Question

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

Solution

Correct option is

x Ïµ R – {–1, 0, 1}

Here,  

               

          

Thus the graph of f (x) is; 

Which is clearly, continuous for x Ïµ R

and differentiability for  

  x Ïµ R – {– 1, 0, 1}

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

      

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

Q4

Find the points of discontinuity of 

Q5

 

   

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

Q6

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

Q7

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

Q8

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.

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