# How do you find the limit of # (sin^4 x)/(x^4)# as x approaches 0?

A very important limit is that:

Thus,

Note that we used the rule

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To find the limit of (sin^4 x)/(x^4) as x approaches 0, we can use L'Hôpital's Rule. Taking the derivative of the numerator and denominator separately, we get 4sin^3 x * cos x and 4x^3, respectively. Evaluating these derivatives at x = 0, we find that the limit is 0.

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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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