# How do you find the limit of # (sin 3x)/ (sin 4x)# as x approaches 0?

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Rewrite the expression to use the limits noted above.

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To find the limit of (sin 3x) / (sin 4x) as x approaches 0, we can use the concept of L'Hôpital's Rule. By applying this rule, we differentiate the numerator and denominator separately with respect to x.

Differentiating the numerator, we get: d/dx (sin 3x) = 3cos 3x.

Differentiating the denominator, we get: d/dx (sin 4x) = 4cos 4x.

Now, we can evaluate the limit by substituting x = 0 into the derivatives we obtained:

lim (x→0) (3cos 3x) / (4cos 4x).

Plugging in x = 0, we have:

(3cos 0) / (4cos 0) = 3/4.

Therefore, the limit of (sin 3x) / (sin 4x) as x approaches 0 is 3/4.

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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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