## Definition of a Limit.

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 $$|f(-x)-L|<\epsilon$$
 PhysOrg.com science news on PhysOrg.com >> King Richard III found in 'untidy lozenge-shaped grave'>> Google Drive sports new view and scan enhancements>> Researcher admits mistakes in stem cell study
 Recognitions: Gold Member Homework Help Science Advisor 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|
 Good.Thanks.

Recognitions:
Gold Member
Staff Emeritus

## 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.