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Math Help - Evaluate the Following Limit

  1. #1
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    Evaluate the Following Limit

    Hi guys:

    I'm having a devil a time figuring out this problem. I could use any step-by-step help ya'll would be willing to lend:

    Evaluate the following limits:

    lim x-->14

    (sqrt of x+2) - 4 / (x-14)^2

    Thanks very much!
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  2. #2
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    Quote Originally Posted by Hamza View Post
    Hi guys:

    I'm having a devil a time figuring out this problem. I could use any step-by-step help ya'll would be willing to lend:

    Evaluate the following limits:

    lim x-->14

    (sqrt of x+2) - 4 / (x-14)^2

    Thanks very much!
    The expression can be re-written as \frac{x - 14}{(x - 14)^2} \cdot \frac{1}{\sqrt{x + 2} + 4} ....
    Last edited by mr fantastic; August 14th 2009 at 09:24 PM. Reason: Fixed an arithmetic error kindly pointed out by Matheagle by not pointing it out.
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  3. #3
    MHF Contributor matheagle's Avatar
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    using conjugates on {\sqrt{x + 2} - 4}

    I get (\sqrt{x + 2} + 4)(\sqrt{x + 2} - 4)=x+2-16=x-14

    In that case I get

    \lim_{x\to 14}{1\over (x-14)(\sqrt{x + 2} + 4)}

    which doesn't exist because you can get plus or minus infinity depending on how you approach 14.
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