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Definition of a Limit. 
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#1
Oct2107, 08:50 AM

P: 196

1. The problem statement, all variables and given/known data
Given a function [tex]f:R\rightarrow R[/tex] and a number L,write down a definition of the statement [tex]\lim_{x\rightarrow\infty}f(x)=L[/tex] 3. The attempt at a solution Is it just [tex]\lim_{x\rightarrow\infty}f(x)=\lim_{x\rightarrow\infty}f(x)[/tex] ? and definition is for [tex]\forall \epsilon>0[/tex] [tex]\exists N[/tex] such that [tex]\forall n>N[/tex] we have [tex]f(x)L<\epsilon[/tex] 


#2
Oct2107, 10:24 AM

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assuming by n you mean x, then yes, this looks like a good dfn, although the usual dfn is that "for all e>0, there is an N<0 such that x<N ==>f(x)L<e"



#3
Oct2107, 10:25 AM

P: 196

Good.Thanks.



#4
Oct2107, 12:40 PM

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Definition of a Limit.
A more "standard" definition of
[tex]\lim_{x\rightarrow\infty}f(x)=L[/tex] would be: "Given [itex]\epsilon> 0[/itex], there exist N such that if x< N, then [itex]f(x)L<\epsilon[/itex]." Notice that in neither this definition nor your definition is N required to be an integer. 


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