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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
    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.

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