Compute lim_{x->0} sin(2x)/x.

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Multiple Choice

Compute lim_{x->0} sin(2x)/x.

Explanation:
The key idea is the standard limit sin t / t → 1 as t → 0. Rewrite the expression as [sin(2x)/(2x)] · 2. As x → 0, 2x → 0, so sin(2x)/(2x) → 1, and the whole expression tends to 2. Equivalently, with u = 2x, you get sin(2x)/x = sin u /(u/2) = 2 · (sin u / u) → 2.

The key idea is the standard limit sin t / t → 1 as t → 0. Rewrite the expression as [sin(2x)/(2x)] · 2. As x → 0, 2x → 0, so sin(2x)/(2x) → 1, and the whole expression tends to 2. Equivalently, with u = 2x, you get sin(2x)/x = sin u /(u/2) = 2 · (sin u / u) → 2.

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