Compute lim_{x->0} (tan x)/x.

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Multiple Choice

Compute lim_{x->0} (tan x)/x.

Explanation:
Near zero, tan x behaves like x because its slope at zero is 1, so the ratio tan x / x should approach 1. Writing tan x as sin x / cos x gives tan x / x = sin x / (x cos x). As x → 0, sin x / x → 1 and cos x → 1, so tan x / x = (sin x / x) * (1 / cos x) → 1 * 1 = 1.

Near zero, tan x behaves like x because its slope at zero is 1, so the ratio tan x / x should approach 1. Writing tan x as sin x / cos x gives tan x / x = sin x / (x cos x). As x → 0, sin x / x → 1 and cos x → 1, so tan x / x = (sin x / x) * (1 / cos x) → 1 * 1 = 1.

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