Question

 is continuous at x = 0, find the values of Aand B. Also find f (0).

Solution

Correct option is

A = – 2, B = 0, f (0) = –1.

As f(x) is continuous at x = 0, 

              

As denominator → 0 as x  → 0,

Numerator should also → 0 as x → 0

Which is possible only if (for f (0) to be finite).

                 

                          

Again we can see that denominator → 0 as x → 0,

∴ Numerator should also approach 0 as x → 0 (for f(0) to be finite) 

  

                        

So, we get     

                    

SIMILAR QUESTIONS

Q1

  

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

Q2

Discuss the continuity of the function .

Q3

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).

Q4

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

                          .

Q5

Let f is a differentiable function such that 

          .

Q6

Let f : R+ → R satisfies the functional equation  

          .  

If f’(1) = e, determine f (x).

Q7

Let f is a differentiable function such that   

     .

Q8

Let f be a function such that  .   

.

Q9

Find and b so that the function:    

 

   

Q10

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