Finite limit at infinity.

$x_0 = +\infty \; , \; l \in \mathbb{R}.$

$\displaystyle \underset{x \rightarrow +\infty}{\lim} f(x) = l \Longleftrightarr... ...0, \exists A>0 \; \vert \; x>A \Longrightarrow \vert f(x)-l\vert < \varepsilon.$

See Figure fig Finite limit of a function at infinity.

Figure 4: Finite limit of a function at infinity.
$\begin{figure}\centerline \mbox{\epsfig{file=FinLimInfPt.eps,height=4cm}}\end{figure}$
$x_0 = -\infty \; , \; l \in \mathbb{R}.$

$\displaystyle \underset{x \rightarrow -\infty}{\lim} f(x) = l \Longleftrightarr... ...0, \exists A<0 \; \vert \; x<A \Longrightarrow \vert f(x)-l\vert < \varepsilon.$

**Figure 4:** Finite limit of a function at infinity.
$\begin{figure}\centerline \mbox{\epsfig{file=FinLimInfPt.eps,height=4cm}}\end{figure}$

Noah Dana-Picard 2007-12-28