# Definition of a Limit.

by azatkgz
Tags: definition, limit
 P: 197 1. The problem statement, all variables and given/known data Given a function $$f:R\rightarrow R$$ and a number L,write down a definition of the statement $$\lim_{x\rightarrow-\infty}f(x)=L$$ 3. The attempt at a solution Is it just $$\lim_{x\rightarrow-\infty}f(x)=\lim_{x\rightarrow\infty}f(-x)$$ ? and definition is for $$\forall \epsilon>0$$ $$\exists N$$ such that $$\forall n>N$$ we have $$|f(-x)-L|<\epsilon$$
 PF Patron HW Helper Sci Advisor P: 4,755 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|f(x)-L|
 P: 197 Good.Thanks.
PF Patron
Thanks
Emeritus
P: 38,404

## Definition of a Limit.

A more "standard" definition of
$$\lim_{x\rightarrow-\infty}f(x)=L$$
would be:

"Given $\epsilon> 0$, there exist N such that if x< N, then $|f(x)-L|<\epsilon$."

Notice that in neither this definition nor your definition is N required to be an integer.

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