für overleaf überarbeitet

Band2/Definitions.tex

@@ -10,7 +10,7 @@
 \usepackage{tikz}
 \usetikzlibrary{arrows.meta,bending,positioning,matrix,fit,arrows,backgrounds}
 \usepackage{circuitikz}
-\usetikzlibrary{circuits.ee.IEC.relay}
+%\usetikzlibrary{circuits.ee.IEC.relay}
 %\usepackage{sanitize-umlaut}
 
 % fuer Stichwortverzeichnis

Band2/Grafiken/B2.1.tex

@@ -0,0 +1,74 @@
+%!tikz editor 1.0
+\documentclass{article}
+\usepackage{tikz}
+\usepackage[graphics, active, tightpage]{preview}
+\usepackage{circuitikz}
+\PreviewEnvironment{tikzpicture}
+
+%!tikz preamble begin
+\usepackage{pgfplots}
+%!tikz preamble end
+
+
+\begin{document}
+%!tikz source begin
+\begin{tikzpicture}[line cap=round,line join=round,x=1cm,y=1cm,scale=3]
+\tikzset{
+        every pin/.style={fill=yellow!50!white,rectangle,rounded corners=3pt,font=\tiny},
+        small dot/.style={fill=black,circle,scale=0.3},}
+\begin{axis}[
+x=2cm,y=2cm,
+axis lines=middle,
+axis line style = {-latex},
+xmin=-2.5,
+xmax=2.5,
+ymin=-0.5,
+ymax=4,
+%ytick={1,2},
+%yticklabels={1,2},
+xtick=\empty,
+xlabel=$x$,
+ylabel=$y$,
+extra x ticks={0.5},
+    extra x tick style={
+        tick label style={anchor=north}},
+    extra x tick labels={$\frac{1}{2}$},
+extra y ticks={0.25},
+     extra y tick style={
+        tick label style={anchor=east}},
+    extra y tick labels={$\frac{1}{4}$},
+enlargelimits = true,
+]
+
+
+
+\draw [thick, dashed] (axis cs: -0.05,1) -- (axis cs: 0.5,1);
+\draw [thick, dashed] (axis cs: 0.5,-0.05) -- (axis cs: 0.5,1);
+
+
+\addplot[domain=-2:2, blue, line width=1,samples=2000] {x^2};
+
+\addplot[color=blue!80!black, only marks, style={mark=*}] coordinates {(0.5,2)};
+
+\draw [ultra thin, dashed] (axis cs: -.05,1/4) -- (axis cs: 1/2,1/4);
+\draw [thick, dashed] (axis cs: 0.5,1) -- (axis cs: 0.5,2);
+
+
+
+\scriptsize{ \node () at (axis cs:2.4,1.8) {$\displaystyle y=\left\{ \begin{array}{rl}
+\frac{x^2-\frac{1}{4}}{x-\frac{1}{2}} & \text{für}\; x \neq \frac{1}{2}\\ \\
+2 & \text{für}\; x = \frac{1}{2}\\
+\end{array}
+\right .$};}
+
+% \draw[] (axis cs:1.3, 0.1) -- (axis cs:1.3, -0.1);
+% \node () at (axis cs:1.3,-0.25) {$x_0$};
+
+% \draw[] (axis cs:1.14,-0.05) -- (axis cs:1.14, 0.05);
+% \node () at (axis cs:0.33,-0.45) {$\frac{1}{\pi}$};
+
+\end{axis}
+\end{tikzpicture}
+%!tikz source end
+
+\end{document}

Band2/Grafiken/B2.9.tex

@@ -0,0 +1,79 @@
+%!tikz editor 1.0
+\documentclass{article}
+\usepackage{tikz}
+\usepackage[graphics, active, tightpage]{preview}
+\usepackage{circuitikz}
+\PreviewEnvironment{tikzpicture}
+
+%!tikz preamble begin
+\usepackage{pgfplots}
+%!tikz preamble end
+
+
+%%%%%%%%%
+%%   convert -density 300 GW001.pdf -quality 100 GW001.png
+%%%%%%%%%
+
+\begin{document}
+%!tikz source begin
+\begin{tikzpicture}
+[line cap=round,line join=round,x=1cm,y=1cm,scale=1]
+\tikzset{
+        every pin/.style={fill=yellow!50!white,rectangle,rounded corners=3pt,font=\tiny},
+        small dot/.style={fill=black,circle,scale=0.3},}
+\begin{axis}[
+x=2cm,y=2cm,
+axis lines=middle,
+axis line style = {-latex},
+xmin=-0.5,
+xmax=3,
+ymin=-0.1,
+ymax=2.5,
+ytick=\empty,
+xtick=\empty,
+xlabel=$x$,
+ylabel=$y$,
+extra x ticks  = {0.75, 1.25,1.75,2.25},
+extra x tick labels= {$x_0$,  $x_3$, $x_2$, $x_1$},
+extra y ticks  = {0.71232, 1.22314, 1.55962, 1.81093},
+extra y tick labels= {$g_r$,  $f(x_3)$, $f(x_2)$, $f(x_1)$}
+]
+
+%\addplot[domain=-2.7:-1.1, blue, line width=1,samples=500] {1/(x^2-1)}; 
+%\addplot[domain=1.1:2.7, blue, line width=1,samples=500] {1/(x^2-1)}; 
+\addplot[domain=0.75:2.65, blue, line width=1,samples=500] {1+ln(x)}; 
+
+
+\addplot[color=blue, only marks, fill=white] coordinates {(0.75,0.71232)};
+
+\draw [dashed, blue] (axis cs: 0.75,-0.05) -- (axis cs: 0.75,0.71232);
+
+\draw [dashed, blue] (axis cs: -0.05,0.71232) -- (axis cs: 0.75,0.71232);
+
+\addplot[color=blue, only marks] coordinates {(1.25,1.22314)};
+
+
+\draw [ blue, thin] (axis cs: 1.25,0) -- (axis cs: 1.25,1.22314);
+
+\draw [ blue, thin] (axis cs: 0, 1.22314) -- (axis cs: 1.25,1.22314);
+
+\addplot[color=blue, only marks] coordinates {(1.75,1.55962)};
+
+\draw [ blue, thin] (axis cs: 1.75,0) -- (axis cs: 1.75,1.55962);
+
+\draw [ blue, thin] (axis cs: 0, 1.55962) -- (axis cs: 1.75,1.55962);
+
+\addplot[color=blue, only marks] coordinates {(2.25,1.81093)};
+
+
+\draw [ blue, thin] (axis cs: 2.25,0) -- (axis cs: 2.25,1.81093);
+
+\draw [ blue, thin] (axis cs: 0, 1.81093) -- (axis cs: 2.25,1.81093);
+
+\end{axis}
+
+
+\end{tikzpicture}
+%!tikz source end
+
+\end{document}

