Consider f(x) = |x|/x for x ≠ 0, and f(0) = 0. Which of the following is true about f(x) at x = 0?

Consider f(x) = |x|/x for x ≠ 0, and f(0) = 0. Which of the following is true about f(x) at x = 0?

• A. Continuous
• B. Removable discontinuity
• C. Jump discontinuity
• D. Infinite discontinuity

Answer: C) Jump discontinuity

Explanation: LHL at x = 0 is lim(x→0⁻) −x/x = −1. RHL at x = 0 is lim(x→0⁺) x/x = 1. Since LHL ≠ RHL and both are finite, it is a jump discontinuity.