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Math Help - limit (MVT)

  1. #1
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    limit (MVT)

    show that Show that cosx>1-(x/2) "x>0 o "x<0
    hint:for x>0, you can use Mean value theorem for f(x)=cosx+(x/2) on [0,x]

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  2. #2
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    Re: limit (MVT)

    I think the best method is to use Taylor's Theorem - it gives the expansion for \cos{x} in powers of x as 1-\frac{x^2}{2}. The error term is \frac{c^4}{24} where c is some number between x and 0. Since this error term is positive, \cos{x}>1-\frac{x^2}{2} for all x\ne{0}.

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