Band2/Grafiken/B2_10.tikz

@@ -0,0 +1,37 @@
+\begin{tikzpicture}
+
+\begin{axis}[
+ x=1cm,y=1cm,
+axis lines=middle,
+      axis x line=middle,
+        axis y line=middle,
+        %enlarge x limits=0.15,
+        %enlarge y limits=0.15,
+        every axis x label/.style={at={(current axis.right of origin)},anchor=north east},
+        every axis y label/.style={at={(current axis.above origin)},anchor=north east},
+xmin=-0.5,
+xmax=6.,
+ymin=-0.5,
+ymax=5,
+ytick={1,...,2},
+xtick={3},
+xlabel=$x$,
+ylabel=$y$,
+]
+
+\addplot[domain=0.75:3, blue!80!black, line width=1,samples=50] {3/x};
+\addplot[domain=3:5, blue!80!black, line width=1,samples=50] {x-1};
+\addplot[color=blue!80!black, only marks, style={mark=*, fill=white}] coordinates {(3,2)};
+\addplot[color=blue!80!black, only marks, style={mark=*	}] coordinates {(3,1)};
+
+\draw [dashed, draw=black] (axis cs: -0.05,1) -- (axis cs: 3,1);
+\draw [dashed, draw=black] (axis cs: -0.05,2) -- (axis cs: 3,2);
+\draw [dashed, draw=black] (axis cs: 3,-0.05) -- (axis cs: 3,2);
+
+\node[] at (axis cs:4.5,4.5) {\footnotesize$y=\left\{\begin{array}{l}
+\frac{3}{x} \text { für } 0<x \leq 3 \\
+x-1 \text { für } x>3
+\end{array}\right.$};
+
+\end{axis}
+\end{tikzpicture}

Band2/Grafiken/B2_11.tikz

@@ -0,0 +1,33 @@
+\begin{tikzpicture}[line cap=round,line join=round,x=1cm,y=1cm]
+\tikzset{
+        every pin/.style={fill=yellow!50!white,rectangle,rounded corners=3pt,font=\tiny},
+        small dot/.style={fill=black,circle,scale=0.3},}
+\begin{axis}[
+x=1.5cm,y=1.5cm,
+axis lines=middle,
+axis line style = {-latex},
+xmin=-0.25,
+xmax=4.2,
+ymin=-0.25,
+ymax=3,
+ytick=\empty,
+xtick=\empty,
+xlabel=$x$,
+ylabel=$y$,
+extra y ticks={1.5},
+ extra y tick style={
+        tick label style={anchor=east}},
+    extra y tick labels={$\displaystyle g$},
+enlargelimits = true,
+]
+\draw [thick, draw=blue!50!black] 
+        (axis cs: -0.05,1.5) -- (axis cs: 5.2,1.5);
+\node[] at (axis cs:2.5,2.5) {$y=f(x)$};
+
+\addplot[domain=1.1:4.4, green!50!black	, line width=1,samples=200] {1.5+(5*e^(-x))*(cos(deg(2*pi*x)))};
+
+\end{axis}
+
+
+
+\end{tikzpicture}

Band2/Grafiken/B2_12.tikz

@@ -0,0 +1,24 @@
+\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1cm,y=1cm]
+\begin{axis}[
+x=1cm,y=1cm,
+axis lines=middle,
+xmin=-5,
+xmax=5,
+ymin=-1.4,
+ymax=5,
+ytick={-1,...,4},
+xtick={-3,...,3},
+xlabel=$x$,
+ylabel=$y$,
+]
+
+
+\addplot[domain=0.5:4, blue, line width=1,samples=50] {1/(x^2)};
+\addplot[domain=-4:-0.5, blue, line width=1,samples=50] {1/(x^2)};
+
+\node[] at (axis cs:2.5,2.5) {$\displaystyle y=\frac{1}{x^2}\; (x \neq 0)$};
+\end{axis}
+
+
+
+\end{tikzpicture}

Band2/Grafiken/B2_3.tikz

@@ -0,0 +1,27 @@
+\begin{tikzpicture}[line cap=round,line join=round,x=1cm,y=1cm]
+\tikzset{
+        every pin/.style={fill=yellow!50!white,rectangle,rounded corners=3pt,font=\tiny},
+        small dot/.style={fill=black,circle,scale=0.5},}
+\begin{axis}[
+        axis x line=middle,
+        x=3cm,
+        width=40mm,
+        height=20mm,
+        xmin=0.5,
+        xmax=3.5,
+        xtick = \empty,
+        x axis line style={thick,-latex},
+        xlabel style={anchor=north west},
+        axis y line=none,
+        anchor=left of origin,
+xlabel=$x$,
+extra x ticks={1, 2, 3},
+extra x tick labels={$x_0 - C$, $x_0$, $x_0+C$},
+]
+\draw [line width=2] (axis cs: 1,0) -- (axis cs: 3,0);
+\addplot[only marks, fill=white, thick] coordinates {(1,0)};
+\addplot[only marks, fill=white, thick] coordinates {(2,0)};
+\addplot[only marks, fill=white, thick] coordinates {(3,0)};
+\end{axis}
+
+\end{tikzpicture}

Band2/Grafiken/B2_4.tikz

@@ -0,0 +1,53 @@
+\begin{tikzpicture}
+[line cap=round,line join=round,x=1cm,y=1cm]
+\tikzset{
+        every pin/.style={fill=yellow!50!white,rectangle,rounded corners=3pt,font=\tiny},
+        small dot/.style={fill=black,circle,scale=0.3},}
+\begin{axis}[
+x=2cm,y=2cm,
+axis lines=middle,
+axis line style = {-latex},
+xmin=-0.75,
+xmax=3.75,
+ymin=-0.5,
+ymax=3.5,
+ytick=\empty,
+xtick=\empty,
+xlabel=$x$,
+ylabel=$y$,
+extra x ticks={0.75, 2, 2.5,2.8},
+extra x tick labels={$x_1$, $x_3$, $x_0$, $x_2$},
+extra y ticks={0.64, 1.5, 2.0625, 2.46},
+extra y tick labels={$f(x_1)$, $f(x_3)$, $g$ , $f(x_2)$},
+]
+
+\addplot[domain=0.5:3.1, blue, line width=1,samples=500] {0.25*(x^2)+0.5};
+
+
+\draw [line width=0.1] (axis cs: 0.75,-0.05) -- (axis cs: 0.75,0.640625);
+\draw [line width=0.1] (axis cs: -0.05,0.640625) -- (axis cs: 0.75,0.640625);
+
+\draw [ultra thin] (axis cs: 2,-0.05) -- (axis cs: 2,1.5);
+\draw [ultra thin] (axis cs: -0.05,1.5) -- (axis cs: 2,1.5);
+
+\draw [loosely dashed, ultra thin] (axis cs: 2.5,-0.05) -- (axis cs: 2.5,2.0625);
+\draw [loosely dashed, thin] (axis cs: -0.05,2.0625) -- (axis cs: 2.5,2.0625);
+
+\draw [ultra thin] (axis cs: 2.8,-0.05) -- (axis cs: 2.8,2.46);
+\draw [ultra thin] (axis cs: -0.05,2.46) -- (axis cs: 2.8,2.46);
+
+
+\addplot[color=blue!80!black, only marks, style={mark=*}] coordinates {(0.75,0.640625)};
+\addplot[color=blue!80!black, only marks, style={mark=*}] coordinates {(2,1.5)};
+
+\addplot[color=blue, only marks, fill=white] coordinates {(2.5,2.0625)};
+
+\addplot[color=blue!80!black, only marks, style={mark=*}] coordinates {(2.8,2.46)};
+
+
+\node () at (axis cs:2.5,2.8) {$\displaystyle y=\left(x\right)$};
+
+\end{axis}
+
+
+\end{tikzpicture}

