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One more limit

  1. Mar 23, 2008 #1
    1. The problem statement, all variables and given/known data
    lim as x goes to 1 from the right of 2^1/x-1=inf

    2. Relevant equations

    solve using delta-epsilon

    3. The attempt at a solution

    i am not sure how to prove an infinite limit, I have a defn that states, If for epsilon>0 there exists an M>0 such that x>M implies |f(x)-L|< epsilon. My main problem is that I am not sure how to do it, and how to get the power of two out of the way
  2. jcsd
  3. Mar 23, 2008 #2
    take the log
  4. Mar 23, 2008 #3
    is the definition right?
  5. Mar 23, 2008 #4
    did you mean lim x->1+ 2^(1/(1-x)) = 0?
    Last edited: Mar 23, 2008
  6. Mar 23, 2008 #5
    no the problem says it goes to inf
  7. Mar 23, 2008 #6
    Oh it's lim x->1+ 2^(1/(x-1)), which is inf yea

    The correct definition is

    lim x->a+ f(x) = inf if for all M > 0 there is a d > 0 s.t. 0 < |x-1| < d and x > 1 implies |f(x)| > M
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