is Continuous At x = 0, Find The Values Of Aand B. Also Find f (0).

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

Discuss the continuity of the function .

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

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

                          .

Let f is a differentiable function such that 

          .

Let f : R⁺ → R satisfies the functional equation  

          .  

If f’(1) = e, determine f (x).

Let f is a differentiable function such that   

     .

Let f be a function such that  .   

.

Find a and b so that the function:    

Find the natural number a for which  where the function f satisfies the relation f (x + y) = f (x) f (y) for all natural number x, y and further f (1) = 2.