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!

Existence of limits

  1. Jan 30, 2009 #1
    In general, what is a good method to prove whether or not a limit exists? For example limit of sin(1/x) as x approaches zero.
     
  2. jcsd
  3. Jan 30, 2009 #2
    Hi, ill recomend you to take a look to the definition of limit:
    For every 'e'>0,exists 'd'>0, such that for /x-x0/<d then
    /f(x)-L/<e
    If that holds, then the function f(x) has limit at the point x0,
    and it is equal to L.
    Of course a bold statement like this doesnt seem to help to much, so here is what you do for practical purpouses:
    the function 1/x has a discontinuity at x=0, so evaluate the
    rightsided and leftsided limits at x=0:
    lim x->0-...1/x=-inf, and lim x->0+...1/x=+inf.
    Then the definition of limit doesnt hold for x0=0 and therefor the limit doesn exists at this point.
    Hope i helped you.
    Have a good day.


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

Have something to add?



Similar Discussions: Existence of limits
  1. Proving a limit exists (Replies: 4)

Loading...