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Homework Help: Limit ln function + ln rules

  1. May 22, 2010 #1
    1. The problem statement, all variables and given/known data

    Find limit lim x->0+ of lnx+1/x

    2. Relevant equations

    1/x = ln e^1/x

    3. The attempt at a solution

    ln x + ln e^1/x = ln x*e^(1/x)
    lim x-> 0+

    ln x + ln e^1/x = ln 0*inf = ln 0 = - inf
    lim x-> 0+

    Source: my self vs http://www.numberempire.com/limitcalculator.php
     

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  2. jcsd
  3. May 22, 2010 #2
    Re: Limit ln function + ln rules - Wolfram Mathematica answers...

    above, pitcure of mathematica solution..
     

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  4. May 22, 2010 #3

    gabbagabbahey

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    [tex]\lim_{x\to x_0} f(x)g(x)=\left(\lim_{x\to x_0} f(x)\right)\left(\lim_{x\to x_0}g(x)\right)[/tex]

    The above property is only true if both the individual limits exist (are finite). But, [tex]\lim_{x\to 0^+}e^{1/x}=\infty[/itex] which isn't finite, and so you can't claim that

    [tex]\lim_{x\to 0^+}xe^{1/x}=\left(\lim_{x\to 0^+}x\right)\left(\lim_{x\to 0^+}e^{1/x}\right)=(0)(\infty)=0[/tex]
     
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