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Limits/continuity - finding largest delta

  1. Apr 1, 2012 #1
    Hey guys, I found this question and it started bugging me:

    find the _largest_ δ such that |x - 5| < δ => |1/x - 1/5| < 1/100.

    This is what I did to try solve the question:

    From |1/x - 1/5| < 1/100 : I got 1/x > 19/100 and so I wanted x < 100/19
    plugging that back into the first inequality it gave δ = 5/19

    But I don't think what I did is right because when I was trying values for x which satisfied this it gave answers which were over 1/100.

    So my question is how would I solve this type question.
    Any help is very much appreciated :)

    Thank you in advance!
     
  2. jcsd
  3. Apr 1, 2012 #2
    I think I know where I went wrong, what I should be doing is finding an upper bound for 1/x rather than a lower bound. The answer I now have is 5/21 and this seems to work.

    If I have gone wrong somewhere, please do point it out =]
     
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