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Math Help - Function

  1. #1
    Junior Member
    Joined
    Aug 2009
    Posts
    62

    Function

    Hi everybody,

    I must show that there exists a function f defined on [-1,+\infty[ such as :

    \{{(\forall x \in [-1,+\infty[)   \sqrt{1+x}=1+\frac{1}{2}x-\frac{1}{8}x^2+x^2\phi(x)\atop\lim_{x\to 0} \phi(x)=0}

    I don't know what to do, can you help me please.

    And thank you anyway.
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  2. #2
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Hi

    Let \phi(x)=\frac{   \sqrt{1+x}-\left(1+\frac{1}{2}x-\frac{1}{8}x^2\right)}{x^2}

    \phi is defined over [-1,0[ U ]0,+\infty[

    You just need to show that \lim_{x\to 0} \phi(x)=0
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