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Math Help - Equation

  1. #1
    Junior Member
    Joined
    Mar 2010
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    Equation

    Hi people,

    I must show that: \forall x \in \mathbb{R}: Arctanx>\frac{x}{1+x^2}

    I don't know how to do it???? can you help me please???
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  2. #2
    MHF Contributor chiph588@'s Avatar
    Joined
    Sep 2008
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    Champaign, Illinois
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    Quote Originally Posted by bhitroofen01 View Post
    Hi people,

    I must show that: \forall x \in \mathbb{R}: Arctanx>\frac{x}{1+x^2}

    I don't know how to do it???? can you help me please???
    It's only true for  x>0 .

    To prove this, show  \tan^{-1}(0)=\frac{0}{0^2+1} .

    Then look at the derivatives.

     \frac{d}{dx}\left(\tan^{-1}(x)\right) = \frac{1}{x^2+1}

     \frac{d}{dx}\left(\frac{x}{x^2+1}\right) = \frac{1}{x^2+1}-\frac{4x^2}{(x^2+1)^2}

    What does this tell you?
    Last edited by chiph588@; April 3rd 2010 at 12:21 PM.
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