Discussion
For \( f(x) = \dfrac{|x|}{x} \), the two one-sided limits at the origin are
Answer: A
For \( x > 0 \) the quotient is \( x/x = 1 \), and for \( x < 0 \) it is \( -x/x = -1 \). So
\[ \lim_{x \to 0^{+}} f(x) = 1, \qquad \lim_{x \to 0^{-}} f(x) = -1. \]
The two disagree, so the two-sided limit does not exist and the origin carries a jump discontinuity of magnitude two
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