How do you find #lim sin(1/x)# as #x->0#?
The limit does not exist.
graph{sin(1/x) [-2.38, 3.094, -1.216, 1.522]}
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To find the limit of sin(1/x) as x approaches 0, we can use the squeeze theorem. Since the range of the sine function is between -1 and 1, we can conclude that -1 ≤ sin(1/x) ≤ 1 for all x ≠ 0. As x approaches 0, the function oscillates infinitely between -1 and 1. Therefore, the limit of sin(1/x) as x approaches 0 does not exist.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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