Topic: Electronics Engineering
Which of the following function have a jump discontinuity at $x=0?$
- A. $g(x)=ln|x|$
- B. $g(x)=1/x^{2}$
- C. $g(x)=\begin{cases}sin(x)/x&,&x\neq0\\ 0,&x=0\end{cases}$
- D. None of these
Answer: C. $g(x)=\begin{cases}sin(x)/x&,&x\neq0\\ 0,&x=0\end{cases}$
Explanation: The limit as x approaches 0 for $sin(x)/x$ is 1. Since $g(0) = 0 \neq 1$, there is a discontinuity.