Band2/Grafiken/B2_5.tikz

@@ -0,0 +1,58 @@
+\begin{tikzpicture}
+[line cap=round,line join=round,x=1cm,y=1cm]
+\tikzset{
+        every pin/.style={fill=yellow!50!white,rectangle,rounded corners=3pt,font=\tiny},
+        small dot/.style={fill=black,circle,scale=0.3},}
+\begin{axis}[
+x=2cm,y=2cm,
+axis lines=middle,
+axis line style = {-latex},
+xmin=-1,
+xmax=3,
+ymin=-0.5,
+ymax=2,
+ytick={1,2},
+yticklabels={1,2},
+xtick=\empty,
+xlabel=$x$,
+ylabel=$y$,
+extra x ticks={0.5},
+    extra x tick style={
+        tick label style={anchor=north}},
+    extra x tick labels={$\frac{1}{2}$},
+enlargelimits = true,
+]
+
+
+
+\draw [thick, dashed] (axis cs: -0.05,1) -- (axis cs: 0.5,1);
+\draw [thick, dashed] (axis cs: 0.5,-0.05) -- (axis cs: 0.5,1);
+
+
+\addplot[domain=-1:0.5, blue, line width=1,samples=2000] {((x^2)-(1/4))/(x-(1/2)};
+\addplot[color=blue!80!black, only marks, style={mark=*, fill=white}] coordinates {(0.5,1)};
+\addplot[domain=0.51:1.5, blue, line width=1,samples=2000] {((x^2)-(1/4))/(x-(1/2)};
+
+\addplot[color=blue!80!black, only marks, style={mark=*}] coordinates {(0.5,2)};
+
+\draw [thick, dashed] (axis cs: -0.05,2) -- (axis cs: 0.5,2);
+\draw [thick, dashed] (axis cs: 0.5,1) -- (axis cs: 0.5,2);
+
+
+
+\scriptsize{ \node () at (axis cs:2.4,1.8) {$\displaystyle y=\left\{ \begin{array}{rl}
+\frac{x^2-\frac{1}{4}}{x-\frac{1}{2}} & \text{für}\; x \neq \frac{1}{2}\\ \\
+2 & \text{für}\; x = \frac{1}{2}\\
+\end{array}
+\right .$};}
+
+% \draw[] (axis cs:1.3, 0.1) -- (axis cs:1.3, -0.1);
+% \node () at (axis cs:1.3,-0.25) {$x_0$};
+
+% \draw[] (axis cs:1.14,-0.05) -- (axis cs:1.14, 0.05);
+% \node () at (axis cs:0.33,-0.45) {$\frac{1}{\pi}$};
+
+\end{axis}
+
+
+\end{tikzpicture}

Band2/Grafiken/B2_6.tikz

@@ -0,0 +1,33 @@
+\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1cm,y=1cm]
+\begin{axis}[
+x=5cm,y=1.5cm,
+axis lines=middle,
+xmin=-1.2,
+xmax=1.2,
+ymin=-1.4,
+ymax=1.4,
+ytick={-1,...,1},
+xtick=\empty,
+xlabel=$x$,
+ylabel=$y$,
+]
+
+
+\addplot[domain=0.05:3.8, red, line width=1,samples=5000] {sin(deg(1/(x)))};
+\addplot[domain=-3.8:-0.05, red,  line width=1,samples=5000] {sin(deg(1/(x)))};
+
+%\draw (-0.32,0.1) node[anchor=north west] {$-\frac{1}{\pi}$};
+%\draw (0.32,0.1) node[anchor=north west] {$\frac{1}{\pi}$};
+ \draw[] (axis cs:-0.32, 0.1) -- (axis cs:-0.32, -0.1);
+ \node () at (axis cs:-0.35,-0.45) {$-\frac{1}{\pi}$};
+
+  \draw[] (axis cs:0.32, 0.1) -- (axis cs:0.32, -0.1);
+ \node () at (axis cs:0.33,-0.45) {$\frac{1}{\pi}$};
+%\node[color=red, font=\footnotesize] at (-1,-0.25) {$f(x)=3x^3 - x^2 - 10x$};
+%\node[color=blue, font=\footnotesize] at (axis cs: 1.1,2.2) {$g(x)=- x^2 + 2x$};
+
+\end{axis}
+
+
+
+\end{tikzpicture}

Band2/Grafiken/B2_8.tikz

@@ -0,0 +1,56 @@
+\begin{tikzpicture}[line cap=round,line join=round,x=1cm,y=1cm]
+\tikzset{
+        every pin/.style={fill=yellow!50!white,rectangle,rounded corners=3pt,font=\tiny},
+        small dot/.style={fill=black,circle,scale=0.3},}
+\begin{axis}[
+x=2cm,y=2cm,
+axis lines=middle,
+axis line style = {-latex},
+xmin=-0.5,
+xmax=3,
+ymin=-0.5,
+ymax=2,
+ytick=\empty,
+xtick=\empty,
+xlabel=$x$,
+ylabel=$y$,
+extra x ticks={1.3},
+    extra x tick style={
+        tick label style={anchor=north}},
+    extra x tick labels={$x_0$},
+ extra y ticks={1.14},
+ extra y tick style={
+        tick label style={anchor=east}},
+    extra y tick labels={$\displaystyle \sqrt{x_0}$},
+enlargelimits = true,
+]
+  \draw [thick, dashed] 
+        (axis cs: -0.05,1.14) -- (axis cs: 1.3,1.14);
+  \draw [thick, dashed] 
+        (axis cs: 1.3,-0.05) -- (axis cs: 1.3,1.14);
+\node[label={180:{}},circle,fill,inner sep=1.5] at (axis cs:1.3,1.14) {};
+\node[label={300:{$0$}},circle,fill,inner sep=1.5] at (axis cs:0,0) {};
+ %       node[pos=0.5, above] {$y=12$};
+ %  \addplot coordinates { (0,1.14) (1.3,1.14) };
+ %   \addplot coordinates { (1,4) (2,6) };
+  %  \draw (axis cs:2,3) -- node[left]{Text} (axis cs:2,6);
+
+\addplot[domain=0:2, blue, line width=1,samples=5000] {sqrt(x)};
+%\addplot[domain=-3.8:-0.05, red,  line width=1,samples=5000] {sin(deg(1/(x)))};
+
+
+\begin{scriptsize}
+ \node () at (axis cs:2.2,1.7) {$\displaystyle y=\sqrt{x}\;(x \neq 0)$};
+\end{scriptsize}
+
+% \draw[] (axis cs:1.3, 0.1) -- (axis cs:1.3, -0.1);
+% \node () at (axis cs:1.3,-0.25) {$x_0$};
+
+% \draw[] (axis cs:1.14,-0.05) -- (axis cs:1.14, 0.05);
+% \node () at (axis cs:0.33,-0.45) {$\frac{1}{\pi}$};
+
+\end{axis}
+
+
+
+\end{tikzpicture}

