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Math Help - SUP/inf question..

  1. #1
    MHF Contributor
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    SUP/inf question..

    i need to find the sup and the inf of

    <br />
f(x)=1/(1+(ln x)^2 )<br /> <br />

    i can find the limit for the function for + infinity
    and - infinity

    but what to do next?
    the sup is the least upper bound
    the limit for +infinity is not SUP
    ??
    Last edited by transgalactic; December 18th 2008 at 08:23 AM.
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  2. #2
    MHF Contributor
    Joined
    Nov 2008
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    France
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    Hi

    f is defined on ]0,+oo[
    f is increasing on ]0,1] and decreasing on [1,+oo[
    The limit for 0 is 0
    The limit for +oo is 0
    f(1) = 1
    Therefore inf f = 0 and sup f = max f = 1
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