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Math Help - Delta-Epsilon Proof

  1. #1
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    Delta-Epsilon Proof

    I have been given some homework in my precal class involving delta-epsilon proofs. I understand how to do them for the most part, but I am confused about proving the limit of a horizontal line.

    Here is one of the problems he gave us:
    lim 3
    x->6

    We are supposed to prove it, but the method he has taught us to follow does not seem to work. I hope it isn't something really simple i just haven't thought about but nobody in the class has figured it out definitively in the two days we have had to work on the problems while our teacher has been away at workshops.
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Jnorman223 View Post
    I have been given some homework in my precal class involving delta-epsilon proofs. I understand how to do them for the most part, but I am confused about proving the limit of a horizontal line.

    Here is one of the problems he gave us:
    lim 3
    x->6

    We are supposed to prove it, but the method he has taught us to follow does not seem to work. I hope it isn't something really simple i just haven't thought about but nobody in the class has figured it out definitively in the two days we have had to work on the problems while our teacher has been away at workshops.
    By Delta-Epsilon proofs do you mean

    \forall\epsilon>0,\exists\delta>0\text{such that}:If0<|x-6|<\delta,then|(3)-3|<\epsilon
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  3. #3
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    yes, he has had us work them by setting the |f(x)-L| equal to the |x-a|. I am not sure how to go about validly solving it in this situation though.
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Jnorman223 View Post
    yes, he has had us work them by setting the |f(x)-L| equal to the |x-a|. I am not sure how to go about validly solving it in this situation though.
    Show us your work as of now and we will help you the best we can
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  5. #5
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    that's the thing...im not sure what to do. The instructor has only gone over these once and it was with functions such as x+3 or simple quadratics.

    Following the steps that worked for the other problems we had, I would need to get |(3)-3| equal to |x-6| thus finding delta in terms of epsilon.
    The only thing i can come up with is...
    |(3)-3|<epsilon
    0<epsilon
    |x-6|<epsilon+|x-6|
    delta=epsilon+|x-6|
    epsilon and delta are just the associated variables but i dont know how to enter the actual character.

    This doesn't seem right, but I am at a complete loss as to what I should do.
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  6. #6
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Jnorman223 View Post
    that's the thing...im not sure what to do. The instructor has only gone over these once and it was with functions such as x+3 or simple quadratics.

    Following the steps that worked for the other problems we had, I would need to get |(3)-3| equal to |x-6| thus finding delta in terms of epsilon.
    The only thing i can come up with is...
    |(3)-3|<epsilon
    0<epsilon
    |x-6|<epsilon+|x-6|
    delta=epsilon+|x-6|
    epsilon and delta are just the associated variables but i dont know how to enter the actual character.

    This doesn't seem right, but I am at a complete loss as to what I should do.
    This link will help you more than I can because it has 10 or so examples..
    http://www.math.jmu.edu/~taal/235_20...silondelta.pdf
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  7. #7
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    If \varepsilon  > 0 then 0 = \left| {3 - 3} \right| < \varepsilon for any \delta what so ever. Your done.
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