Band2/Grafiken/B2_9.tikz

@@ -0,0 +1,56 @@
+\begin{tikzpicture}
+[line cap=round,line join=round,x=1cm,y=1cm,scale=1]
+\tikzset{
+        every pin/.style={fill=yellow!50!white,rectangle,rounded corners=3pt,font=\tiny},
+        small dot/.style={fill=black,circle,scale=0.3},}
+\begin{axis}[
+x=2cm,y=2cm,
+axis lines=middle,
+axis line style = {-latex},
+xmin=-0.5,
+xmax=3,
+ymin=-0.1,
+ymax=2.5,
+ytick=\empty,
+xtick=\empty,
+xlabel=$x$,
+ylabel=$y$,
+extra x ticks  = {0.75, 1.25,1.75,2.25},
+extra x tick labels= {$x_0$,  $x_3$, $x_2$, $x_1$},
+extra y ticks  = {0.71232, 1.22314, 1.55962, 1.81093},
+extra y tick labels= {$g_r$,  $f(x_3)$, $f(x_2)$, $f(x_1)$}
+]
+
+%\addplot[domain=-2.7:-1.1, blue, line width=1,samples=500] {1/(x^2-1)}; 
+%\addplot[domain=1.1:2.7, blue, line width=1,samples=500] {1/(x^2-1)}; 
+\addplot[domain=0.75:2.65, blue, line width=1,samples=500] {1+ln(x)}; 
+
+
+\addplot[color=blue, only marks, fill=white] coordinates {(0.75,0.71232)};
+
+\draw [dashed, blue] (axis cs: 0.75,-0.05) -- (axis cs: 0.75,0.71232);
+
+\draw [dashed, blue] (axis cs: -0.05,0.71232) -- (axis cs: 0.75,0.71232);
+
+\addplot[color=blue, only marks] coordinates {(1.25,1.22314)};
+
+
+\draw [ blue, thin] (axis cs: 1.25,-0.05) -- (axis cs: 1.25,1.22314);
+
+\draw [ blue, thin] (axis cs: -0.05, 1.22314) -- (axis cs: 1.25,1.22314);
+
+\addplot[color=blue, only marks] coordinates {(1.75,1.55962)};
+
+\draw [ blue, thin] (axis cs: 1.75,-0.05) -- (axis cs: 1.75,1.55962);
+
+\draw [ blue, thin] (axis cs: -0.05, 1.55962) -- (axis cs: 1.75,1.55962);
+
+\addplot[color=blue, only marks] coordinates {(2.25,1.81093)};
+
+
+\draw [ blue, thin] (axis cs: 2.25,-0.05) -- (axis cs: 2.25,1.81093);
+
+\draw [ blue, thin] (axis cs: -0.05, 1.81093) -- (axis cs: 2.25,1.81093);
+
+\end{axis}
+\end{tikzpicture}

