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

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To find the limit of (x^(3 sin x)) as x approaches 0, we can use the concept of L'Hôpital's Rule. By taking the natural logarithm of the expression, we can rewrite it as (3 sin x) ln(x). Applying L'Hôpital's Rule, we differentiate the numerator and denominator with respect to x. The derivative of 3 sin x is 3 cos x, and the derivative of ln(x) is 1/x. Taking the limit as x approaches 0, we get (3 cos 0) / (1/0), which simplifies to 3/0. Since the denominator approaches 0, and the numerator is a constant, the limit is undefined.

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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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