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Homework Help: Limit at infinity problem

  1. Aug 16, 2007 #1
    Can someone give me a hint on how to evaluate the following limit?

    [tex]
    \stackrel{lim}{T\rightarrow\infty} (Texp(c/T) - T)
    [/tex]

    I tried multiplying the numerator and denominator by the conjugate (because that sometimes helps) and got:

    [tex]
    (T^2exp(2c/T) - T^2) / (Texp(c/T) + T)
    [/tex]

    But I'm not sure what I can do from there...
     
  2. jcsd
  3. Aug 16, 2007 #2
    You can express it as

    [tex]\lim_{x\rightarrow\infty} \frac{e^{c/x} - 1}{x^{-1}}}[/tex]

    Then apply l'hopital's rule
     
  4. Aug 16, 2007 #3

    Curious3141

    User Avatar
    Homework Helper

    Even faster, just observe that c/T -> 0 as T-> inf and use Maclaurin's for e^(c/T) up to the first order term.
     
  5. Aug 16, 2007 #4

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Here's a typesetting tip:

    \lim_{x \to a}

    results in

    [tex]\lim_{x \to a}[/tex]

    Furthermore, if you wanted to create your own custom one, you would do this:

    \mathop{\mathrm{Hur}}_{a = 1}^{b = 7}

    to get

    [tex]\mathop{\mathrm{Hur}}_{a = 1}^{b = 7}[/tex]
     
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