Question

 

Solution

Correct option is

continuous at x = 0 for all ai  & differentiable atx = 0 for all a2k + 1 = 0.

We know that | x |r, r = 0, 1, 2 … are all continuous every where.

Since, | x |, | x |3, | x |5, …… are not differentiable at x = 0. 

Whereas | x |2, | x |4,……. are every where differentiable. 

 is not differentiable at x = 0, if any one of a1a3,a5,... is non-zero. 

Thus, for f (x) to be differentiable at x = 0, we must have

       a1 = a3 = a5 … = 0 

i.e., a2k + 1 = 0.

SIMILAR QUESTIONS

Q1

      

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

Q2

Find the points of discontinuity of 

Q3

 

   

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

Q4

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

Q5

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

Q6

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.

Q7

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

Q8

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

Q9

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

Q10

The number of points in (1, 3), where is not differentiable is: