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1. Homework Statement
Consider the sequence a_n = abs(sin(x))^(1/x)
Find the lim a_n if it exists
2. Homework Equations
None. This is for my calc 2 class.
3. The Attempt at a Solution
We are studying the sandwich theorem, so I thought 0 < M^(1/x) < abs(sin(x))^(1/x) < 1^(1/x).
(Because I assumed that sequences imply x = 1, 2, 3, 4 ..., so sin(x) never equals 0).
Since M^(1/x) and 1 both tend to 1, I reasoned a_n must go to 1.
Consider the sequence a_n = abs(sin(x))^(1/x)
Find the lim a_n if it exists
2. Homework Equations
None. This is for my calc 2 class.
3. The Attempt at a Solution
We are studying the sandwich theorem, so I thought 0 < M^(1/x) < abs(sin(x))^(1/x) < 1^(1/x).
(Because I assumed that sequences imply x = 1, 2, 3, 4 ..., so sin(x) never equals 0).
Since M^(1/x) and 1 both tend to 1, I reasoned a_n must go to 1.
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