In a function `2f(x)+ xf(1/x)-2f(|sqrt2sin(pi(x+1/4))|)=4cos^2[(pix)/2]+xcos(pi/x)`. Prove that: 1. f(2)+f(1/2)=1 2. f(2)+f(1)=0

A function y=f(x) satisfies f(x)=-(1)/(x^(2))-pi^(2)sin(pi x);f'(2)=pi+(1)/(2) and f(1)=0. The value of f((1)/(2))

A function y=f(x) satisfies f''(x)=-(1)/(x^(2))-pi^(2)sin(pi x)f'(2)=pi+(1)/(2) and f(1)=0 then value of f((1)/(2)) is

If x^(4)f(x)-sqrt(1-sin2 pi x)=|f(x)|-2f(x) then f(-2) equals

If the function f(x) = (1-sinx)/(pi-2x)^2 , x!=pi/2 is continuous at x=pi/4 , then find f(pi/2) .

A function y=f(x) satisfies A function y=f(x) satisfies f" (x)= -1/x^2 - pi^2 sin(pix) ; f'(2) = pi+1/2 and f(1)=0 . The value of f(1/2) then

The function f(x)= xcos(1/x^2) for x != 0, f(0) =1 then at x = 0, f(x) is

Let f:RtoR be a function such that f(x)=x^(3)+x^(2)f'(1)+xf''(2)+f'''(3) for x in R Consider the following 1. f(2)=f(1)-f(0) 2.f''(2)-2f'(1)=12 Which of the above is/are correct ?

If f(x)=sin(2x^(2)-2[x]) for 0

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2)(0)=1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .