Let y = f(x) be a differentiable function, `AA x in R` and satisfies,
`f(x) = x+ int_(0)^(1)x^(2)z f(z) dz + int_(0)^(1)x z^(2) f(z) dz`, then

Let f(x) be a differentiable function in the interval (0, 2) then the value of int_(0)^(2)f(x)dx

Let f is a differentiable function such that f'(x) = f(x) + int_(0)^(2) f(x) dx, f(0) = (4-e^(2))/(3) , find f(x).

Let f:RtoR be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt . f(x) increases for

Let f be a differentiable function satisfying [f(x)]^(n)=f(nx)" for all "x inR. Then, f'(x)f(nx)

Let f(x) be a fourth differentiable function such f(2x^2-1)=2xf(x)AA x in R, then f^(iv)(0) is equal

Let f(x) be continuous and differentiable function for all reals and f(x + y) = f(x) - 3xy + f(y). If lim_(h to 0)(f(h))/(h) = 7 , then the value of f'(x) is

Let f : R rarr R be a differentiable function at x = 0 satisfying f(0) = 0 and f'(0) = 1, then the value of lim_(x to 0) (1)/(x) . sum_(n=1)^(oo)(-1)^(n).f((x)/(n)) , is

Let f be differentiable function satisfying f((x)/(y))=f(x) - f(y)"for all" x, y gt 0 . If f'(1) = 1, then f(x) is

Let f : (0, oo) rarr R be a continuous function such that f(x) = int_(0)^(x) t f(t) dt . If f(x^(2)) = x^(4) + x^(5) , then sum_(r = 1)^(12) f(r^(2)) , is equal to

f(x) is a continuous and differentiable function. f'(x) ne 0 and |{:(f'(x),f(x)),(f''(x),f'(x)):}|=0 . If f(0)=1 and f'(0)=2 then f(x)=....