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Math Help - critical limit problem

  1. #1
    Junior Member
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    critical limit problem

    hi
    well................ this is my first thread on this site

    my name is mohamed and iam at engineering faculty first grade well i was solving an excersise preparing for my next week exam and i found tough proble i spent hours trying to solve it but i failed i wish if any one can help me here he problem is


    lim [lnX - 1]/X - e
    X tends to "e"

    and something else can any one help me howto write maths sympols here excuseme i dont do on forums alot

    thxxxxxxx
    Last edited by mr fantastic; December 27th 2008 at 06:47 AM. Reason: Got rid of the 1000 pt font etc
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by mohamedsafy View Post

    hi

    well................ this is my first thread on this site



    my name is mohamed and iam at engineering faculty first grade well i was solving an excersise preparing for my next week exam and i found tough proble i spent hours trying to solve it but i failed i wish if any one can help me here he problem is





    lim [lnX - 1]/X - e

    X tends to "e"



    and something else can any one help me howto write maths sympols here excuseme i dont do on forums alot



    thxxxxxxx
    This is an application of the derivative

    f'(c)=\lim_{x\to{c}}\frac{f(x)-f(c)}{x-c}

    So in your case f(x)=\ln(x), c=e f(c)=\ln(e)=1

    So

    \lim_{x\to{e}}\frac{\ln(x)-1}{x-e}=\left(\ln(x)\right)'\bigg|_{x=e}=\frac{1}{e}
    Last edited by mr fantastic; December 27th 2008 at 06:49 AM. Reason: Edited quote to match edited post
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  3. #3
    Junior Member
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    thxxxxx

    thxx alot that was sooo helpful
    Last edited by mr fantastic; December 27th 2008 at 06:49 AM. Reason: Deleted excessive use of smilies.
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