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How can I find the limit of the integral?

  1. Aug 9, 2017 #1
    1. The problem statement, all variables and given/known data
    Hi! I need to find the limit when x-> +infinity of (integral from x to x^2 of (sqrt(t^3+1)dt))/x^5

    2. Relevant equations


    3. The attempt at a solution
    The integral of (sqrt(t^3+1)dt) can only be estimated, so sqrt(t^3+1)=(t^(3/2))*sqrt(1+1/t^3) should I use the maclaurin series first for the function sqrt(1 + 1/t^3) (but f`(0) = infinity and I also can`t use maclaurin series for sqrt(t^3+1) as t is infinity) and then take integral for the first several elements? please help, I don`t understand how should I solve this problem.
    P.S. Sorry for my bad English :/
     

    Attached Files:

  2. jcsd
  3. Aug 9, 2017 #2

    Dick

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    Homework Helper

    Have you thought about trying to apply l'Hopital's theorem?
     
  4. Aug 9, 2017 #3
    You need neither Maclaurin nor l'Hopital, this question is much simpler.
    For very large x, the integral must be essentially the integral over t^(3/2) (Though you may want to find a solid reasoning for that, for example with a Taylor series). The rest is very simple.
     
  5. Aug 9, 2017 #4
    Thank you very much!) Such a simple solution)
     
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