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added example

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Martin Thoma 2012-09-29 17:48:16 +02:00
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tikz/quadratic-function-uniform-continuity/quadratic-function-uniform-continuity.tex Normal file
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\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}
\usepackage{amssymb,amsmath}
\usepackage{pgfplots}
\usepackage{tikz}
\usetikzlibrary{arrows, positioning, calc, intersections, decorations.pathreplacing}
\newcommand\tikzmark[1]{%
\tikz[overlay,remember picture,baseline] \coordinate [anchor=base] (#1);}
\newcommand\DrawBrace[3]{%
\draw [decorate,decoration={brace,amplitude=5pt,mirror,raise=2pt}]
(#1) -- (#2) node [midway,xshift=15pt] {$\displaystyle #3$};
}
\begin{document}
\begin{preview}
\begin{tikzpicture}[/pgf/declare function={f=x^2;}]
\pgfplotsset{
right segments/.code={\pgfmathsetmacro\rightsegments{#1}},
right segments=3,
right/.style args={#1:#2}{
ybar interval,
domain=#1+((#2-#1)/\rightsegments):#2+((#2-#1)/\rightsegments),
samples=\rightsegments+1,
x filter/.code=\pgfmathparse{\pgfmathresult-((#2-#1)/\rightsegments)}
}
}
\pgfplotsset{
left segments/.code={\pgfmathsetmacro\leftsegments{#1}},
left segments=3,
left/.style args={#1:#2}{
ybar interval,
domain=#1:#2,
samples=\leftsegments+1,
x filter/.code=\pgfmathparse{\pgfmathresult}
}
}
\begin{axis}[
axis lines=middle,
width=15cm, height=15cm, % size of the image
grid = major,
grid style={dashed, gray!30},
xmin= 0, % start the diagram at this x-coordinate
xmax= 4.3, % end the diagram at this x-coordinate
ymin= 0, % start the diagram at this y-coordinate
ymax=17, % end the diagram at this y-coordinate
axis background/.style={fill=white},
ylabel=y,
xlabel=x,
tick align=outside,
tension=0.08,
legend style={at={(0.25,0.91)}, anchor=north}]
\addplot[ultra thick, red, samples=1000] {f};
\addplot [
black!80,
fill=green,
opacity=.3,
left segments=4,
left=0:4
] {f};
\legend{$f: \mathbb{R^+} \rightarrow \mathbb{R^+} ~~~ f(x) = x^2$};
%\node[coordinate,label=$\delta$] at (axis cs:0.5,0) {};
\node[coordinate,label=$\delta$] at (axis cs:1.5,0) {};
\node[coordinate,label=$\delta$] at (axis cs:2.5,0) {};
\node[coordinate,label=$\delta$] at (axis cs:3.5,0) {};
\coordinate (a) at (axis cs:1,1);
\coordinate (b) at (axis cs:2,4);
\coordinate (c) at (axis cs:3,9);
\coordinate (d) at (axis cs:4,16);
\draw[ultra thick, blue,dashed](a -| current plot begin) -- (a);
\draw[ultra thick, blue,dashed](a |- current plot begin) -- (a);
\draw[ultra thick, blue,dashed](b -| current plot begin) -- (b);
\draw[ultra thick, blue,dashed](b |- current plot begin) -- (b);
\draw[ultra thick, blue,dashed](c -| current plot begin) -- (c);
\draw[ultra thick, blue,dashed](c |- current plot begin) -- (c);
\draw[ultra thick, blue,dashed](d -| current plot begin) -- (d);
\draw[ultra thick, blue,dashed](d |- current plot begin) -- (d);
\coordinate (x1) at (axis cs: 0, 1);
\coordinate (x2) at (axis cs: 0, 4);
\coordinate (x3) at (axis cs: 0, 9);
\coordinate (x4) at (axis cs: 0,16);
\DrawBrace{x1}{x2}{\varepsilon_1};
\DrawBrace{x2}{x3}{\varepsilon_2};
\DrawBrace{x3}{x4}{\varepsilon_3};
\end{axis}
\end{tikzpicture}
\end{preview}
\end{document}