Band2/Grafiken/Horner01.tikz

@@ -0,0 +1,203 @@
+%!TEX root=Band2.tex
+
+%\begin{tikzpicture}[>=latex]
+%
+%\draw[cyan, densely dotted] (-2,0) grid (12,14);
+%\useasboundingbox (-2,0) rectangle (12,14);
+%
+%%nodes=draw,
+%\matrix (m1) [anchor=west,draw,row sep=6mm,column sep=5mm,matrix of nodes,column 6/.style={anchor=base west}, left delimiter=\{ ] at (1, 12)
+%{
+%\phantom{a} & $3$  & $0$\footnotemark & $1$ & $-5 $ & $2$ \\
+%\phantom{a}  & \phantom{a} & $6$ & $12$ & $26$ & $42$\\
+%$2$ & $3$ & $6$ & $13$ & $21$ & $44=g(2)$\\
+%};
+%
+%\matrix (m2) [anchor=west,draw,row sep=6mm,column sep=5mm,matrix of nodes,column 5/.style={anchor=base west}, left delimiter=\{ ] at (1, 9)
+%	{
+%\phantom{a} & \phantom{a} & $6$ & $24$ & $74$\\
+%	$2$ & $3$ &	$12$ & $37$ & $95=g'(2)$ \\
+%};
+%
+%\matrix (m3) [anchor= west,draw,row sep=6mm,column sep=5mm,matrix of nodes,column 4/.style={anchor=base west} , left delimiter=\{] at (1, 6.5)
+%{
+%\phantom{a} & \phantom{a} & $6$ & $36$\\
+%	$2$ & $3$ &	$18$ &  $73=\frac{g''(2)}{2!}$ \phantom{a}\\
+%};
+%
+%\matrix (m4) [anchor= west,draw,row sep=6mm,column sep=5mm,matrix of nodes,column 3/.style={anchor=base west} , left delimiter=\{] at (1, 4)
+%{
+%\phantom{a} & \phantom{a} & $6$\\
+%	$2$ & $3$ &	  $24=\frac{g'''(2)}{3!}$ \phantom{a}\\
+%};
+%
+%\matrix (m5) [anchor= west,draw,row sep=6mm,column sep=5mm,matrix of nodes,column 4/.style={anchor=base west} , left delimiter=\{] at (1, 2)
+%{
+%\phantom{a} &$3=\frac{g^{4}(2)} {4!}$ \\
+%};
+%
+%\draw ([xshift=.1cm]m1-1-1.north east) -- ([xshift=.1cm,yshift=-0.3cm]m5-1-1.south east);
+%
+%\draw ([yshift=-.25cm]m1-2-1.south west) -- ([yshift=-.25cm,xshift=1.2cm]m1-2-6.south east);
+%
+%\draw ([yshift=-.25cm]m2-1-1.south west) -- ([yshift=-.25cm,xshift=1.3cm]m2-1-5.south east);
+%
+%\draw ([yshift=-.25cm]m3-1-1.south west) -- ([yshift=-.25cm,xshift=16mm]m3-1-4.south east);
+%
+%\draw ([yshift=-.25cm]m4-1-1.south west) -- ([yshift=-.25cm,xshift=18mm]m4-1-3.south east);
+%
+%%\draw ([yshift=-.25cm]m5-1-1.south west) -- ([yshift=-.25cm,xshift=3mm]m5-1-2.south east);
+%%\draw ([yshift=2mm]m1-3-6.north west) -- ([yshift=-1mm]m1-3-6.south west);
+%	
+%	%\draw ([yshift=-.25cm]m1-2-6.south west) -- ([yshift=-.25cm,xshift=4mm]m1-2-6.south east);
+%	
+%%	\draw ([yshift=-.15cm]m1-3-6.south west) -- 	([yshift=-.15cm]m1-3-6.south east);
+%	
+%
+%\node[circle,draw] (del-left-1) at ($0.5*(m1-3-1.south west)+0.5*(m1-1-1.north west)$){};
+%\node[circle,draw] (del-left-2) at ($0.5*(m2-2-1.south west)+0.5*(m2-1-1.north west)$){};
+%\node[circle,draw] (del-left-3) at ($0.5*(m3-2-1.south west)+0.5*(m3-1-1.north west)$){};
+%\node[circle,draw] (del-left-4) at ($0.5*(m4-2-1.south west)+0.5*(m4-1-1.north west)$){};
+%\node[circle,draw] (del-left-5) at ($0.5*(m5-1-1.south west)+0.5*(m5-1-1.north west)$){};
+%\node[left=10pt] at (del-left-1.west) {1. Schritt};
+%\node[left=10pt] at (del-left-2.west) {2. Schritt};
+%\node[left=10pt] at (del-left-3.west) {3. Schritt};
+%\node[left=10pt] at (del-left-4.west) {4. Schritt};
+%\node[left=10pt] at (del-left-5.west) {5. Schritt};
+%
+%%\draw ($(m1-2-5.north east)!0.5!(m1-2-5.north west)$) -- ($(m1-2-5.south east)!0.5!(m2-2-2.south west)$);
+%%\draw($(m1-2-5.north east)!50!(m1-2-6.north west)$)--($(m1-3-5.south east)!50!(m1-3-6.south west)$);
+%%\draw([yshift=3mm]m1-3-6.north west)--(m1-3-6.south west);
+%
+%\hhlline{m5}{1}{2};
+%
+%%	\node[rectangle,draw] (del-left-2) at ($(m2-2-1)-(m2-1-1)$) {\tikz{\path (m2-2-2.north east) rectangle (m2-2-1.south west);}};
+%
+%
+%
+% %\mymatrixbracetop{2}{6}{$E'$}
+%
+%%\node[font=\color{red}] at (m2.center){X};
+%
+%%\foreach \xy in {$1*(m2-1-1)$, $1*(m2-2-1)$}{
+%%    \node at (\xy) {\xy};
+%%}
+%
+%\end{tikzpicture} \footnotetext{Man beachte, ...}
+
+\begin{tikzpicture}[>=latex]
+	
+%\draw[cyan, densely dotted] (-2,0) grid (8.5,9.5);
+\useasboundingbox (-2,0) rectangle (8.5,9.5);
+	
+%nodes=draw,
+\matrix (m1) [anchor=west,row sep=2mm,column sep=5mm,matrix of math nodes,column 6/.style={anchor=base west}, left delimiter=\{ ] at (1, 8.4)
+{
+	\phantom{a} & 3  & 0\footnotemark & 1 & -5  & 2 \\
+	\phantom{a}  & \phantom{a} & 6 & 12 & 26 & 42\\
+	2 & 3 & 6 & 13 & 21 & 44=g(2)\\
+};
+	
+\matrix (m2) [anchor=west,row sep=2mm,column sep=5mm,matrix of math nodes, column 5/.style={anchor=base west}, left delimiter=\{ ] at (1, 6.4)
+{
+	\phantom{a} & \phantom{a} & 6 & 24 & 74\\
+	2 & 3 &	12 & 37 & 95=g'(2) \\
+};
+	
+\matrix (m3) [anchor=west,row sep=2mm,column sep=5mm,matrix of math nodes,column 4/.style={anchor=base west}, left delimiter=\{ ] at (1, 4.5)
+{
+	\phantom{a} & \phantom{a} & 6 & 36\\
+	2 & 3 &	18 &  73=\frac{g''(2)}{2!} \\
+};
+	
+\matrix (m4) [anchor=west,row sep=2mm,column sep=5mm,matrix of math nodes,column 3/.style={anchor=base west}, left delimiter=\{ ] at (1, 2.4)
+{
+	\phantom{a} & \phantom{a} & 6\\
+	2 & 3 &	 24=\frac{g'''(2)}{3!} \\
+};
+
+\matrix (m5) [anchor=west,row sep=2mm,column sep=5mm,matrix of math nodes,column 2/.style={anchor=base west}, left delimiter=\{ ] at (1, 0.7)
+{
+	\phantom{a} &  3=\frac{g^{(4)}(2)}{4!} \\
+};
+	
+\node[circle] (del-left-1) at ($0.5*(m1-3-1.south west)+0.5*(m1-1-1.north west)$){};
+\node[left=10pt] at (del-left-1.west) {1. Schritt};
+	
+	%\draw ($(m1-2-5.north east)!0.5!(m1-2-5.north west)$) -- ($(m1-2-5.south east)!0.5!(m2-2-2.south west)$);
+	%\draw($(m1-2-5.north east)!50!(m1-2-6.north west)$)--($(m1-3-5.south east)!50!(m1-3-6.south west)$);
+	%\draw([yshift=3mm]m1-3-6.north west)--(m1-3-6.south west);
+%\draw ([yshift=-3mm]m1-2-1.south west) -- ([yshift=-3mm,xshift=10mm]m1-2-6.south east);
+
+\draw ($0.5*(m1-2-1.south west)+0.5*(m1-3-1.north west)$) -- ([xshift=5mm]$0.5*(m1-2-6.south east)+0.5*(m1-3-6.north east)$);
+
+\draw ([yshift=1mm]m1-3-6.north west) -- (m1-3-6.south west);
+\draw (m1-3-6.south west) -- (m1-3-6.south east);
+
+\draw ($0.5*(m2-1-1.south west)+0.5*(m2-2-1.north west)$) -- ([xshift=5mm]$0.5*(m2-1-5.south east)+0.5*(m2-2-5.north east)$);
+
+%Ende Zeile 2 
+%vert
+\draw ([yshift=1mm]m2-2-5.north west) -- (m2-2-5.south west);
+%horiz
+\draw (m2-2-5.south west) -- (m2-2-5.south east);
+
+
+%Trennlinie
+\draw ([yshift=1.5mm]$0.5*(m3-1-1.south west)+0.5*(m3-2-1.north west)$) -- ([xshift=5mm]$0.5*(m3-1-4.south east)+0.5*(m3-2-4.north east)$);
+\node[circle] (del-left-2) at ($0.5*(m2-2-1.south west)+0.5*(m2-1-1.north west)$){};
+\node[left=10pt] at (del-left-2.west) {2. Schritt};
+
+\node[circle] (del-left-3) at ([yshift=-1mm]$0.5*(m3-1-1.south west)+0.5*(m3-2-1.north west)$){};
+\node[left=10pt] at (del-left-3.west) {3. Schritt};
+
+\draw ([yshift=1mm]m3-2-4.north west) -- (m3-2-4.south west);
+\draw (m3-2-4.south west) -- (m3-2-4.south east);
+
+%\draw ([yshift=-3mm,thick]m2-1-1.south west) -- ([yshift=-3mm,xshift=10mm]m2-1-5.south east);	
+
+\draw ([yshift=1.5mm]$0.5*(m4-1-1.south west)+0.5*(m4-2-1.north west)$) -- ([xshift=5mm]$0.5*(m4-1-3.south east)+0.5*(m4-2-3.north east)$);
+
+\draw ([yshift=1mm]m4-2-3.north west) -- (m4-2-3.south west);
+\draw (m4-2-3.south west) -- (m4-2-3.south east);
+
+
+\node[circle] (del-left-4) at ([yshift=-1mm]$0.5*(m4-1-1.south west)+0.5*(m4-2-1.north west)$){};
+\node[left=10pt] at (del-left-4.west) {4. Schritt};
+
+\draw ($0.5*(m1-2-1.south west)+0.5*(m1-3-1.north west)$) -- ([xshift=5mm]$0.5*(m1-2-6.south east)+0.5*(m1-3-6.north east)$);
+
+\draw ([yshift=1mm]m1-3-6.north west) -- (m1-3-6.south west);
+\draw (m1-3-6.south west) -- (m1-3-6.south east);
+
+\draw ($0.5*(m2-1-1.south west)+0.5*(m2-2-1.north west)$) -- ([xshift=5mm]$0.5*(m2-1-5.south east)+0.5*(m2-2-5.north east)$);
+
+
+\draw ([yshift=1mm]m3-2-4.north west) -- (m3-2-4.south west);
+\draw (m3-2-4.south west) -- (m3-2-4.south east);
+
+%\draw ([yshift=-3mm,thick]m2-1-1.south west) -- ([yshift=-3mm,xshift=10mm]m2-1-5.south east);	
+
+\node[circle] (del-left-5) at ([yshift=1mm]$0.5*(m5-1-1.south west)+0.5*(m5-1-1.north west)$){};
+\node[left=10pt] at (del-left-5.west) {5. Schritt};
+
+	
+\draw (m5-1-2.north west) -- (m5-1-2.south west);
+\draw (m5-1-2.south west) -- (m5-1-2.south east);
+	
+	
+\draw ([yshift=5.5mm]m5-1-1.north west)-- ([yshift=1mm]m5-1-2.north east);
+
+\draw(m1-1-1.north east)--([yshift=-2mm]m5-1-1.south east);
+
+	%\mymatrixbracetop{2}{6}{$E'$}
+	
+	%\node[font=\color{red}] at (m2.center){X};
+	
+	%\foreach \xy in {$1*(m2-1-1)$, $1*(m2-2-1)$}{
+		%    \node at (\xy) {\xy};
+		%}
+	
+\end{tikzpicture} \footnotetext{Man beachte, ...}
+
+\newpage

