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Question about limit fact

  1. Jul 9, 2014 #1
    Hi, I'm having trouble understanding the following fact about limits :
    If f(x)<=g(x) for all x on (a,b) (except possibly at c) and a<c<b then,
    lim f(x) <= lim g(x)
    x -> c x->c
    Here's how I interpret the definition : We have two functions f(x) and g(x), and the inequality f(x)<=g(x) hold true for all values that are not c. (That our interval (a,b)) If we were to evaluate the functions at c (considering that we can do it for our two functions.) then the inequality wouldn't hold anymore. (For example, f(x) would be superiro to g(x))
    Please tell me if I have any errors.
    THank you!
    If you want to read more, go here : http://tutorial.math.lamar.edu/Classes/CalcI/ComputingLimits.aspx
     
  2. jcsd
  3. Jul 9, 2014 #2

    mathman

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    The definition includes the phrase "except possibly at c". This means the limit inequalty will hold. At c the inequalty may or may not hold delepnding on the definition.

    Example: f(x) = 1 for x ≠ c, f(c) = k. g(x) = 2 for all x. Then the limits as x -> c satisfy f(x) < g(x). However at c it will depend on whether or not k > 2.
     
  4. Jul 9, 2014 #3
    I was wondering, when we consider several functions at once in the same graph, is it ok if this whole is not a function itself ??? Do we care about whether this whole is function or not ?
     
  5. Jul 9, 2014 #4

    HallsofIvy

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    What "whole" are you talking about? How are you combining these "several functions"?
     
  6. Jul 9, 2014 #5
    Nah, its okay, no need for that anymore.
     
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