Question

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

Solution

Correct option is

5

We know [.] is not continuous at integral points. 

Thus, f (x) = [sin x + cos x] will be discontinuous at those points, where

sin x +  cos x is an integer, which is the case for, 

          .  

Thus, the number of points at which f (x) is discontinuous is 5.

SIMILAR QUESTIONS

Q1

If f (x) = x + tan and g(x) is the inverse of f (x) then g’ (x) is equal to:

Q2

If f (x) is differentiable function and (f (x). g(x)) is differentiable at x = a, then

Q3

        

Determine the value of ‘a’ if possible, so that the function is continuous

Q4

 for all real x and y. If f ’ (0) exists and equals to –1and f (0) = 1, find f ’(x).

Q5

Now if it is given that there exists a positive real δ, such that f (h) = h for 0 < h < δ then find f’(x) and hence f (x).

Q6

Let f  be an even function and f ’(0) exists, then find f’(0).

Q7

Let f (x) = xnn being non-negative integer. Then find the value of n for which the equality f’(a + b) = f ’(a) + f ’ (b) is valid for all, ab > 0

Q8

 

Q9

Find the set of points where x2 |x| is true thrice differentiable.

Q10

  

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