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Find the limit question: Kinda confusing.

  1. Sep 23, 2012 #1
    1. The problem statement, all variables and given/known data

    Image here shows the question:

    3538hfq.png

    2. Relevant equations



    3. The attempt at a solution

    I thought the answer would be limit = infinity

    I dont understand how to find the limit to this question.
     
  2. jcsd
  3. Sep 23, 2012 #2

    jbunniii

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    Try simplifying the expression |4 - x| / (x - 4). Consider two cases separately: x < 4 and x > 4.
     
  4. Sep 23, 2012 #3
    Thats what I did. I got to x < 4 and x > 4

    After that, what do I do?
     
  5. Sep 23, 2012 #4
    isnt this undefined?
     
  6. Sep 23, 2012 #5

    jbunniii

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    What were your results?

    What is |4 - x| / (x - 4) when x < 4?

    What is |4 - x| / (x - 4) when x > 4?
     
  7. Sep 23, 2012 #6
    My results were -1
     
  8. Sep 23, 2012 #7

    jbunniii

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    For both cases? If so, the limit would be -1.

    However, you made a mistake in one of the cases.
     
  9. Sep 23, 2012 #8
    I did???
     
  10. Sep 23, 2012 #9

    jbunniii

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    You did, if you got -1 for both cases.

    To see what went wrong, please answer these two questions:

    What does |4 - x| simplify to, if x > 4?
    What does |4 - x| simplify to, if x < 4?

    Your answers shouldn't contain any absolute values.
     
  11. Sep 23, 2012 #10
    What does |4 - x| simplify to, if x > 4?
    What does |4 - x| simplify to, if x < 4?

    I am sorry, I dont understand :(
     
  12. Sep 23, 2012 #11
    I think what is messing me up is the absolute value bars
     
  13. Sep 23, 2012 #12
    The absolute value function is defined as:

    |a| = -a if a<0
    |a| = a if a>=0

    This is what you have to work with.
     
  14. Sep 23, 2012 #13
    Ahhh...So, then my calc comes out as -1 and 1, therefore it does not equal so its undefined?
     
  15. Sep 23, 2012 #14

    jbunniii

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    Correct, the limit from the left doesn't equal the limit from the right, so the overall limit does not exist.
     
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