what is limit (x^3-8)/(x-2) if x go to 2?

Expert Answers

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We going to calculate this limit just putting the value of the limit in place of x:

`lim(x->2) (x^3-8)/(x-2) = (8-8)/(2-2) =>`  `lim(x->2) (x^3-8)/(x-2) = 0/0`

The limit didn't work so we will try factoring.

By factoring (`x^3-8` ) in `(x - 2)(x^2+4x+4)`  we get:

`lim(x->2) (x - 2)(x^2+4x+4)/(x - 2) = lim(x->2) (x^2+4x+4)`

We  will put the value of the limit in place of x:

`lim(x->2) (x^2+4x+4)= 16`

Your answer is `lim(x->2) (x^3-8)/(x-2) = 16.`

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