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