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Differential Calculus> Find the number of point of discontinuity...

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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.

Lovey , 10 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 10 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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