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# Calculus/-

Question
I am taking Calculus and I am trying to learn ahead a bit (super-nerd), but I am having trouble with this problem.

Find the lim of (x^(3)-8)/(x^(2)-4) when x->2 (I believe this means when x approaches 2?)

Hi John,
The best way to do it would be by factorization;
x³ - 8 = (x - 2)(x² + 2x + 4)
x² - 4 = (x - 2)(x + 2)
So,
lim x→2 [(x³ - 8 / x² - 4) / (x² - 4)] = lim x→2 [(x - 2)(x² + 2x + 4) / (x - 2)(x + 2)]
= lim x→2 [(x² + 2x + 4) / (x + 2)]
= (2² + 2(2) + 4) / (2 + 2)
= 12/4
= 3

Regards

Calculus

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