%@AUTEUR:Guillaume Connan

verbatimtex
%&latex
\documentclass{article}
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\begin{document}
etex

input courbes;
input geo;

color vert_e, turquoise, orange, vert_fonce, rose, vert_mer, bleu_ciel, or, rouge_v,bleu_m,bleu,bleu_f;
vert_e:=(0,0.790002,0.340007);
turquoise:=(0.250999,0.878399,0.815699);
orange:=(0.589999,0.269997,0.080004);
vert_fonce:=(0,1.4*0.392193,0);
rose:=(1.0, 0.752907, 0.796106);
bleu_ciel:=(1.2*0.529405,1.2*0.807794,1);%.2*0.921598);
or:=(1,0.843104,0);
rouge_v:=(0.829997,0.099994,0.119999);
bleu_m:=(0.7*0.529405,0.7*0.807794,0.7);%*0.921598);
bleu_f:=(0.211762,0.3231176,0.3686392);
bleu:=(0.529405,0.807794,1);

%%%  ARBRE ASYMPTOTIQUE

% Metapost TeX macro
% Title: Diagramme1.dia
% Creator: Dia v0.93


beginfig(11);

  x = 0.4500000cm; y = -0.6500000cm;
  
  draw (5.150000x,20.100000y)--(12.710566x,16.496103y)
  withpen pencircle scaled 0.1000x;
  
  path p;
  p = (13.049076x,16.334745y)--(12.705301x,16.775562y)--(12.710566x,16.496103y)--(12.490158x,16.324216y)--cycle;
  fill p withpen pencircle scaled 0.1000x;
  
  draw (13.049076x,16.334745y)--(12.705301x,16.775562y)--(12.710566x,16.496103y)--(12.490158x,16.324216y)--cycle
  withpen pencircle scaled 0.1000x;
  
  draw (5.000000x,20.086638y)--(12.764874x,23.981728y)
  withpen pencircle scaled 0.1000x;
  
  path p;
  p = (13.100065x,24.149870y)--(12.541049x,24.149141y)--(12.764874x,23.981728y)--(12.765238x,23.702220y)--cycle;
  fill p withpen pencircle scaled 0.1000x;
  
  draw (13.100065x,24.149870y)--(12.541049x,24.149141y)--(12.764874x,23.981728y)--(12.765238x,23.702220y)--cycle
  withpen pencircle scaled 0.1000x;
  
  draw (15.450000x,24.000000y)--(19.530353x,20.503401y)
  withpen pencircle scaled 0.1000x;
  
  path p;
  p = (19.815104x,20.259388y)--(19.598112x,20.774572y)--(19.530353x,20.503401y)--(19.272761x,20.394905y)--cycle;
  fill p withpen pencircle scaled 0.1000x;
  draw (19.815104x,20.259388y)--(19.598112x,20.774572y)--(19.530353x,20.503401y)--(19.272761x,20.394905y)--cycle
  withpen pencircle scaled 0.1000x;
  
  draw (15.400000x,24.050000y)--(19.833137x,27.916654y)
  withpen pencircle scaled 0.1000x;
  
  path p;
  p = (20.115743x,28.163148y)--(19.574607x,28.022894y)--(19.833137x,27.916654y)--(19.903264x,27.646086y)--cycle;
  fill p withpen pencircle scaled 0.1000x;
  
  draw (20.115743x,28.163148y)--(19.574607x,28.022894y)--(19.833137x,27.916654y)--(19.903264x,27.646086y)--cycle
  withpen pencircle scaled 0.1000x;
  draw (23.600000x,28.100000y)--(31.690877x,25.248451y)
  withpen pencircle scaled 0.1000x;
  path p;
  p = (32.044554x,25.123801y)--(31.656085x,25.525786y)--(31.690877x,25.248451y)--(31.489885x,25.054216y)--cycle;
  fill p withpen pencircle scaled 0.1000x;
  
  draw (32.044554x,25.123801y)--(31.656085x,25.525786y)--(31.690877x,25.248451y)--(31.489885x,25.054216y)--cycle
  withpen pencircle scaled 0.1000x;
  
  draw (23.800000x,28.100000y)--(31.793624x,31.067231y)
  withpen pencircle scaled 0.1000x;
  
  drawarrow (23.800000x,28.100000y)--(31.793624x,((31.067231+25.24845)/2)*y)
  withpen pencircle scaled 0.2x;
  
  path p;
  p = (32.145185x,31.197730y)--(31.589438x,31.258105y)--(31.793624x,31.067231y)--(31.763437x,30.789358y)--cycle;
  fill p withpen pencircle scaled 0.1000x;
  
  draw (32.145185x,31.197730y)--(31.589438x,31.258105y)--(31.793624x,31.067231y)--(31.763437x,30.789358y)--cycle
  withpen pencircle scaled 0.1000x;
  
  label.urt(btex $\infty$ ou pas de limite : pas d'asymptote ($x\mapsto x^2$) etex scaled 1.6,(13.450000x,16.350000y));
  label.urt(btex $a$ etex scaled 1.6,(13.950000x,24.250000y));
  label.urt(btex  $a=0$ : direction asymptotique horizontale ($x\mapsto \ln x$) etex scaled 1.6,(20.500000x,20.200000y));
  label.urt(btex $a\neq 0$ etex scaled 1.6,(20.550000x,28.186638y));
  label.urt(btex $\displaystyle\lim_{x\to+\infty}\big(f(x)-ax\big)=\infty$  ($x\mapsto x+\sqrt{x}$) etex scaled 1.6,(32.700000x,25.336638y));
  label.urt(btex branche parabolique dans la direction  $y=ax$ etex scaled 1.6,(32.700000x,26.336638y));
  
  label.urt(btex $\displaystyle\lim_{x\to+\infty}\big(f(x)-ax\big)=b$  ($x\mapsto x+\frac{1}{x}$) etex scaled 1.67988,(32.800000x,31.286638y));
  label.urt(btex asymptote d'équation $y=ax+b$ etex scaled 1.6,(32.800000x,32.286638y));
  label.urt(btex $\big(f(x)-ax\big)$ n'admet pas de limite ($x\mapsto x+\sin x$) etex scaled 1.6,(32.3x,((31.067231+25.24845)/2-0.25)*y));
  label.urt(btex direction asymptotique d'équation $y=ax$ etex scaled 1.6,(32.3x,((31.067231+25.24845)/2+0.75)*y));
  
  label.urt(btex  $\displaystyle\lim_{x\to+\infty}\frac{f(x)}{x}$ etex scaled 1.6,(0.1x,21y));
endfig;
end