# How do you find the limit of #(((2+x)^3) -8 )/ x# as x approaches 0?

12

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To find the limit of (((2+x)^3) - 8) / x as x approaches 0, we can simplify the expression and apply the limit.

First, expand the numerator using the binomial theorem: (2+x)^3 = 8 + 12x + 6x^2 + x^3.

Next, subtract 8 from the numerator: (8 + 12x + 6x^2 + x^3) - 8 = 12x + 6x^2 + x^3.

Now, divide the simplified numerator by x: (12x + 6x^2 + x^3) / x = 12 + 6x + x^2.

Finally, take the limit as x approaches 0: lim(x→0) (12 + 6x + x^2) = 12 + 0 + 0 = 12.

Therefore, the limit of (((2+x)^3) - 8) / x as x approaches 0 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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