Band2/Grafiken/Horner02.tikz

@@ -0,0 +1,56 @@
+%!TEX root=Band2.tex
+\begin{tikzpicture}[>=latex]
+	
+%\draw[cyan, densely dotted] (-2,0) grid (12,14);
+\useasboundingbox (-2,0) rectangle (12,14);
+	
+%nodes=draw,
+\matrix (m1) [anchor=west,row sep=2mm,column sep=5mm,matrix of math nodes,column 7/.style={anchor=base west}] at (1, 12)
+	{
+		\phantom{a} & 1  & 3 & 5 & 7  & 6 & 2 \\
+		\phantom{a}  & \phantom{a} & -1 & -2 & -3 & -4 & -2\\
+		-1 & 1 & 2 & 3 & 4 & 2 & 0=g(-1)\\
+	};
+	
+\matrix (m2) [anchor=west,row sep=2mm,column sep=5mm,matrix of math nodes, column 6/.style={anchor=base west}] at (1, 10)
+	{
+		\phantom{a} & \phantom{a} & -1 & -1 & -2 & -2\\
+		-1 & 1 & 1 & 2 & 2 & 0=g'(-1) \\
+	};
+	
+\matrix (m3) [anchor=west,row sep=2mm,column sep=5mm,matrix of math nodes,column 5/.style={anchor=base west}] at (1, 8.1)
+{
+	\phantom{a} & \phantom{a} & -1 & 0 & -2\\
+	-1 & 1 & 0 & 2 & 0=\frac{g''(-1)}{2!} \\
+};
+	
+\matrix (m4) [anchor=west,row sep=2mm,column sep=5mm,matrix of math nodes,column 4/.style={anchor=base west}] at (1, 6)
+{
+	\phantom{a} & \phantom{a} & -1 & 1\\
+	-1 & 1 & -1 &	 3=\frac{g'''(-1)}{3!} \neq 0 \\
+};
+
+
+\draw ($0.5*(m1-2-1.south west)+0.5*(m1-3-1.north west)$) -- ([xshift=5mm]$0.5*(m1-2-7.south east)+0.5*(m1-3-7.north east)$);
+
+\draw ([yshift=1mm]m1-3-7.north west) -- (m1-3-7.south west);
+\draw (m1-3-7.south west) -- (m1-3-7.south east);
+
+\draw ($0.5*(m2-1-1.south west)+0.5*(m2-2-1.north west)$) -- ([xshift=5mm]$0.5*(m2-1-6.south east)+0.5*(m2-2-6.north east)$);
+
+\draw ([yshift=1mm]m2-2-6.north west) -- (m2-2-6.south west);
+\draw (m2-2-6.south west) -- (m2-2-6.south east);
+
+\draw ([yshift=1.5mm]$0.5*(m3-1-1.south west)+0.5*(m3-2-1.north west)$) -- ([xshift=5mm]$0.5*(m3-1-5.south east)+0.5*(m3-2-5.north east)$);
+
+\draw ([yshift=1mm]m3-2-5.north west) -- (m3-2-5.south west);
+\draw (m3-2-5.south west) -- (m3-2-5.south east);
+
+\draw ([yshift=1.5mm]$0.5*(m4-1-1.south west)+0.5*(m4-2-1.north west)$) -- ([xshift=12mm]$0.5*(m4-1-4.south east)+0.5*(m4-2-4.north east)$);
+
+\draw ([yshift=1mm]m4-2-4.north west) -- (m4-2-4.south west);
+\draw (m4-2-4.south west) -- (m4-2-4.south east);
+
+\draw([xshift=2mm]m1-1-1.north east)--([xshift=2mm,yshift=-2mm]m4-2-1.south east);
+
+\end{tikzpicture}

