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Limits and finding a constant value 'k'

  1. Sep 25, 2007 #1
    Stick with me here, I don't know how to use something to add an equation in here!

    1. The problem statement, all variables and given/known data

    Find a value of the constant k such that the limit exists:

    lim x->4 (x^2 - k^2) / (x-4)

    3. The attempt at a solution

    I KNOW the solution is the limit will exist iff k = -4 and k = 4.

    My problem is - does the numerator have to cancel out the denominator in order for a limit to exist? Or is that just the case here?

    Cause the solution is:


    So the only way for the denominator (x-4) to cancel out would be if k = -4 or 4... so i'm just wondering if that's a general rule?

  2. jcsd
  3. Sep 25, 2007 #2


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    The rule is that if the denominator goes to zero, the only way you can have a limit is if the numerator also goes to zero. For reasons that should be obvious if you think about how division works.
  4. Sep 25, 2007 #3


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    Staff Emeritus
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    Go back and review the limit theorems. Pay particular attention to the details on the one for division; a surprising number of people completely ignore them, and then have trouble dealing with limits that have a division in them. :frown:

    By applying the fact the limit exists, you should be able to determine something about the thing of which you're taking the limit.
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