As x approaches 0, what is the limit of sin(2x)/x?

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Multiple Choice

As x approaches 0, what is the limit of sin(2x)/x?

Explanation:
The limit hinges on the standard small-angle behavior of sine: as y approaches 0, sin(y) behaves like y, so sin(y)/y → 1. If we set y = 2x, then as x → 0, y → 0 and sin(2x)/(2x) → 1. Therefore sin(2x)/x = [sin(2x)/(2x)] · 2 → 1 · 2 = 2. The limit is 2.

The limit hinges on the standard small-angle behavior of sine: as y approaches 0, sin(y) behaves like y, so sin(y)/y → 1. If we set y = 2x, then as x → 0, y → 0 and sin(2x)/(2x) → 1. Therefore sin(2x)/x = [sin(2x)/(2x)] · 2 → 1 · 2 = 2. The limit is 2.

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