If f(x) is differentiable and strictly increasing function, then the value of `lim_(xto0)(f(x^2)-f(x))/(f(x)-f(0))` is

If f''(0)=k,kne0 , then the value of lim_(xto0)(2f(x)-3f(2x)+f(4x))/(x^2) is

If f (x) is differentiable and f'(4) =5, then the vlaue of lim_(xto2) (f(4) -f(x^(2)))/(x-2) is equal to-

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

Let f(x) be a twice-differentiable function and f''(0)=2. Then evaluate lim_(xto0) (2f(x)-3f(2x)+f(4x))/(x^(2)).

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

Let f:R to R be a differentiable function and f(1)=4 and f'(1)=2 , then the value of lim_(x to 1) int_(4)^(f(x))(2t)/(x-1)dt 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: RvecR be differentiable and strictly increasing function throughout its domain. Statement 1: If |f(x)| is also strictly increasing function, then f(x)=0 has no real roots. Statement 2: When xvecooorvec-oo,f(x)vec0 , but cannot be equal to zero.

If f (1) =1 f'(1)=2 then the value of lim _(xto1) (sqrt(f(x))-1)/(sqrtx-1) is-

The value of lim_(xto0)f(x) where f(x)=(x^(3)+x^(2))/(2x^(3)-27x^(2))