# How do you find #lim_(xtooo)(Cos(x)/x)#?

Because the upper bound of cos(x) is 1 and the lower bound is -1:

We know the limits of the two bounds to be 0:

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It should tend to zero.

graph{(cos(x))/x [-10, 10, -5, 5]}

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Hence

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To find the limit of (cos(x)/x) as x approaches infinity, we can use L'Hôpital's rule. Taking the derivative of the numerator and denominator separately, we get (-sin(x)/1). As x approaches infinity, sin(x) oscillates between -1 and 1, so the limit of (-sin(x)/1) as x approaches infinity does not exist. Therefore, the limit of (cos(x)/x) as x approaches infinity is also undefined.

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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.

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