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Math Help - Limits and negative infinity

  1. #1
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    Limits and negative infinity

    Hello, my name is Erik and I知 looking for help regarding an explanation (or a proof) of why the following concept is true. (My teacher cannot give me one and neither can the calculus manual, they both simply state that this is just how it is)

    problem:
    img508.imageshack.us/img508/4498/problemap1.gif

    I知 not sure I知 using the correct notation in solving this problem but really what I知 looking for is the proof or explanation why this is possible and why this is how it should be solved.

    Thanks

    Erik
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  2. #2
    Eater of Worlds
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    Are you wondering why it is divided by -x?.

    It is helpful to manipulate the function so that powers of x become powers of 1/x.

    This can be done by dividing the numerator and denominator by

    \sqrt{x^{2}}=|x|

    Since x\rightarrow{-\infty}, the values of x are eventually negative, so we can replace |x| by -x where desireable.

    Does that help any?.
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  3. #3
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    Quote Originally Posted by galactus View Post
    Are you wondering why it is divided by -x?.

    It is helpful to manipulate the function so that powers of x become powers of 1/x.

    This can be done by dividing the numerator and denominator by

    \sqrt{x^{2}}=|x|

    Since x\rightarrow{-\infty}, the values of x are eventually negative, so we can replace |x| by -x where desireable.

    Does that help any?.
    I understand why we have to divide by -x my question is more or less why this can be done. How could i communicate that since x->-inf i can write x as -x? If im understanding this right i might as well write -x as x since it is just variables. But this does not work since if i write it as x i wont solve it properly.

    Thanks alot

    Erik
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    You can do this

    Quote Originally Posted by tyro89 View Post
    I understand why we have to divide by -x my question is more or less why this can be done. How could i communicate that since x->-inf i can write x as -x? If im understanding this right i might as well write -x as x since it is just variables. But this does not work since if i write it as x i wont solve it properly.

    Thanks alot

    Erik
    You can do this using the definition of |x|... |x|=-x,\forall{x}<0 and |x|=x,\forall{x}>0
    Last edited by Mathstud28; April 14th 2008 at 05:33 PM.
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  5. #5
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    Quote Originally Posted by Mathstud28 View Post
    You can do this using the definition of |x|... |x|=-x,\forall{x}<0 and |x|=x,\forall{x}>0
    Thanks a lot i get it now
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