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