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Need help with limit question

  1. Feb 24, 2012 #1
    1. The problem statement, all variables and given/known data
    Lim x^2-16/4-x
    x→4


    2. Relevant equations



    3. The attempt at a solution

    I factored it, and ended up with (x-4)(x+4)/(4-x)

    Cant cancel anything out, so I plug in 4 back into it, and end up with 8 as the limit. But the book says that the answer is -8?
     
  2. jcsd
  3. Feb 24, 2012 #2

    SammyS

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    What is -(x-4) ?
     
  4. Feb 24, 2012 #3
    Wouldnt that just be 0? Also why is there a - before the (x-4)?
     
  5. Feb 24, 2012 #4

    Mark44

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    Why do you think it would be zero?

    Hint: Distributive property.

    As a side note, if you have a hard time understanding how -(x - 4) might possibly be related to 4 - x, I think you will have a really hard time in more advanced topics such as limits.
     
  6. Feb 24, 2012 #5

    SammyS

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    I'm not asking you to take the limit of -(x-4).

    Simplify -(x-4).

    Alternatively, factor a (-1) out of (x-4).
     
  7. Feb 24, 2012 #6
    Where did you get the - before the (x-4) though?
     
  8. Feb 24, 2012 #7

    SammyS

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    Don't worry about that until you answer the question I asked.

    It may be clear to you after that.
     
  9. Feb 24, 2012 #8
    So if i distribute the - it will be -x+4, which cancels with the denominator, and im left with x+4. I plug in 4 for x and get 8?
     
  10. Feb 24, 2012 #9

    SammyS

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    Almost correct.

    Yes, you're right about -(x-4) = -x + 4. Of course that is the same as 4 - x .

    So rewrite your expression with a denominator of -(x - 4).

    Do you see why I had the "-" sign out front of the (x-4) in my previous posts?
     
  11. Feb 24, 2012 #10

    Sorry..I just cant understand how the "-" sign came out of nowhere, and why i have to rewrite the denominator as -(x-4)
     
  12. Feb 24, 2012 #11

    SammyS

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    Didn't you determine that -(x-4) is -x + 4 ?

    Well, that's the same as 4 - x, which is the denominator.

    4 - x is the same as -(x - 4).

    So, replace the denominator, which is 4 - x, with -(x - 4) because they're equivalent.

    In general, a - b = -(b - a) .
     
  13. Feb 24, 2012 #12
    So then wouldnt they both cancel anyways leaving me with just (x+4)?
     
  14. Feb 24, 2012 #13

    SammyS

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    If the denominator is -(x-4) then there is also a "-" sign left uncancelled.
     
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