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Thread: Limit of Quotients help

  1. #1
    Newbie
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    Limit of Quotients help

    I've just started my semester of Calculus and I find limits relatively easy except for these type of questions. Any help would be appreactied, I just need to see it worked out and then I would understand it.

    Lim 1/x-1 + 1/x+1 DIVIDED BY x
    x-0

    I got to:

    lim 1/x-1 + 1/x+1
    x-0
    DIVIDED BY
    lim x
    x-0


    but I dont know what to do after.


    Thanks!
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  2. #2
    MHF Contributor chisigma's Avatar
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    near Piacenza (Italy)
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    If the requested limit is...

    $\displaystyle \displaystyle \lim_{x \rightarrow 0} \frac{\frac{1}{x-1}+\frac{1}{x+1}}{x}$ (1)

    ... then the most confortable way is to use the elementary algebra...

    $\displaystyle \displaystyle \frac{\frac{1}{x-1}+\frac{1}{x+1}}{x}= \frac{\frac{x+1+x-1}{x^{2}-1}}{x}= \frac{\frac{2x}{x^{2}-1}}{x}= \frac{2}{x^{2}-1}$ (2)

    May be that the requested limit is different from (1)... in any case the Latex is very useful to avoid misundestanding ...

    Kind regards

    $\displaystyle \chi$ $\displaystyle \sigma$
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  3. #3
    Senior Member BAdhi's Avatar
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    Gampaha, Sri Lanka
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    I guess this what your question is,

    [tex]\lim_{x\rightarrow 0}\frac{\frac{1}{x-1}+\frac{1}{x+1}}{x} [\tex]

    if so, simplify and get the following, and rest will be much easy

    $\displaystyle lim_{x\rightarrow 0} \frac{2}{x^2-1}$
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