Limits Continuity And Differentiability Question 13
Question: A point where function $ f(x)=[sin[x]] $ is not continuous in $ (0,2\pi ) $ , [.] denotes the greatest integer $ \le x $ , is
Options:
A) (3, 0)
B) (2, 0)
C) (1, 0)
D) none of these
Show Answer
Answer:
Correct Answer: D
Solution:
For $ 0\le x<1,f(x)=\sin x=0, $
$ 1\le x<2,f(x)=\sin(1)=0, $
$ 2\le x<3,f(x)=\sin(2)=0, $
$ 3\le x<4,f(x)=\sin(3)=0, $
$ 4\le x<5,f(x)=\sin(4)\approx0.7568, $
Hence, there is discontinuity at point $ ( 4,-1 ) $
BETA
