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Limits Approaching Infinity

  1. Sep 27, 2008 #1
    1. The problem statement, all variables and given/known data

    Lim ((e[tex]^{2}[/tex])-([tex]\frac{t-3}{3}([/tex] * e^[tex]^{\frac{t}{3}})[/tex]))
    t -> [tex]-\infty[/tex]

    [sorry for the formatting, I tried my best! that is "The limit as t approaches negative infinity of e squared minus (t-3/3) e to the t/3)]"]
    2. Relevant equations
    I am solving improper integrals to find out if this is convergent or divergent and do not remember how to show on paper to solve for a limit.

    3. The attempt at a solution
    Well, if memory serves, the limit as we approach negative infinity is a horizontal asymptote, right? But I only remember those silly little coefficient tricks to find a horizontal asymptote. Otherwise, I'd just look on a calculator. Someone tried to explain it to me and said I should think of it as going towards positive infinity first and then negate it ... but even with positive infinity I don't no where to start!

    Your detailed instructions/explanations would be awesome!! I really want to understand how to do this by hand.
  2. jcsd
  3. Sep 27, 2008 #2


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    Staff Emeritus
    Science Advisor

    [tex]\left(e^2- \frac{t-3}{3}\right)e^{-t/3}[/tex]
    [tex]e^2- \frac{t-3}{3}e^{-t/3}[/tex]?

    In either case it looks pretty straight forward to me: e-x, times any power of t, goes to 0 as x goes to infinity.
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