For a differentiable function `f(x)`, if `f'(2)=2 and f'(3)=1`, then the value of `lim_(xrarr0)(f(x^(2)+x+2)-f(2))/(f(x^(2)-x+3)-f(3))` is equal to

If f''(0)=k,kne0 then the value of lim_(xrarr0)(2f(x)-3f(2x)+f(4x))/(x^(2)) is

If f'(2)=6 and f'(1)=4 ,then lim_(x rarr0)(f(x^(2)+2x+2)-f(2))/(f(1+x-x^(2))-f(1)) is equal to ?

A differentiable function satisfies 3f^(2)(x)f'(x)=2x. Given f(2)=1 then the value of f(3) is

Let f:R rarr R be differentiable at x = 0. If f(0) = 0 and f'(0)=2 , then the value of lim_(xrarr0)(1)/(x)[f(x)+f(2x)+f(3x)+….+f(2015x)] is

Let f:RrarrR be differentiable at x=0 . If f(0)=0 and f'(0)=2 ,then the value of lim_(xrarr0)1/x[f(x)+f(2x)+f(3x)+.....+f(2015x)] is

Let f : R to R be a differentiable function satisfying f'(3) + f'(2) = 0 , Then underset(x to 0) lim ((1+f(3+x)-f(3))/(1+f(2-x)-f(2)))^(1/x) is equal to

Let f(x) be a twice-differentiable function and f'(0)=2. The evaluate: lim_(x rarr0)(2f(x)-3f(2x)+f(4x))/(x^(2))

Let f : R to R be a differentiable function satisfying f'(3) + f'(2) = 0 , Then lim_(x to 0) ((1+f(3+x)-f(3))/(1+f(2-x)-f(2)))^(1/x) is equal to