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Martin Thoma 2012-09-23 14:51:55 +02:00
parent 20514561f3
commit d5dfcc6ee5
1 changed files with 22 additions and 7 deletions
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29
tikz/stetigkeit-differenzierbarkeit/stetigkeit-differenzierbarkeit.tex
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@ -55,6 +55,7 @@
\draw[fill=yellow!20,yellow!20, rounded corners] (-1.85, 0.70) rectangle (13.4,-6.85);
\draw[fill=lime!20,lime!20, rounded corners] (-1.75, 0.45) rectangle (7.3,-6.75);
\draw[fill=purple!20,purple!20, rounded corners] (-1.65,-1.55) rectangle (7.2,-6.65);
\draw[fill=blue!20,blue!20, rounded corners] ( 4.55,-3.45) rectangle (13.1,-6.55);
\draw (0, 0) node[algebraicName] (A) {gleichmäßig stetig}
(3, 0) node[explanation] (B) {
\begin{minipage}{0.90\textwidth}
@ -62,8 +63,8 @@
$\forall \varepsilon >0 \ \exists \delta=\delta(\varepsilon)>0\colon\\ |f(x)-f(z)| < \varepsilon\\ \forall x,z \in D \text{ mit } |x-z|<\delta$
\end{minipage}
}
(6, 0) node[example, draw=lime, fill=lime!15] (X) {\tiny$f(x)=\sin(x)$}
(6,-1) node[example, draw=lime, fill=lime!15] (X) {\tiny$g(x)=\cos(x)$}
(6, 0) node[example, draw=lime, fill=lime!15] (X) {\tiny$f_5(x)=\sin(x)$}
(6,-1) node[example, draw=lime, fill=lime!15] (X) {\tiny$f_6(x)=\cos(x)$}
(0,-2) node[algebraicName, purple] (C) {Lipschitz-stetig}
(3.5,-2) node[explanation] (X) {
\begin{minipage}{90\textwidth}
@ -74,13 +75,14 @@ $:\Leftrightarrow \exists L\ge 0: |f(x)-f(z)|\le L|x-z|\ \forall x,z \in D$
}
(12,-6) node[example, draw=black, fill=black!15] (G) {\tiny$f_2(x) = e^x$}
(0,-6) node[example, draw=red, fill=red!15] (K) {\tiny$h(x) = |x|$}
(6,-6) node[example, draw=red, fill=red!15, pattern=north east lines wide, pattern color=black!25] (N) {\tiny$f_1(x) = 42$}
(0,-6) node[example, draw=red, fill=red!15] (K) {\tiny$f_4(x) = |x|$}
(6,-6) node[example, draw=red, fill=red!15, pattern=north east lines wide, pattern color=black!25] (N) {\tiny$f_7(x) = 42$}
(6,-4) node[example, draw=red, fill=red!15, pattern=north east lines wide, pattern color=black!25] (ANCHORD) {\tiny$f_3(x) = 42$}
(12,-2) node[example, draw=yellow, fill=yellow!15] (Q) {\tiny$f_4(x) = |x|$}
(12,-2) node[example, draw=yellow, fill=yellow!15] (Q) {\tiny$f_1(x) = |x|$}
(9, 0) node[algebraicName] (O) {Stetige Funktionen}
(9, 0) node[algebraicName] (O) {stetig}
(12,0) node[explanation] (X) {
\begin{minipage}{0.9\textwidth}
\tiny
@ -91,8 +93,21 @@ $:\Leftrightarrow \exists L\ge 0: |f(x)-f(z)|\le L|x-z|\ \forall x,z \in D$
\end{minipage}
}
(12,-4) node[example, draw=black, fill=black!15] (P) {\tiny$f_3(x) = \frac{1}{x}$};
(12,-4) node[example, draw=black, fill=black!15] (P) {\tiny$g_1(x) = \frac{1}{x}$}
(9, -4) node[algebraicName] (random1) {differenzierbar}
(9.8, -4.7) node[explanation] (X) {
\begin{minipage}{0.9\textwidth}
\tiny
$f$ heißt differenzierbar in $x_0 :\Leftrightarrow$\\
$\lim_{h \rightarrow 0} \frac{f(x_0+h) - f(x_0)}{h}$
existiert
\end{minipage}
};
% differenzierbar
\draw[blue, thick, rounded corners] ($(ANCHORD.north west)+(-0.5,0.2)$) rectangle ($(G.south east)+(0.2,-0.2)$);
% LP-Stetig
\draw[purple, thick, rounded corners] ($(C.north west)+(-0.3,0.1)$) rectangle ($(N.south east)+(0.3,-0.3)$);
% gleichmäßig stetig