan ^(-1)x] d x is equal to (where [.] denotes the greatest integer function)

If F(x)=(sinpi[x])/({x}) then F(x) is (where {.} denotes fractional part function and [.] denotes greatest integer function and sgn(x) is a signum function)

The function, f(x)=[|x|]-|[x]| where [] denotes greatest integer function:

f(x) = 1 + [cosx]x in 0 leq x leq pi/2 (where [.] denotes greatest integer function) then