# How do you find the Limit of #(sin^3 x) / (sin x - tan x)# as x approaches 0?

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To find the limit of (sin^3 x) / (sin x - tan x) as x approaches 0, we can use L'Hôpital's Rule. Taking the derivative of the numerator and denominator separately, we get (3sin^2 x * cos x) / (cos^2 x - sec^2 x). Simplifying further, we have (3sin^2 x * cos x) / (-sin^2 x). Canceling out the sin^2 x term, we are left with 3cos x / -1, which simplifies to -3cos x. Evaluating this expression as x approaches 0, we find that the limit is -3.

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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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