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Math Help - Finding f(x) and g(x) - limit

  1. #1
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    Finding f(x) and g(x) - limit

    Hi again, after a loong brake. Hope, i posted this question to right forum(calculus).
    Question is;

    \displaystyle \lim_{x \to a} f(x) DNE

    \displaystyle \lim_{x \to a} g(x) Converges

    \displaystyle \lim_{x \to a} f(x) - g(x) Converges

    Find f(x) and g(x).

    Last edited by Lafexlos; December 17th 2010 at 08:27 PM.
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    f(x)=1/x , g(x)=x , a=0
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  3. #3
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    i think "a" should remain as itself, and that way your answer converts to this.
    f(x)=1/(x-a) and g(x)=(x-a)
    when you appy this to f(x)-g(x);

     \displaystyle \lim_{x \to a} f(x) - g(x) = \lim_{x \to a} \frac {1-(x-a)^2}{x-a}

    i couldn't understand how it's converges.
    btw, my head is really full today, cuz of exams. so if it's answer is too easy sorry for bothering.
    edit: and sorry again for my bad grammer. =)
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  4. #4
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by Also sprach Zarathustra View Post
    f(x)=1/x , g(x)=x , a=0
    I don't think this works...
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  5. #5
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    I don't think it is possible.

    If the limit of f(x) - g(x) and g(x) exists, then the limit of f(x) = (f(x) - g(x)) + g(x) exists.
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  6. #6
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    I don't know if it is possible.
    Not nice example:

    f(x):
    1 for rational
    0 for irrational

    g(x):
    1 for rational.

    And
    f(x)-g(x) for rational.
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  7. #7
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    Quote Originally Posted by zzzoak View Post
    I don't know if it is possible.
    Not nice example:

    f(x):
    1 for rational
    0 for irrational

    g(x):
    1 for rational.
    What is g for x irrational? If you mean that g is not defined for x irrational then \lim_{x\to a} g(x) does not exist. In order that \displaytype\lim_{x\to a} g(x) exist, you would have to have g(x)= 1 for x irrational also (at least close to a) and in that case, \lim_{x\to a} f(x)- g(x) would not exist.

    And
    f(x)-g(x) for rational.
    Again, not defined for irrational x and so the limit would not exist.

    There are no such f and g for the reason snowtea cited.
    Last edited by HallsofIvy; December 18th 2010 at 05:37 AM.
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  8. #8
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    Thanks guys. Really helped.
    My friend -who asked question- missed some information. After i get all information, if i still cant solve, i'll ask again with no missing info.
    Sorry for taking your time. =/
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