1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?