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

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

f'(3)+f'(2)=0 Find the lim_(x rarr0)((1+f(3+x)-f(3))/(1+f(2-x)-f(2)))^((1)/(x))

Let f : R to R be a differentiable function such that f(2) = -40 ,f^1(2) =- 5 then lim_(x to 0)((f(2 - x^2))/(f(2)))^(4/(x^2)) is equal to

Let F : R to R be a differentiable function having : f(2) = 6, f'(2) = 1/48 Then lim_(x to 2) int_(6)^(f(x)) (4 t^3)/(x-2) dt equals :

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 a. 0 b. -log2 c. 1 d. e

Let f(x) be a differentiable function satisfying f(y)f(x/y)=f(x) AA , x,y in R, y!=0 and f(1)!=0 , f'(1)=3 then

Let f : (-1,1) to R be a differentiable function with f(0) = -1 and f'(0) = 1 . Let g(x) = [f(2f(x)+2)]^(2) , then g'(0)=

If f:R rarr R is continuous function satisfying f(0) =1 and f(2x) -f(x) =x, AAx in R , then lim_(nrarroo) (f(x)-f((x)/(2^(n)))) is equal to

If f:R rarr R is continous function satisying f(0) =1 and f(2x) -f(x) =x, AAx in R , then lim_(nrarroo) (f(x)-f((x)/(2^(n)))) is equal to

Let f:R to R be a positive increasing function with lim_(x to oo) (f(3x))/(f(x))=1 . Then lim_(x to oo) (f(2x))/(f(x))=