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John O' Meara
John O' Meara is offline
#3
Nov4-09, 02:24 PM
P: 330
Limit definition: Let f(x)be defined for all x in some open interval containing the number a, with the possible exception that f(x) need not be defined at a. We will write

[tex]\lim_{x \rightarrow a}f(x)=L[/tex]

if given any number epsilon > 0 we can find a number delta > 0 such that
|f(x) - L| < epsilon if 0 < |x - a| < delta.

If L plays the role of epsilon in the definition above, what plays the role of |f(x) - L|. I just do not get it yet. Thanks.