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The number of points where \mathrm{f(x)=[\sin x+\cos x]} (where [ ] denotes the greatest integer function), \mathrm{x \in(0,2 \pi)} is not continuous is

Option: 1

3


Option: 2

4


Option: 3

5


Option: 4

6


Answers (1)

best_answer

f(x) will be discontinuous at those points, where \sin x+\cos x is an integer, which is the

case for x \in\left\{\frac{\pi}{2}, \frac{3 \pi}{4}, \pi, \frac{3 \pi}{2}, \frac{7 \pi}{4}\right\} Thus f(x) is discontinuous exactly for five values of x.

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Rishi

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