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Homework Help: Evaulating Limit Question

  1. Oct 17, 2011 #1
    1. The problem statement, all variables and given/known data
    Evaluate the limits
    lim x->2 f(x) if f(x) = 3, x an integer, or 1, otherwise.

    2. Relevant equations

    3. The attempt at a solution
    I just 3 was the answer because I thought 2 is an integer and if x is an integer then the answer is 3. I was rather shocked to find that the answer is 1. I understand the definition of limits but I think I'm obviously mistaken about something. Thanks.
  2. jcsd
  3. Oct 17, 2011 #2


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    If you're shocked by that limit, then it's clear that you don't understand the definition of limits.
  4. Oct 17, 2011 #3


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    What is your intuitive understanding of what a limit is, appplejack?
  5. Oct 17, 2011 #4
    lim x->c f(x)=L
    as 'x' approaches c 'a number' from both sides (-,+) and F(x)= approaches L from both side (-,+).
    Last edited: Oct 17, 2011
  6. Oct 17, 2011 #5


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    That's about right. But the definition of a limit doesn't say anything about the value of f(c) does it? It just talks about the value of f(x) where x is 'close to c'. Not equal to c.
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