Question
Question: The number of points where f(x) = [sinx + cosx] (where [.] denotes the greatest integer function), x...
The number of points where f(x) = [sinx + cosx] (where [.] denotes the greatest integer function), x∈(0, 2π) is not continuous is
A
3
B
4
C
5
D
6
Answer
5
Explanation
Solution
f(x) will be discontinuous at those points, where sinx + cosx is an integer, which is the case for
. Thus f(x) is discontinuous exactly for five values of x. Hence