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A question about uniform continuity (analysis)

  1. Dec 16, 2012 #1
    1. The problem statement, all variables and given/known data

    For question 19.2 in this link:

    http://people.ischool.berkeley.edu/~johnsonb/Welcome_files/104/104hw7sum06.pdf [Broken]

    I came up with a different proof, but I'm not sure if it is correct...

    2. Relevant equations



    3. The attempt at a solution

    Let [tex]|x-y|< \delta[/tex]

    For [tex]|f(x)-f(y)| = |x^2 - x^y| = |x-y||x+y| < \delta|x+y|[/tex], we know that the largest that |x+y| can be is 6. So if we let [tex]\delta= \epsilon/6 [/tex]...

    We will have

    [tex] |f(x)-f(y)| = |x^2 - x^y| = |x-y||x+y| < \delta|x+y| < (\epsilon/6)(6) = \epsilon [/tex]

    If this is true for the largest possibility, then it must be possible for all of them...

    Do you think my answer is correct, or is there something that I'm missing?

    Thanks in advance
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Dec 16, 2012 #2

    mfb

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    Staff: Mentor

    The last < should be a <=, but apart from that it is fine.
     
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