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!

Question

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!

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

however, that is not how to factor

anonymous · Answer

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

liizzyliizz · Answer

Curse my algebra skills ! D:

anonymous · Answer

plus two, not minus two

anonymous · Answer

oh sorry its +2x not -2x

anonymous · Answer

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

liizzyliizz · Answer

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

liizzyliizz · Answer

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

anonymous · Answer

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

anonymous · Answer

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

liizzyliizz · Answer

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 :(