Question

Find and b so that the function:    

 

   

Solution

Correct option is

Since continuous for x ∈ [0, π],

∴ f (x) is continuous at x = π/4 and x = π/2 and hence to discuss continuity

At              x = π/4 and x = π/2.   

Now at x = π/4  

                 

Again, Right hand limit at x = π/4

             

                                

  

for continuity, these three must be equal

At x = π/2  

Left hand limit at x = π/2  

                

LHL = b                                                              …(iv)

Right hand limit at x = π/2  

                

RHL = – a – b                               …(v)

and                       

For Continuity, these three must be equal

 

Solving (a) and (b), we get:

          

SIMILAR QUESTIONS

Q1

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

Q2

  

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

Q3

Discuss the continuity of the function .

Q4

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).

Q5

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

                          .

Q6

Let f is a differentiable function such that 

          .

Q7

Let f : R+ → R satisfies the functional equation  

          .  

If f’(1) = e, determine f (x).

Q8

Let f is a differentiable function such that   

     .

Q9

Let f be a function such that  .   

.

Q10

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