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Homework Help: Find delta from a particular epsilon

  1. Jun 1, 2010 #1
    I'm learning how to find delta from a particular epsilon. I'm not understanding a step in the solution for the problem listed below:

    Here's the problem:
    lim(x→3)x^2=9

    Solution:
    |x^2-9|<.05
    -.05<x^2-9<.05
    2.9916..<x<3.0083
    2.9916..-3<x-3<3.0083..-3
    -.0083..<x-3<.0083..
    delta=.0083

    I don't understand how:
    8.95<x^2<9.05
    calculates to:
    2.9916..<x<3.0083..
    Could someone please explain this to me.. in simple terms. Cheers!
     
  2. jcsd
  3. Jun 1, 2010 #2

    Mark44

    Staff: Mentor

    Take the square root of each member.
     
  4. Jun 1, 2010 #3
    Ah.. I guess I was looking at it for so long that I overlooked the obvious. Thanks for the help!
     
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