# How do you evaluate the limit #tan(4x)/x# as x approaches #0#?

The limit equals

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To evaluate the limit of tan(4x)/x as x approaches 0, we can use L'Hôpital's Rule. Taking the derivative of both the numerator and denominator, we get 4sec^2(4x)/1. Substituting x=0 into this expression, we find that the limit is 4. Therefore, the limit of tan(4x)/x as x approaches 0 is 4.

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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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