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Homework Help: Increasing Sequence

  1. Nov 5, 2005 #1
    Suppose f:[a,b)->R is such that lim(x->b-)=+inf. Prove that there exists an increasing sequence {x_n} in (a,b) such that f(x_n)>n for all n.

    I don't know where to start. It would be easy if I can prove that f is strictly increasing after some point. f might not be continuous so I can't simply look for all f(x) in the form x^2 or something... Too many possibilities. Any pointers will be helpful!
    Last edited by a moderator: Nov 5, 2005
  2. jcsd
  3. Nov 5, 2005 #2


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    Homework Helper

    What do you have for a definition of lim(x->b-)=+inf ? This will tell you where to start.
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