Let f(x) = (e^(1/x) − 1)/(e^(1/x) + 1) for x ≠ 0, and f(0) = 0. Which statement is correct regarding x = 0?

Let f(x) = (e^(1/x) − 1)/(e^(1/x) + 1) for x ≠ 0, and f(0) = 0. Which statement is correct regarding x = 0?

• A. Continuous at x = 0
• B. LHL = 1
• C. RHL = −1
• D. LHL = −1 and RHL = 1

Answer: D) LHL = −1 and RHL = 1

Explanation: As x→0⁻, 1/x → −∞, e^(1/x) → 0, so LHL = (0 − 1)/(0 + 1) = −1. As x→0⁺, 1/x → ∞, e^(1/x) → ∞, taking e^(1/x) common gives RHL = 1. Jump discontinuity.