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Homework Help: Help with limit expression

  1. Nov 1, 2005 #1

    daniel_i_l

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    Is it correct to think about the expresion:
    "the limit of f(x) is b when x->a" as saying that for every x thats very close to a but not a (in the deleted neighborhood of a) there is a f(x) thats very close to b (in the neibourhood of b) - or is that not precise enough?
     
  2. jcsd
  3. Nov 1, 2005 #2

    Galileo

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    It's definately not precise enough for a mathematical definition. What do you mean by 'very close to a'. What is 'very close'?
    The idea of [itex]\lim_{x\to a}f(x)=b[/itex] is that you can make f(x) as close as you want to b by choosing x close enough (but not equal to) a. By close I mean that the distance |f(x)-b| can be made as small as we want. How small? Smaller than any given positive number.

    http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/preciselimdirectory/PreciseLimit.html
     
  4. Nov 1, 2005 #3
    Might want to use 'gets closer' instead of 'is close to'

    Thats pretty much the epsilon delta method.
     
  5. Nov 1, 2005 #4

    daniel_i_l

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    Thanks guys for making that clear.
     
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