# How do you find the limit of #(sin12x)/x# as x approaches zero?

Use L'Hôpital's rule with

L'Hôpital's rule says that if:

then

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To find the limit of (sin12x)/x as x approaches zero, we can use the limit definition of the derivative. By taking the derivative of sin(12x) with respect to x, we get 12cos(12x). Evaluating this derivative at x=0 gives us 12cos(0) = 12. Therefore, the limit of (sin12x)/x as x approaches zero is 12.

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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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