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Math Help - Prove using epsilon - delta definition of a limit?

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    Prove using epsilon - delta definition of a limit?

    How can I prove lim x->1 (x^2 + 4x) = 5 and lim x->2 (1/x^2) = 1/4 using the epsilon - delta definition of a limit?
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    MHF Contributor FernandoRevilla's Avatar
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    For example:

    |x^2+4x-5|<\epsilon \Leftrightarrow \ldots \Leftrightarrow |x-1||x+5|<\epsilon

    Now, use that |x+5| is bounded on [0,2] .


    Fernando Revilla
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    why bounded on [0,2]? How did you get these intervals? And why |x + 5|? Why not x-1?
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    Quote Originally Posted by colerelm1 View Post
    why bounded on [0,2]? How did you get these intervals? And why |x + 5|? Why not x-1?
    Because the limit involves x\to 1, the definition will include |x-1|<\delta and not |x+5|.
    Thus you need to bound the other factor.
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