Finite limit at infinity.

  1. $ 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}
  2. $ x_0 = -\infty \; , \; l \in \mathbb{R}.$

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



Noah Dana-Picard 2007-12-28