# How do you find the limit of #(x^2 - 64) / ((x^(1/3)) -2)# as x approaches #8#?

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To find the limit of (x^2 - 64) / ((x^(1/3)) -2) as x approaches 8, we can substitute 8 into the expression and simplify. Plugging in 8, we get (8^2 - 64) / ((8^(1/3)) -2). Simplifying further, we have (64 - 64) / (2 - 2), which results in 0/0. This is an indeterminate form. To evaluate the limit, we can use L'Hôpital's Rule. Taking the derivative of the numerator and denominator separately, we get (2x) / (1/3 * x^(-2/3)). Simplifying this, we have 6x^(5/3). Plugging in 8, we get 6 * 8^(5/3), which equals 48. Therefore, the limit of (x^2 - 64) / ((x^(1/3)) -2) as x approaches 8 is 48.

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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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