Let `f(x)` be a twice-differentiable function and `f"(0)=2.` The evaluate: `("lim")_(xvec0)(2f(x)-3f(2x)+f(4x))/(x^2)`

Let f(x) be twice differentiable function such that f'(0) =2 , then, lim_(xrarr0) (2f(x)-3f(2x)+f(4x))/(x^2) , is

" Let "_(f(x)" be a twice differentiable function and "f''(0)=5*" If "lim_(x rarr0)(3f(x)-4f(3x)+f(9x))/(x^(2))=m," then "_(m-115)" is equal to ")

Evaluate the following using :L ' Hospital 's rule . (i) if f(x) be a twice differentiable function and f'' (0) =2 , then find underset(x to 0) lim (2f(x)-3f(3x)+f(4x))/x^(2) (ii) if f(a) =2, f' (a) = 1, g (a) =2 , then find underset(x to 0) (g(x)f(a) -g(a)f(x0))/(x-a) (iii) underset( x to 0) (1/x - 1 /(sin x) ) (iv) lim(x to 0+) x In x (v) underset(x to 0) | cot x|^( sin x) (vi) underset(x to 0) (tan x + 4 tan 2x -3 tan 3x)/(x^(2) tan x)

If f(x) is a twice differentiable function such that f(0)=f(1)=f(2)=0 . Then

Let f'(x) be continuous at x=0 and f'(0)=4 then value of lim_(x rarr0)(2f(x)-3f(2x)+f(4x))/(x^(2))

LEt f(x) be a differentiable function and f'(4)=5. Then,lim_(x rarr2)(f(4)-f(x^(2)))/(x-2) equals

If f'(x)=k,k!=0, then the value of lim_(x rarr0)(2f(x)-3f(2x)+f(4x))/(x^(2)) is

If f (x) is a thrice differentiable function such that lim _(xto0)(f (4x) -3 f(3x) +3f (2x) -f (x))/(x ^(3))=12 then the vlaue of f '''(0) equais to :

Let f(x) be a strictly increasing and differentiable function,then lim_(x rarr0)(f(x^(2))-f(x))/(f(x)-f(0))