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Limits - HELP!

  1. Nov 11, 2007 #1
    1. The problem statement, all variables and given/known data

    2 Questions, both find xn as n tends to infinity.


    2. Relevant equations

    3. The attempt at a solution

    Have attempted question one but am unsure if (1/n)log(n^2) tends to 0, and if it does do i need to prove it? I dont know how to do the second q, i know that sin(expn) oscillates between -1 and 1 and exp(-n) tends to 0 as n tends to infinity
  2. jcsd
  3. Nov 11, 2007 #2


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    Staff Emeritus
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    Yes, (1/n) log(n^2) = (2/n)log(n) goes to 0. You might prove that by looking at 2ln(x)/x^2 and using L'Hopital's rule.

    As for the second one, since sin is always between -1 and 1, you really just need to show that [itex]\sqrt{n}/(n+ e^{-n})< \sqrt{n}/n[/itex] (since [itex]e^{-n}[/itex] is always positive) converges to 0.
  4. Nov 11, 2007 #3
    thanks :smile:
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