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Math Help - Analysis epsilon delta limit

  1. #1
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    Analysis epsilon delta limit

    I'm having trouble knowing how to rearrange the inequality
    The question is

    Using epsilon, delta methods show that

    lim f(x)= 2+x/x^2 = 3
    {x->1}

    I've gotten as far as saying | 2+x/x^2 - 3 | < epsilon

    so is the delta part.. 0 < x-1 < delta ?????

    I know all the steps but can't reach an inequality i'm happy with... I don't want to continue if i'm doing it wrong, time is of the essence!

    Do I have to make the epsilon inequality similar to the delta one when i relate them? Or have I got it all wrong

    Any help would be very much appreciated!

    Thank you
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  2. #2
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    Quote Originally Posted by DBsHo View Post
    I'm having trouble knowing how to rearrange the inequality
    The question is

    Using epsilon, delta methods show that

    lim f(x)= 2+x/x^2 = 3
    {x->1}

    I've gotten as far as saying | 2+x/x^2 - 3 | < epsilon

    so is the delta part.. 0 < x-1 < delta ?????

    I know all the steps but can't reach an inequality i'm happy with... I don't want to continue if i'm doing it wrong, time is of the essence!

    Do I have to make the epsilon inequality similar to the delta one when i relate them? Or have I got it all wrong

    Any help would be very much appreciated!

    Thank you
    Start by noting that \left| \frac{2 + x}{x^2} - 3\right| = \left| \frac{(3x + 2)(x - 1)}{x^2}\right|.

    And you might want to read this: http://www.mathhelpforum.com/math-he...ta-proofs.html
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