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Homework Help: Basic limit question

  1. Apr 14, 2010 #1
    1. The problem statement, all variables and given/known data

    [tex]
    \begin{align*}
    f(t) = \lim_{k \to \infty} f_k(t) = \lim_{k \to \infty} \frac{1 - kt^2}{1 +
    kt^2} = \lim_{k \to \infty} \frac{\frac{1}{k} - t^2}{\frac{1}{k} +
    t^2} = \frac{0 - t^2}{0 + t^2} = - \frac{t^2}{t^2}
    \end{align*}
    [/tex]

    What is the value of limit function [tex]f[/tex] when [tex]t = 0[/tex]? Is it [tex]0[/tex] or [tex]-1[/tex] or undefined? What is the reasoning behind it?

    Does anyone know any good websites or books to catch up on these material?

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 14, 2010 #2

    HallsofIvy

    User Avatar
    Science Advisor

    None of the above!

    If [itex]t\ne 0[/itex] then the limit is -1, obviously.

    If t= 0, go back to the original formula: if t= 0, then
    [tex]\frac{1- kt}{1+ kt}= \frac{1- 0}{1+ 0}= \frac{1}{1}= 1[/tex]
    which is independent of k. The limit, if t= 0, is 1.
     
  4. Apr 14, 2010 #3
    Thanks for your reply. I have one question about getting to the solution.

    When should I use the original formula first and when should I take the limit first?
     
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