Question

Let f is a differentiable function such that   

     .

Solution

Correct option is

It is given that:

           

   

Integrating above expression both sides,  

                                                [k being constant of integration]

From (i) and (ii) we get  

            

Now to find constant of integration k;

Integrating both sides from 0 to 2, we get,

          

From (ii) and (iv) we get,    

          

Putting k = 1in (iii) we get,  

                  

SIMILAR QUESTIONS

Q1

 

Q2

Find the set of points where x2 |x| is true thrice differentiable.

Q3

Find the number of points where f (x) = [sin x + cos x(where [.] denotes greatest integral function), x Ïµ [0, 2π] is not continuous.

Q4

  

differentiable function in [0, 2], find a and b. (where [.] denotes the greatest integer function).

Q5

Discuss the continuity of the function .

Q6

Let f : → R, such that f’ (0) = 1 and f (x +2y) = f (x) + f (2y) + ex+2y (x + 2y) – x. ex – 2y. e2y + 4xy∀ xy Ïµ R. Find f (x).

Q7

If g(x) is continuous function in [0, ∞) satisfying g(1) = 1. If

                          .

Q8

Let f is a differentiable function such that 

          .

Q9

Let f : R+ → R satisfies the functional equation  

          .  

If f’(1) = e, determine f (x).

Q10

Let f be a function such that  .   

.