liizzyliizz
  • liizzyliizz
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!
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Use L'Hopital's rule..... Or break x^3-8 as (x-2)(x^2-2x+4)
anonymous
  • 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
anonymous
  • anonymous
however, that is not how to factor

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anonymous
  • anonymous
no it is \[x^3-8=(x-2)(x^2+2x+4)\]
liizzyliizz
  • liizzyliizz
Curse my algebra skills ! D:
anonymous
  • anonymous
plus two, not minus two
anonymous
  • anonymous
oh sorry its +2x not -2x
anonymous
  • anonymous
then replace x by 2, get 4+4+4=12
liizzyliizz
  • liizzyliizz
*cry* lol these small fails will be the death of me.
liizzyliizz
  • liizzyliizz
I know how to do Limits, but the algebra part was driving me insane O.o
anonymous
  • 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 \[3\times 2^2=12\]
anonymous
  • anonymous
yeah the algebra is always the tricky part, idea is easy part
liizzyliizz
  • 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 :(

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