Which of the following functions have a jump discontinuity at x = 0

A

$$g(x) = \ln \mid x \mid$$

B

$$g(x) = \frac{1}{x^{2}}$$

C

$$\begin{cases}\frac{\sin(x)}{x} & x \neq 0\\0 & x = 0\end{cases}$$

D

None of the above