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mathefhtw/Der_Betrag_in_R.tex

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+\subsection{11\_1 Der Betrag in $\mathbb R$}
+
+\begin{tabbing}
+\tabumg
+\>wird f<>r $x\in\mathbb R$ mit $|x|$ bezeichnet\\
+\>ist definiert durch $
+\left| x \right| = \left\{ {\begin{array}{*{20}c}
+   {x\text{   falls  }x \ge 0}  \\
+   { - x\text{   falls  }x < 0}  \\
+\end{array}} \right.$\\
+\\
+Veranschaulichungen:\\
+\>auf der Zahlengeraden:
+
+\end{tabbing}
+%\vspace{-10mm}
+\begin{figure}[h]
+\begin{center}
+%\includegraphics{11_1_1}
+
+
+\begin{tikzpicture}[scale=1.2]
+
+    \draw [thick](-2.5,0) -- (3.5,0);
+    \draw [thick, style=dotted](3.5,0) -- (4,0);
+    \draw [thick, style=dotted](-3,0) -- (-2.5,0);
+
+    \foreach \x/\xtext in {-2/x_2,0,1, 3/x_1}
+      \draw[xshift=\x cm, thick] (0pt,1pt) -- (0pt,-1pt) node[below,fill=white]
+            {$\xtext$};
+
+    \draw[snake=brace, mirror snake, color=blue] (-2,-0.4) -- (0,-0.4) node[midway,sloped,below] {$|x_1|$};
+    \draw[snake=brace, mirror snake, color=red] (0,-0.4) -- (3,-0.4) node[midway,sloped,below] {$|x_2|$};
+
+\end{tikzpicture}
+  \end{center}
+\end{figure}
+\vspace{-15mm}
+\begin{tabbing}
+\tabumg
+\>\>\>$x$ ist der Abstand von $x$ vom Nullpunkt\\
+\\
+\>durch den Funktionsgraphen:
+\end{tabbing}
+\vspace{-10mm}
+\begin{figure}[h]
+\begin{center}
+\includegraphics{11_1_2}
+  \end{center}
+\end{figure}
+\vspace{-10mm}
+\begin{tabbing}
+\tabumg
+Rechenregeln:\\
+\>$|x\cdot y|=xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx$
+\end{tabbing}