From 8176bc828e2f9ed7356a5dd846c28341f685409f Mon Sep 17 00:00:00 2001 From: Sven Riwoldt Date: Tue, 13 Feb 2024 19:15:10 +0100 Subject: [PATCH] =?UTF-8?q?f=C3=BCr=20overleaf=20=C3=BCberarbeitet?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Band2/Definitions.tex | 2 +- Band2/Grafiken/B.2.10.png | Bin 0 -> 48054 bytes Band2/Grafiken/B.2.11.png | Bin 0 -> 46644 bytes Band2/Grafiken/B.2.12.png | Bin 0 -> 61161 bytes Band2/Grafiken/B.2.15.png | Bin 0 -> 51624 bytes Band2/Grafiken/B.2.3.png | Bin 0 -> 18471 bytes Band2/Grafiken/B.2.4.png | Bin 0 -> 144834 bytes Band2/Grafiken/B.2.5.png | Bin 0 -> 115121 bytes Band2/Grafiken/B.2.6.png | Bin 0 -> 110876 bytes Band2/Grafiken/B.2.8.png | Bin 0 -> 97623 bytes Band2/Grafiken/B.2.9.png | Bin 0 -> 45852 bytes Band2/Grafiken/B2.1.tex | 74 +++++++++++++ Band2/Grafiken/B2.9.tex | 79 ++++++++++++++ Band2/Grafiken/B2_1.png | Bin 0 -> 116034 bytes Band2/Grafiken/B2_10.tikz | 37 +++++++ Band2/Grafiken/B2_11.tikz | 33 ++++++ Band2/Grafiken/B2_12.tikz | 24 +++++ Band2/Grafiken/B2_13.png | Bin 0 -> 45870 bytes Band2/Grafiken/B2_14.png | Bin 0 -> 52944 bytes Band2/Grafiken/B2_16.png | Bin 0 -> 31887 bytes Band2/Grafiken/B2_17.png | Bin 0 -> 37004 bytes Band2/Grafiken/B2_18.png | Bin 0 -> 40336 bytes Band2/Grafiken/B2_19.png | Bin 0 -> 97317 bytes Band2/Grafiken/B2_2.png | Bin 0 -> 61912 bytes Band2/Grafiken/B2_3.tikz | 27 +++++ Band2/Grafiken/B2_4.tikz | 53 +++++++++ Band2/Grafiken/B2_5.tikz | 58 ++++++++++ Band2/Grafiken/B2_6.tikz | 33 ++++++ Band2/Grafiken/B2_7.png | Bin 0 -> 236422 bytes Band2/Grafiken/B2_8.tikz | 56 ++++++++++ Band2/Grafiken/B2_9.tikz | 56 ++++++++++ Band2/Grafiken/Horner01.tikz | 203 +++++++++++++++++++++++++++++++++++ Band2/Grafiken/Horner02.tikz | 56 ++++++++++ Band2/Grenzwert.tex | 68 ++++++------ 34 files changed, 827 insertions(+), 32 deletions(-) create mode 100644 Band2/Grafiken/B.2.10.png create mode 100644 Band2/Grafiken/B.2.11.png create mode 100644 Band2/Grafiken/B.2.12.png create mode 100644 Band2/Grafiken/B.2.15.png create mode 100644 Band2/Grafiken/B.2.3.png create mode 100644 Band2/Grafiken/B.2.4.png create mode 100644 Band2/Grafiken/B.2.5.png create mode 100644 Band2/Grafiken/B.2.6.png create mode 100644 Band2/Grafiken/B.2.8.png create mode 100644 Band2/Grafiken/B.2.9.png create mode 100644 Band2/Grafiken/B2.1.tex create mode 100644 Band2/Grafiken/B2.9.tex create mode 100644 Band2/Grafiken/B2_1.png create mode 100644 Band2/Grafiken/B2_10.tikz create mode 100644 Band2/Grafiken/B2_11.tikz create mode 100644 Band2/Grafiken/B2_12.tikz create mode 100644 Band2/Grafiken/B2_13.png create mode 100644 Band2/Grafiken/B2_14.png create mode 100644 Band2/Grafiken/B2_16.png create mode 100644 Band2/Grafiken/B2_17.png create mode 100644 Band2/Grafiken/B2_18.png create mode 100644 Band2/Grafiken/B2_19.png create mode 100644 Band2/Grafiken/B2_2.png create mode 100644 Band2/Grafiken/B2_3.tikz create mode 100644 Band2/Grafiken/B2_4.tikz create mode 100644 Band2/Grafiken/B2_5.tikz create mode 100644 Band2/Grafiken/B2_6.tikz create mode 100644 Band2/Grafiken/B2_7.png create mode 100644 Band2/Grafiken/B2_8.tikz create mode 100644 Band2/Grafiken/B2_9.tikz create mode 100644 Band2/Grafiken/Horner01.tikz create mode 100644 Band2/Grafiken/Horner02.tikz diff --git a/Band2/Definitions.tex b/Band2/Definitions.tex index 047ed29..b632ac0 100644 --- a/Band2/Definitions.tex +++ b/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 diff --git a/Band2/Grafiken/B.2.10.png b/Band2/Grafiken/B.2.10.png new file mode 100644 index 0000000000000000000000000000000000000000..0e4844521704c0508f84a573fdec11103e4af569 GIT binary patch literal 48054 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+\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} \ No newline at end of file diff --git a/Band2/Grafiken/B2.9.tex b/Band2/Grafiken/B2.9.tex new file mode 100644 index 0000000..0df0b6c --- /dev/null +++ b/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} \ No newline at end of file diff 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0000000..e0285c7 --- /dev/null +++ b/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} \ No newline at end of file diff --git a/Band2/Grafiken/B2_9.tikz b/Band2/Grafiken/B2_9.tikz new file mode 100644 index 0000000..9a34262 --- /dev/null +++ b/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} diff --git a/Band2/Grafiken/Horner01.tikz b/Band2/Grafiken/Horner01.tikz new file mode 100644 index 0000000..6d8fb44 --- /dev/null +++ b/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 diff --git a/Band2/Grafiken/Horner02.tikz b/Band2/Grafiken/Horner02.tikz new file mode 100644 index 0000000..844fe43 --- /dev/null +++ b/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} diff --git a/Band2/Grenzwert.tex b/Band2/Grenzwert.tex index 4893492..fcb3182 100644 --- a/Band2/Grenzwert.tex +++ b/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}

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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} \ No newline at end of file diff --git a/Band2/Grafiken/B2_4.tikz b/Band2/Grafiken/B2_4.tikz new file mode 100644 index 0000000..26a04b1 --- /dev/null +++ b/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} diff --git a/Band2/Grafiken/B2_5.tikz b/Band2/Grafiken/B2_5.tikz new file mode 100644 index 0000000..3b6e682 --- /dev/null +++ b/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} \ No newline at end of file diff --git a/Band2/Grafiken/B2_6.tikz b/Band2/Grafiken/B2_6.tikz new file mode 100644 index 0000000..f4f6a2d --- /dev/null +++ b/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 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