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Math Help - A limit proof

  1. #1
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    Acolman, Mexico
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    A limit proof

    Hi,

    I am having a hard time trying to prove this.

    If,
    lim f(x) = L and f(x)>0, then L>=0.
    x->a

    (I am supposed to prove it by contradiction)
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  2. #2
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    Quote Originally Posted by akolman View Post
    Hi,

    I am having a hard time trying to prove this.

    If,
    lim f(x) = L and f(x)>0, then L>=0.
    x->a

    (I am supposed to prove it by contradiction)
    If L<0 then there exists \epsilon > 0 so that L+\epsilon < 0. This means there exists \delta > 0 so that for all 0<|x-a|<\delta we have f(x) < L + \epsilon < 0 and so f(x) < 0 on (a-\delta,a+\delta)\setminus \{ a\}.
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