Aus Online Mathematik Brückenkurs 2

Diese Aktion ist beschränkt auf Benutzer, die einer der Gruppen „Administratoren, approved“ angehören.

Quelltext dieser Seite:

<noinclude>Dies ist eine Figur die in [[Lösung 1.3:1a|Lösung 1.3:1a]] verwendet wird, und in der Programmierungssprache [http://en.wikipedia.org/wiki/Metapost Metapost] geschrieben ist. Die Figur kann editiert werden indem man auf "Editieren" drückt. <center> </noinclude> <metapost> verbatimtex \documentclass{report} etex verbatimtex \usepackage{amsmath} etex verbatimtex \begin{document} etex vardef startdashed expr p = save t; numeric t[]; t1 := arctime 7bp of p; draw subpath(t1,length p) of p; draw subpath(t1,0) of p dashed dashpattern(off 12/9 bp on 9/9 bp); enddef; vardef enddashed expr p = save t; numeric t[]; t2 := arctime (arclength p -7bp) of p; draw subpath(0,t2) of p; draw subpath(t2,length p) of p dashed dashpattern(off 12/9 bp on 9/9 bp); enddef; vardef startenddashed expr p = save t; numeric t[]; t1 := arctime 7bp of p; t2 := arctime (arclength p -7bp) of p; draw subpath(t1,t2) of p; draw subpath(t1,0) of p dashed dashpattern(off 12/9 bp on 9/9 bp); draw subpath(t2,length p) of p dashed dashpattern(off 12/9 bp on 9/9 bp); enddef; vardef startshy expr p = save q, t; path q; numeric t[]; q := fullcircle scaled 2.0pt shifted point 0 of p; t := xpart (p intersectiontimes q); subpath(t,infinity) of p enddef; vardef endshy expr p = save q, t; path q; numeric t[]; q := fullcircle scaled 4.0pt shifted point infinity of p; t := xpart (p intersectiontimes q); subpath(0,t) of p enddef; vardef startendshy expr p = save q,r,s,t; path q,r; numeric s[],t[]; q := fullcircle scaled 3.5pt shifted point 0 of p; r := fullcircle scaled 2.0pt shifted point infinity of p; s := xpart (p intersectiontimes q); t := xpart (p intersectiontimes r); subpath(s,t) of p enddef; beginfig(1); dx := 8.30219pt; % horizontal distance between grid lines dy := dx; % vertical distance between grid lines Lx_lft := 7*dx+2pt; % Length of the left-hand part of the x-axis Lx_rt := 5*dx+2pt; % Length of the right-hand part of the x-axis Ly_lwr := 3*dy+4pt; % Length of the lower part of the y-axis Ly_upr := 7*dy+4pt; % Length of the upper part of the y-axis ahangle := 30; % Angle of the arrow tip ahlength := 5bp; % Length of the arrow tip color lightblue, lightgrey; lightblue := (0.2,0.6,1); lightgrey := 0.5white; % Background grid pickup pencircle scaled 0.1pt; for x=dx step dx until infinity: exitif x>Lx_rt-2pt; draw (x,-Ly_lwr)--(x,Ly_upr) withcolor lightblue; endfor for x=-dx step -dx until -infinity: exitif x<-Lx_lft+2pt; draw (x,-Ly_lwr)--(x,Ly_upr) withcolor lightblue; endfor for y=dy step dy until infinity: exitif y>Ly_upr-2pt; draw (-Lx_lft,y)--(Lx_rt,y) withcolor lightblue; endfor for y=-dy step -dy until -infinity: exitif y<-Ly_lwr+2pt; draw (-Lx_lft,y)--(Lx_rt,y) withcolor lightblue; endfor % The coordinate axes pickup pencircle scaled 0.4pt; drawarrow (-Lx_lft,0)--(Lx_rt,0); label.rt(btex \small\strut $x$ etex, (Lx_rt,0)); drawarrow (0,-Ly_lwr)--(0,Ly_upr); label.top(btex \small\strut $y$ etex, (0,Ly_upr)); % The graph vardef f(expr x) = (3/4)*(x**2) enddef; vardef df(expr x) = (3/4)*2*x enddef; path p_graph; p_graph := (-4*2dx,f(-4)*2dy){(1,df(-4)*dy/dx)} for x=-3.5 step 0.5 until 4: ..{(1,df(x)*dy/dx)}(x*2dx,f(x)*2dy) endfor; s := xpart (p_graph intersectiontimes ((-Lx_lft,Ly_upr)--(0,Ly_upr))); t := xpart (p_graph intersectiontimes ((0,Ly_upr)--(Lx_rt,Ly_upr))); p_graph := subpath(s,t) of p_graph; % Draw the decreasing part of the graph s := xpart (p_graph intersectiontimes ((0,-10pt)--(0,10pt))); drawoptions(withcolor lightblue withpen pencircle scaled 0.6pt); linecap:=butt; startdashed subpath(-infinity,s) of p_graph; linecap := rounded; drawoptions(); % Draw the increasing part of the graph drawoptions(withcolor 0.6[lightblue,white] withpen pencircle scaled 0.6pt); linecap:=butt; enddashed subpath(s,infinity) of p_graph; linecap := rounded; drawoptions(); % Tick marks pickup pencircle scaled 0.4pt; for x=2dx step 2dx until infinity: exitif x>Lx_rt-3pt; draw (x,-1.5pt)--(x,1.5pt); endfor %for x=-2dx step -2dx until -infinity: % exitif x<-Lx_lft+2pt; % draw (x,-1.5pt)--(x,1.5pt); %endfor for y=2dy step 2dy until infinity: exitif y>Ly_upr-5pt; draw (-1.5pt,y)--(1.5pt,y); endfor for y=-2dy step -2dy until -infinity: exitif y<-Ly_lwr+2pt; draw (-1.5pt,y)--(1.5pt,y); endfor % Draw the thick line along the negative x-axis pickup pencircle scaled 0.4pt; for x=-1.8pt step -1.5pt until -infinity: exitif x<-Lx_lft+0pt; draw (x-0.4pt,-1.8pt)--(x+0.4pt,1.8pt) withcolor lightblue; endfor % Draw the dot in x=0 pickup pencircle scaled 3.6pt; drawdot (0,0) withcolor lightblue; % Rescale the image picture p; p := currentpicture; currentpicture := nullpicture; addto currentpicture also p scaled 1.5; endfig; end. </metapost> <noinclude></center></noinclude>

Zurück zur Seite Hauptseite.