limit as x approaches 0: sinx/x
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To evaluate the limit as x approaches 0 of sin(x)/x, we can use the squeeze theorem.
First, we know that sin(x) is always between -1 and 1, since sine is a periodic function that oscillates between these values. Therefore, -1/x ≤ sin(x)/x ≤ 1/x.
As x approaches 0, -1/x and 1/x both approach negative and positive infinity, respectively. This means that sin(x)/x is squeezed between these two functions, and also approaches infinity (or negative infinity, depending on which side of 0 you approach from).
Therefore, we can conclude that the limit as x approaches 0 of sin(x)/x equals infinity (or negative infinity).
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