1. Limited time only! Sign up for a free 30min personal 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!

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




Similar Discussions: Basic limit question
  1. Basic Limits Question (Replies: 7)

  2. Basic limit question (Replies: 5)

  3. Basic Limit Question (Replies: 1)

  4. Basic limit question (Replies: 4)

Loading...