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Math Help - Precise Definition of a Limit Problem

  1. #1
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    Precise Definition of a Limit Problem



    Here's my problem. Here's what I tried:

    |f(x)-3| < 0.6 whenever 0 < |x-5| < \delta
    |f(x)-3| < 0.6 = -0.6 < f(x)-3 < 0.6 = 2.4 < f(x) < 3.6
    The graph tells me that 2.4 < f(x) < 3.6 when 4 < x < 5.7
    What I'm not completely sure about is what to do from here.
    I think delta is 0.7, but I'm not sure how to conclude that mathematically.

    Is this problem asking to find the smallest value of delta that the limit of f(x) at x is less then 0.6 away from 3?
    Last edited by Lord Voldemort; September 26th 2009 at 12:35 PM.
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  2. #2
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    Quote Originally Posted by Lord Voldemort View Post


    Here's my problem. Here's what I tried:

    |f(x)-3| < 0.6 whenever 0 < |x-5| < \delta
    |f(x)-3| < 0.6 = -0.6 < f(x)-3 < 0.6 = 2.4 < f(x) < 3.6
    The graph tells me that 2.4 < f(x) < 3.6 when 4 < x < 5.7
    What I'm not completely sure about is what to do from here.
    I think delta is 0.7, but I'm not sure how to conclude that mathematically.

    Is this problem asking to find the smallest value of delta that the limit of f(x) at x is less then 0.6 away from 3?
    All they want you to do here is choose one of the two lines x=4 and x=5.7 as delta. The one you choose is the one closest to x=5.

    The reason being is that what you are saying is that when x is in between this line, f(x) is between the lines y=2.4 and y=3.6.

    There's no math involved here. They wanted you to do this problem graphically. If they wanted you do do this analytically, they would have said so.
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  3. #3
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    Cool, I think I actually understand these proofs now.
    Maybe this problem wasn't so useless after all.
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