Question

Which of the following functions have finite number of points of discontinuity?

• A. $\tan x$
• B. $x[x]$
• C. $\cot x$
• D. None of these

Hint:

Functions with infinite domains that repeat (periodic) or jump at integers usually have infinite discontinuities.

Answer 1

The Correct Option is D

Step 1: Concept
Evaluate the points of discontinuity for each periodic or step function.

Step 2: Meaning
Periodic functions like $\tan x$ and $\cot x$ have infinite vertical asymptotes.

Step 3: Analysis $\tan x$ is discontinuous at $x = (2n+1)\pi/2$, and $\cot x$ at $x = n\pi$ for all integers $n$. $[x]$ is discontinuous at every integer.

Step 4: Conclusion
All listed functions have an infinite number of points of discontinuity. Thus, none have a finite number. Final Answer: (D)