Limits Continuity And Differentiability Question 51
Question: Which of the following functions have finite number of points of discontinuity? (where $ [\cdot ] $ represents greatest integer functions)
Options:
A) $ tanx $
B) $ x\text{ }[x] $
C) $ \frac{| x |}{x} $
D) $ \sin [n\pi x] $
Show Answer
Answer:
Correct Answer: C
Solution:
$ f(x)=\tan x $ is discontinuous when $ x=(2n+1)\pi /2,n\in I $
$ f(x)=x[x] $ is discontinuous when $ x=k,k\in I $
$ f(x)=\sin [n\pi x] $ is discontinuous when $ n\pi x=k,k\in I $
Thus, all the above functions have infinite number of points of discontinuity.
But $ f(x)=\frac{| x |}{x} $ is discontinuous when $ x=0 $ only.
BETA
