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Homework Help: Improper integral

  1. Apr 2, 2009 #1
    1. The problem statement, all variables and given/known data
    integral from 2 to infinty 1/(x-sqrt(x))
    3. The attempt at a solution
    my teacher wants us to compare it to another function in the form 1/x^p
    and not integrate it so
    would i compare it to 1/x and then do the limit comparison test
    limit as x approaches infinity
    i came out with a finite number and since 1/x divegres therefore 1/(x-sqrt(x)) diverges
    is this correct.
  2. jcsd
  3. Apr 3, 2009 #2


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    Science Advisor
    Homework Helper

    Hi cragar! :smile:

    That'll do, but you don't actually need the limit comparison test in this case, since 1/(x - √x) is always larger than 1/x :wink:
  4. Apr 3, 2009 #3
    so you are saying since it is larger than something that diverges then it to will diverge.
    i see.
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