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Find the number of point of discontinuity of the function in 0 to 2(pi). f(x) = [sinx + cosx] [] is an integral part function.

Find the number of point of discontinuity of the function in 0 to 2(pi).
f(x) = [sinx + cosx]
[] is an integral part function.

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:Hello student, please find answer to your question
f(x) = [sinx + cosx]
f(x) = [\sqrt{2}sin(x+\frac{\pi }{4})]
f(x) = 1, 0\leq x\leq \frac{\pi }{2}
= 0, \frac{\pi }{2}< x\leq \frac{3\pi }{4}
= -1, \frac{3\pi }{4}< x\leq \pi
= -2, \pi < x< \frac{3\pi }{2}
= -1, \frac{3\pi }{2} \leq x< \frac{7\pi }{4}
= 0, \frac{7\pi }{4} \leq x< 2\pi
= 1, x = 2\pi
So there are 6 points of discontinuity.

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