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Homework Help: Need some help evaluating a limit

  1. Sep 16, 2012 #1
    1. The problem statement, all variables and given/known data

    [tex] \lim_{t→∞}\frac{sin (t)}{\sqrt{t}} [/tex]

    2. Relevant equations

    3. The attempt at a solution
    This was actually part of a larger problem about improper integrals. The problem has been reduced to this, but I have no idea how to proceed from here. I know that sin(x) behaves very bizarrely at infinity, so I don't know if L'Hopital's rule can even be applied here.

    My intuition tells me that the answer is 0, but how can we prove this? Must we refer to the ε-δ definition?

  2. jcsd
  3. Sep 16, 2012 #2
    What are the maximum and minimum possible values that sin(t) can ever achieve?
  4. Sep 16, 2012 #3


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    Staff Emeritus
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    Use the squeeze theorem.

    What's [itex] \lim_{t→∞}\ 1/\sqrt{t}\ ?[/itex]

    How about giving us the entire problem?
  5. Sep 16, 2012 #4
    Are you familiar with the squeeze theorem?
  6. Sep 16, 2012 #5
    Ah, good old squeeze theorem why didn't I think of that?

    Thanks guys!

  7. Sep 16, 2012 #6
    The original problem (for Sammy):

    [tex] \int^{π}_{0}\frac{dt}{\sqrt{t}+sin(t)} [/tex]

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