%@AUTEUR:Guillaume Connan
prologues:=2;

verbatimtex
%&latex
\documentclass{article}
\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);

vardef axes =
  drawarrow (ux*xmin,0) -- (ux*xmax,0); % axe des x
  drawarrow ((0,uy*ymin) -- (0,uy*ymax))  ; % axe des y
  label.lrt(btex $x$ etex,(xmax*ux,0)); % label de l'axe des x
  label.urt(btex $y$ etex,(0,ymax*uy)); % label de l'axe des y
enddef;

beginfig(1);

% Déclarations des constantes %
 ux:=1cm; uy:=0.5ux;
 xmin:=-.5; xmax:=9;
 ymin:=-0.5; ymax:=9;
 coefficient:=1; % coefficient d'échelle
 
%Tracé des axes
 axes;
 label.llft(btex $0$ etex,(-.1*ux,-.15*uy));
 
 vardef f(expr x) =0.3*x*x enddef;
 
 vardef trace (suffix g)(expr a,b,inc) =
   save i; numeric i;
   for i=a step inc until b:
     (i*ux,f(i)*uy) ..
   endfor (b*ux,f(b)*uy)
 enddef;
 
 draw (trace(g,0,5,.10))  withcolor bleu_m withpen pencircle scaled 2bp;

 vardef f(expr x) =sqrt(x/0.3)enddef;
 
 vardef trace (suffix g)(expr a,b,inc) =
   save i; numeric i;
   for i=a step inc until b:
     (i*ux,f(i)*uy) ..
   endfor (b*ux,f(b)*uy)
 enddef;
 
 draw (trace(g,0,8,.10))  withcolor vert_e withpen pencircle scaled 2bp;
 
 draw ((0,0)--(8*ux,8*uy)) dashed evenly withcolor 0.5*bleu withpen pencircle scaled 2bp;
 
 label.urt(btex $y=x^{2n}$ etex scaled 1.5, (5*ux,0.3*25*uy)) withcolor bleu_m;
 label.urt(btex $y=\sqrt[2n]{x}$ etex scaled 1.5, (8*ux,f(8)*uy)) withcolor vert_e;
 
endfig;
end