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Finding Delta

  1. Oct 17, 2007 #1
    1. The problem statement, all variables and given/known data

    Find a delta such that |f(x)-l|< epsilon for all x satisfying 0<|x-a|< delta

    f(x)=(x^4)+(1/x); a=1; l=2

    2. Relevant equations

    Lemma Theorem

    3. The attempt at a solution

    0<|x-1|<delta; |(x^4)+(1/x)-2|<epsilon

    |x^4-1|<epsilon/2 and |(1/x)-1|<epsilon/2

    Then I applied third item of the Lemma which is

    if y0 not equal to 0;

    |y-y0|<min(|y0|/2,(epsilon*|y0|^2)/2)

    then y not equal to 0 and;

    |(1/y)-(1/y0)|<epsilon



    Then I concluded that the |(1/x)-1|<epsilon/2 part of the solution as;

    |x-1|<min(1/2,epsilon/2)

    However, I could not find any approach for the |x^4-1|<epsilon/2

    Which method shall I apply here?

    Any helps will be appreciated.
     
  2. jcsd
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