Band2/Grenzwert.tex

@@ -18,12 +18,12 @@ Als Vorbereitung auf den Grenzwertbegriff für Funktionen behandeln wir das
 
 \begin{figure}[h]
 	\begin{minipage}[b]{.4\linewidth} % [b] => Ausrichtung an \caption
-		\includegraphics[width=\linewidth]{B.2.1}
+		\includegraphics[width=\linewidth]{Grafiken/B2_1.png}
 		\caption{}\label{fig:b2.2.1}
 	\end{minipage}
 	\hspace{.1\linewidth}% Abstand zwischen Bilder
 	\begin{minipage}[b]{.4\linewidth} % [b] => Ausrichtung an \caption
-		\includegraphics[width=\linewidth]{B.2.2}
+		\includegraphics[width=\linewidth]{Grafiken/B2_2.png}
 		\caption{}\label{fig:b2.2.2}
 	\end{minipage}
 \end{figure}
@@ -58,7 +58,7 @@ $$
 	\centering
 %	\includegraphics[width=0.5\linewidth]{B.2.3}
 	%\frame{
-		\input{B2.3.tikz}
+		\input{Grafiken/B2_3.tikz}
 		%}
 	\caption{}
 	\label{fig:b2.2.3}
@@ -80,7 +80,7 @@ In Bild \ref{fig:b2.2.4} haben wir die ersten drei Glieder einer Folge $\left(x_
 \begin{figure}[h]
 	\centering
 	%\includegraphics[width=0.5\linewidth]{B.2.4}
-	\input{B2.4.tikz}
+	\input{Grafiken/B2_4.tikz}
 	\caption{}
 	\label{fig:b2.2.4}
 \end{figure}
@@ -126,7 +126,7 @@ In Bild \ref{fig:b2.2.4} haben wir die ersten drei Glieder einer Folge $\left(x_
 	\begin{figure}[h]
 		\centering
 		%\includegraphics[width=0.5\linewidth]{B.2.5}
-		\input{B2.5.tikz}
+		\input{Grafiken/B2_5.tikz}
 		\caption{}
 		\label{fig:b2.2.5}
 	\end{figure}
@@ -167,7 +167,7 @@ In Bild \ref{fig:b2.2.4} haben wir die ersten drei Glieder einer Folge $\left(x_
 
 \begin{figure}[h]
 	\centering
-	\input{B2.6.tikz}
+	\input{Grafiken/B2_6.tikz}
 	\caption{}
 	\label{fig:b2.2.6}
 \end{figure}
@@ -231,7 +231,7 @@ Eine geometrische Deutung dieses Satzes gibt Bild \ref{fig:b2.2.7}. Mit den dort
 
 \begin{figure}[h]
 	\centering
-	\includegraphics[width=0.5\linewidth]{B.2.7}
+	\includegraphics[width=0.5\linewidth]{Grafiken/B2_7.png}
 	\caption{}
 	\label{fig:b2.2.7}
 \end{figure}
@@ -254,7 +254,7 @@ um $y=g$ ein , $\delta$-Streifen" um $x=x_0$ existiert, so daß alle Punkte der
 
 	\begin{figure}[h]
 		\centering
-		\input{B2.8.tikz}
+		\input{Grafiken/B2_8.tikz}
 		\caption{}
 		\label{fig:b2.2.8}
 	\end{figure}
@@ -286,7 +286,7 @@ Für die Existenz des Grenzwertes $\lim _{x \rightarrow x_0} \sqrt{x}$ ist die V
 
 	\begin{figure}[h]
 		\centering
-		\input{B2.9.tikz}
+		\input{Grafiken/B2_9.tikz}
 		\caption{}
 		\label{fig:b2.2.9}
 	\end{figure}
@@ -323,7 +323,7 @@ Das folgende Beispiel zeigt, daß der Begriff des einseitigen Grenzwertes auch f
 
 	\begin{figure}[h]
 		\centering
-		\input{B2.10.tikz}
+		\input{Grafiken/B2_10.tikz}
 		\caption{}
 		\label{fig:b2.2.10}
 	\end{figure}
@@ -372,7 +372,7 @@ Geometrisch bedeutet $\lim _{x \rightarrow+\infty} f(x)=g$, daß sich die Bildku
 
 \begin{figure}[h]
 	\centering
-	\input{B2.11.tikz}
+	\input{Grafiken/B2_11.tikz}
 	\caption{}
 	\label{fig:b2.2.11}
 \end{figure}
@@ -393,7 +393,7 @@ Im Zusammenhang mit den folgenden Beispielen sei an die Bildkurven der jeweilige
 
 	\begin{figure}[h]
 		\centering
-		\input{B2.12.tikz}
+		\input{Grafiken/B2_12.tikz}
 		\caption{}
 		\label{fig:b2.2.12}
 	\end{figure}
@@ -432,8 +432,6 @@ Ist $x$ eine Variable für die Zeit, dann bedeutet die Existenz von $\lim _{x \r
 
 Die Geschwindigkeit\footnote{In \textcolor{red}{4.2.2.} werden wir die Geschwindigkeit einer geradlinigen Bewegung exakt definieren.} $v$ eines fallenden Körpers der Masse $m$ ist unter der Annahme eines geschwindigkeitsproportionalen Luftwiderstands (Proportionalitätsfaktor $k>0$ ) durch
 
-\end{beispiel}
-
 $$
 	v=\left(v_0-\frac{m \mathrm{~g}}{k}\right) \mathrm{e}^{-\frac{k}{m} t}+\frac{m \mathrm{~g}}{k} \quad(t \geqq 0)
 $$
@@ -444,38 +442,46 @@ gegeben ( $t$ : Zeit, $v_0$ : Geschwindigkeit zur Zeit $t=0, \mathrm{~g}$ : Erdb
 
 d.h., nach hinreichend langer Zeit $t$ hat die Geschwindigkeit $v$ nahezu den konstanten Wert $\frac{m \mathrm{~g}}{k}$. In Bild 2.13 haben wir $v$ als Funktion von $t$ für den Fall $v_0<\frac{m \mathrm{~g}}{k}$ dargestellt.
 
