## liizzyliizz 4 years ago lim x^3-8/x-2 as x ->2 i know this is easy. but by hand im not getting 12 as the answer. (Something with my factoring i bet) but im tired and i cant think straight help!

1. anonymous

Use L'Hopital's rule..... Or break x^3-8 as (x-2)(x^2-2x+4)

2. anonymous

factor the numerator as the difference of two cubes and cancel, as notsobright wrote. you probably have not made it to l'hopital yet

3. anonymous

however, that is not how to factor

4. anonymous

no it is $x^3-8=(x-2)(x^2+2x+4)$

5. liizzyliizz

Curse my algebra skills ! D:

6. anonymous

plus two, not minus two

7. anonymous

oh sorry its +2x not -2x

8. anonymous

then replace x by 2, get 4+4+4=12

9. liizzyliizz

*cry* lol these small fails will be the death of me.

10. liizzyliizz

I know how to do Limits, but the algebra part was driving me insane O.o

11. anonymous

soon you will be able to do this in your head. you will say "the derivative of $x^3-8$ is $3x^2$ and $3\times 2^2=12$

12. anonymous

yeah the algebra is always the tricky part, idea is easy part

13. liizzyliizz

yeah I understand the calculus part and the concepts. its the factoring that i mess up in, and those negative signs get to me all the time :(