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Lim. Sin(1/theta)
Theta-0

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Answer:

the limit of sin(1/θ) as θ approaches 0 is equal to 0.

Explanation:

To evaluate this limit:

lim θ→0 sin(1/θ)

we can use the squeeze theorem. First, we note that -1 ≤ sin(1/θ) ≤ 1 for all values of θ, since the sine function oscillates between -1 and 1.

Next, we consider the limit of two other functions, -1/|θ| and 1/|θ|, as θ approaches 0:

lim θ→0 -1/|θ| = -∞

lim θ→0 1/|θ| = ∞

Since sin(1/θ) is always between -1/|θ| and 1/|θ|, we can apply the squeeze theorem to conclude that:

lim θ→0 sin(1/θ) = 0

Therefore, the limit of sin(1/θ) as θ approaches 0 is equal to 0.

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