\ANG{
Geben sie gebrochen rationale Funktionen an, die folgende Eigenschaften haben:
\begin{enumerate}
\item $\D\lim_{x\to\infty}a(x)=2$, $\D\lim_{x\to -\infty}a(x)=2$
\item $\D\lim_{x\to\infty}b(x)=\frac13$, $\D\lim_{x\to -\infty}b(x)=\frac13$
\item $\D\lim_{x\to\infty}c(x)=\infty$, $\D\lim_{x\to -\infty}c(x)=-\infty$
\item $\D\lim_{x\to\infty}d(x)=-\infty$, $\D\lim_{x\to -\infty}d(x)=-\infty$
\item $\D\lim_{x\to 2+0}e(x)=\infty$, $\D\lim_{x\to 2-0}e(x)=-\infty$
\item $\D\lim_{x\to -3+0}f(x)=-\infty$, $\D\lim_{x\to -3-0}f(x)=-\infty$
\item $\D\lim_{x\to 1}g(x)=0$, $\D\lim_{x\to 2\pm 0}g(x)=\infty$
\item $\D\lim_{x\to 5}h(x)=0$, $\D\lim_{x\to 2\pm 0}h(x)=-\infty$
\end{enumerate}

}
\LSG{
\begin{enumerate}
\item z.\ B.\ $\D a(x)=\frac{2x^2+x}{x^2+1}$
\item z.\ B.\ $\D b(x)=\frac{x^3+x^2+x}{3x^3-x^2+x}$
\item z.\ B.\ $\D c(x)=\frac{x^3+2}{x^2+2x+2}$
\item z.\ B.\ $\D d(x)=\frac{x^4+x^3+x}{-x^2+x-6}$
\item z.\ B.\ $\D e(x)=\frac{1}{x-2}$
\item z.\ B.\ $\D f(x)=-\frac{1}{(x+3)^2}$
\item z.\ B.\ $\D g(x)=\frac{x-1}{(x-2)^2}$
\item z.\ B.\ $\D h(x)=\frac{x-5}{(x-2)^2}$
\end{enumerate}
}
