What is lim_{x→0} (sin x)/x?

• A. 0
• B. 1
• C. ∞
• D. -1

Answer: (B)

Near zero, sin x behaves like x, so their ratio tends to 1. A clean way to see this rigorously is the squeeze: for all x with |x| < π/2, cos x ≤ sin x / x ≤ 1. Since cos x → 1 as x → 0 and the upper bound is the constant 1, the Squeeze Theorem gives sin x / x → 1. Equivalently, the Taylor expansion sin x = x - x^3/6 + ... leads to sin x / x = 1 - x^2/6 + ..., which also tends to 1. Therefore, the limit is 1.