-\section{Bestimmte und unbestimmte Divergenz}
-Besitzt eine Funktion $f$ für eine der "`Bewegungen"'
-
 	\begin{figure}[ht]
 		\centering
-		\includegraphics[width=0.5\linewidth]{B.2.13}
+		\includegraphics[width=0.5\linewidth]{Grafiken/B2_13.png}
 		\caption{}
 		\label{fig:b2.2.13}
 	\end{figure}
+\end{beispiel}
 
+\section{Bestimmte und unbestimmte Divergenz}
 
-HIERHIERHIERHIERHIER
+Besitzt eine Funktion $f$ für eine der "`Bewegungen"'
 
 \begin{align}
 x \rightarrow x_0 ; \quad x \rightarrow x_0+0, x \rightarrow x_0-0 ; \quad x \rightarrow+\infty, x \rightarrow-\infty
 \end{align}
 
-einen Grenzwert, dann heißt sie für diese „Bewegung“ konvergent, andernfalls divergent. Wie für Zahlenfolgen kann man auch für Funktionen zwei Arten der Divergenz unterscheiden.
+einen Grenzwert, dann heißt sie für diese "`Bewegung"' konvergent, andernfalls divergent. Wie für Zahlenfolgen kann man auch für Funktionen zwei Arten der Divergenz unterscheiden.
 
 \begin{definition}\label{def:2.4}
-Die Funktion $f$ heißt bestimmt\marginpar[\textbf{D.2.4}]{\textbf{D.2.4}} divergent gegen $+\infty(\text{bzw.}-\infty)$ für eine der
+Die Funktion $f$ heißt\textbf{ bestimmt}\marginpar[\textbf{D.2.4}]{\textbf{D.2.4}} \textbf{divergent gegen} $+\infty(\text{bzw.}-\infty)$ für eine der "`Bewegungen"' (2.17) der unabhängigen Variablen $x$, wenn für jede diese "`Bewegung"' realisierende Folge\footnote{Man sagt z. B., die Folge $\left(x_n\right)$ \textit{realisiere} die "`Bewegung"' $x \rightarrow x_0+0$, wenn $x_n>x_0$ für alle $n$ und $\lim _{n \rightarrow \infty} x_n=x_0$ gilt.} $\left(x_n\right)$ in $D(f)$ die Folge $\left(f\left(x_n\right)\right)$ bestimmt divergent gegen $+\infty($ bzw. $-\infty)$ ist.
 
+
+Ist $f$ für eine der "`Bewegungen"' (2.17) weder konvergent noch bestimmt divergent, so heißt $f$ für diese "`Bewegung"' \textbf{unbestimmt divergent}.
 \end{definition}
 
-„Bewegungen“ (2.17) der unabhängigen Variablen $x$, wenn für jede diese „Bewegung“ realisierende Folge $\left.{ }^1\right)\left(x_n\right)$ in $D(f)$ die Folge $\left(f\left(x_n\right)\right)$ bestimmt divergent gegen $+\infty($ bzw. $-\infty)$ ist.
 
-Ist $f$ für eine der „Bewegungen“ (2.17) weder konvergent noch bestimmt divergent, so heißt $f$ für diese „Bewegung“ unbestimmt divergent.
 Ist $f$ bestimmt divergent gegen $+\infty$ für $x \rightarrow x_0$, so schreibt man
 $$
 	\lim _{x \rightarrow x_0} f(x)=+\infty
 $$
-und sagt auch, $f$ habe für $x \rightarrow x_0$ den uneigentlichen Grenzwert $+\infty$. Analoge Schreibund Sprechweisen sind in den anderen Fällen bestimmter Divergenz üblich.
+und sagt auch, $f$ habe für $x \rightarrow x_0$ den \textit{uneigentlichen Grenzwert} $+\infty$. Analoge Schreib- und Sprechweisen sind in den anderen Fällen bestimmter Divergenz üblich.
+
+\begin{beispiel} \label{bsp:2.12}
+
+
+
+\end{beispiel}
+
+
+
 
 HIERHIERHIERHIERHIER
 
@@ -489,7 +495,7 @@ Beispiel 2.13: Es soll die Grenzwertaussage
 $$
 	\lim _{x \rightarrow+0} \ln x=-\infty
 $$
-bewiesen werden. Es sei $\left(x_n\right)$ eine Nullfolge mit $x_n>0$ für alle $n$. Zu jeder (insbeson\footnote{Man sagt z. B., die Folge $\left(x_n\right)$ realisiere die "Bewegung“ $x \rightarrow x_0+0$, wenn $x_n>x_0$ für alle $n$ und $\lim _{n \rightarrow \infty} x_n=x_0$ gilt.}
+bewiesen werden. Es sei $\left(x_n\right)$ eine Nullfolge mit $x_n>0$ für alle $n$. Zu jeder (insbeson
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -742,7 +748,7 @@ Mit dem Begriff der Stetigkeit einer Funktion $f$ an einer Stelle $x_0$ will man
 
 \begin{figure}
 	\centering
-	\includegraphics[width=0.7\linewidth]{B.2.17}
+	\includegraphics[width=0.7\linewidth]{Grafiken/B2_17.png}
 	\caption{}
 	\label{fig:b}
 \end{figure}
@@ -802,7 +808,7 @@ Beispiel 3.3: Die geradlinige Bewegung einer Punktmasse wird durch die Weg-ZeitF
 
 \begin{figure}
 	\centering
-	\includegraphics[width=0.7\linewidth]{B.2.18}
+	\includegraphics[width=0.7\linewidth]{Grafiken/B2_18.png}
 	\caption{}
 	\label{fig:b}
 \end{figure}
@@ -842,7 +848,7 @@ Da auch $f(0)=0$ gilt, ist $f$ an der Stelle $x=0$ stetig. Das Bild von $f$ best
 
 \begin{figure}
 	\centering
-	\includegraphics[width=0.7\linewidth]{B2.19}
+	\includegraphics[width=0.7\linewidth]{Grafiken/B2_19.png}
 	\caption{}
 	\label{fig:b2}
 \end{figure}
@@ -1081,9 +1087,9 @@ $\left\{\begin{array}{l}x^n: \quad a_n=b_{n-1}, \\ x^{n-1}: a_{n-1}=b_{n-2}-x_0
 %\end{tikzpicture}
 
 %\tracingmacros=2 \tracingcommands=2
-\newpage
+\newpage    
 
 
-\input{Horner01.tikz}
+\input{Grafiken/Horner01.tikz}
 \newpage
-\input{Horner02.tikz}
+\input{Grafiken/Horner02.tikz}