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lim_(θ→0) sin(θ/2) / θ is

1. 0.5
2. 1
3. 2
4. not defined

Correct answer: 0.5

Solution

As θ approaches 0, the limit can be evaluated using the small angle approximation for sine, where sin(x) is approximately equal to x. Thus, sin(θ/2) approaches θ/2, leading to the limit simplifying to (θ/2) / θ, which equals 0.5.

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