Let F : R to R be a differentiable funct...

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 :

A

18

B

12

C

36

D

24

Verified by Experts

The correct Answer is:

A

Similar Questions

Explore conceptually related problems

Let f : R to R be a differentiable function and f(1) = 4 , then the value of lim_(x to 1) int_4^(f(x)) (2t)/(x - 1) dt is :

If f(2) = 2 and f^(')(2) = 1 , then lim_(x rarr 2) (2x^(2)-4 f(x))/(x-2) =

Let f(2)=4 and f'(2)=4 . Then lim_(xto2)(xf(2)-2f(x))/(x-2) is given by :

If f(2) = 4 and f^(')(2) =1 then lim_(x rarr 2) (x f(2)-2f (x))/(x-2)

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))=

Let f(x), g(x) be differentiable functions and f(1) = g(1) = 2, then : lim_(x rarr 1) (f(1) g(x) - f(x) g(1) - f(1) + g(1))/(g(x) - f(x)) equals :

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

Let f be differentiable for all x. If f(1)= -2, f'(x) ge 2 for all x in [1, 6] , then :

Let f : R rarr R be a function defined by f(x) = x^3 + 5 . Then f^-1(x) is