Question

      

Determine a and b such that f (x) is continuous at x = 0.

Solution

Correct option is

a = 2/3, b = e2/3

Since f is continuous at x = 0.

Therefore, RHL = LHL = f (0)  

 RHL at x = 0  

     

                 

Again LHL at x = 0: 

  

                   

                   

and    f (0) = b.                                                        …(iii) 

Thus,          e2/3 = ea = b    ⇒    a = 2/3 and b = e2/3

SIMILAR QUESTIONS

Q1

Let y = (x) be defined parametrically as y = t2 + t |t|x = 2t – |t|t Ïµ R Then at x = 0, find (x) and discuss continuity.

Q2

 for what value of kf (x) is continuous at x = 0?

Q3

Find the points of discontinuity of 

Q4

 

   

Determine the form of g(x) = f ( f (x)) and hence find the point of discontinuity if g, if any.

Q5

The left hand derivative of f (x) = [x] sin (πx) at x = kk is an integer, is:

Q6

Which of the following functions is differentiable at x = 0?

Q7

Let f (x) = [n + p sin x], x Ïµ (0, π), n Ïµ Z and p is a prime number, where [.] denotes the greatest integer function. Then find the number of points where f (x) is not Differential.

Q8

, then draw the graph of f (x) in the interval [–2, 2] and discuss the continuity and differentiability in [–2, 2]

Q9

Fill in the blank, statement given below let . The set of points where f (x) is twice differentiable is ……………. .

Q10

The function f (x) = (x2 – 1) |x2 – 3x +2| + cos ( | | ) is not differentiable at