Let `f` be a real-valued function satisfying `f(x)+f(x+4)=f(x+2)+f(x+6)` Prove that `int_x^(x+8)f(t)dt` is constant function.

Let f be a real-valued function such that f(x)+2f((2002)/x)=3xdot Then find f(x)dot

Let f:R -(0,oo) be a real valued function satisfying int_0^x tf(x-t) dt =e^(2x)-1 then f(x) is

f is a real valued function from R to R such that f(x)+f(-x)=2 , then int_(1-x)^(1+X)f^(-1)(t)dt=

Statement 1: Let f: RvecR be a real-valued function AAx ,y in R such that |f(x)-f(y)|<=|x-y|^3 . Then f(x) is a constant function. Statement 2: If the derivative of the function w.r.t. x is zero, then function is constant.

If f(x) is a polynomial function satisfying f(x)dotf(1/x)=f(x)+f(1/x) and f(4)=65 ,t h e nfin df(6)dot

Let f(x) be a differentiable function such that f(x)=x^2 +int_0^x e^-t f(x-t) dt then int_0^1 f(x) dx=

Suppose f is a real function satisfying f(x+f(x))=4f(x)a n df(1)=4. Then the value of f(21) is 16 21 64 105

Let f be a differentiable function satisfying int_(0)^(f(x))f^(-1)(t)dt-int_(0)^(x)(cost-f(t)dt=0 and f((pi)/2)=2/(pi) The value of lim_(x to 0)(cosx)/(f(x)) is equal to where [.] denotes greatest integer function

Let f be a differentiable function satisfying int_(0)^(f(x))f^(-1)(t)dt-int_(0)^(x)(cost-f(t)dt=0 and f((pi)/2)=2/(pi) The value of int_(0)^(pi//2) f(x)dx lies in the interval

If f is a real valued function such that f(x+y) = f(x) + f(y) and f(1)=5, then the value of f(100) is