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

If f(x)=cos[pi^2]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

Draw the graph of f(x) = cos pi[x] , where [*] represents the greatest integer function. Find the period of the function.

If f(x)=sin([x]pi)/(x^2+x+1) where [.] denotes the greatest integer function, then (A) f is one-one (B) f is not one-one and not constant (C) f is a constant function (D) none of these

let f(x)=(sin4pi[x])/(1+[x]^(2)) , where px] is the greatest integer less than or equal to x then

Prove that int_(-pi/2)^(2pi)[cot^(-1)x]dx ,where [dot] denotes the greatest integer function.

The right hand derivative of f(x)=[x]t a npix a tx=7 is (where [.] denotes the greatest integer function) 0 b. 7pi c. -7pi d. none of these

f: Rvec[-1,oo)a n df(x)=1n([|s in2x|+|cos2x|]) (where [.] is the greatest integer function.) Then, (a) f(x)h a sr a ngZ (b) f(x)i sp e r iod i c function (c) f(x)i sin v e r t i b l ein[0,pi/4] (d) f(x) is into function

The right hand derivative of f(x)=[x]t a npix at x=7 is (where [.] denotes the greatest integer function) a. 0 b. 7pi c. -7pi d. none of these

The function f(x)=tan^(-1)(sinx+cosx) is an increasing function in (-pi/2,pi/4) (b) (0,pi/2) (-pi/2,pi/2) (d) (pi/4,pi/2)