Fichier Cours-1S.mp (figure 9) — Modifié le 17 Septembre 2009 à 00 h 43

Cours-1S.mp (figure 9)
Source

prologues:=2;

verbatimtex
 %\documentclass{article}
 %\usepackage[latin1]{inputenc}
 %\usepackage[frenchb]{babel}
 %\usepackage{amsmath}
 %\begin{document}
etex



beginfig(1)
  u:=1cm;
%figure(-2.6u,-1.2u,4.3u,4.3u);

pair O,I,J,A,B,C,D,M,N;
path p;
O=(0,0);
I=(u,0);
J=(0,u);
%repere(O,I,J):
Xmin=-2.6u;
Xmax=4u;
Ymin=-1.5u;
Ymax=4u;

drawarrow (Xmin,0)--(Xmax,0);
drawarrow (0,Ymin)--(0,Ymax);
%drawarrow O--I withpen pencircle scaled 1.5pt;
%drawarrow O--J withpen pencircle scaled 1.5pt;
A=(-1.5u,-1.45u);
B=(u,0);
C=(1.8u,1.5u);% avec lignes de rappel
M=(3.2u,2.7u);% idem
D=(4u,3.5u);

draw A..B..C..M..D withcolor blue withpen pencircle scaled 1pt;
label.rt(btex $C_f$ etex, (.7u,-.7u)) withcolor blue;
draw (xpart(C),0)--C--(0,ypart(C)) withcolor blue dashed evenly;
label.bot(btex $a$ etex,(xpart(C),0)) withcolor blue;
label.lft(btex $f(a)$ etex, (0,ypart(C))) withcolor blue;

draw (xpart(M),0)--M--(0,ypart(M)) withcolor blue dashed evenly;
label.bot(btex $b$ etex,(xpart(M),0)) withcolor blue;
label.lft(btex $f(b)$ etex, (0,ypart(M))) withcolor blue;

label.bot(btex $a<b$ etex,(.5*xpart(C)+.5*xpart(M),-.5u));
label.lft(btex $f(a)<f(b)$ etex, (-.5u,.5ypart(C)+.5ypart(M)));


endfig;

beginfig(2)  %fct strict dec
%figure(-2.6u,-1.2u,4.3u,4.3u);
pair O,I,J,A,B,C,D,M,N;
path p;
O=(0,0);
I=(u,0);
J=(0,u);
%repere(O,I,J);
Xmin:=-2.6u;
Xmax:=4u;
Ymin:=-1.5u;
Ymax:=4u;

drawarrow (Xmin,0)--(Xmax,0);
drawarrow (0,Ymin)--(0,Ymax);
%--
A=(-2u,3u);
C=(.7u,1.7u);
M=(1.8u,.5u);
B=(3.2u,-.5u);
D=(4u,-u);

draw A..C..M..B..D withcolor blue withpen pencircle scaled 1pt;
label.urt(btex $C_f$ etex, B) withcolor blue;
draw (xpart(C),0)--C--(0,ypart(C)) withcolor blue dashed evenly;
label.bot(btex $a$ etex,(xpart(C),0)) withcolor blue;
label.lft(btex $f(a)$ etex, (0,ypart(C))) withcolor blue;

draw (xpart(M),0)--M--(0,ypart(M)) withcolor blue dashed evenly;
label.bot(btex $b$ etex,(xpart(M),0)) withcolor blue;
label.lft(btex $f(b)$ etex, (0,ypart(M))) withcolor blue;

label.bot(btex $a<b$ etex,(.5*xpart(C)+.5*xpart(M),-.5u));
label.lft(btex $f(a)>f(b)$ etex, (-.5u,.5ypart(C)+.5ypart(M)));
endfig;


beginfig(3)
  %%%%%%%%%%%%%%%%%%%%%%%%%
  % fonctions associées : %
  % g(x) = f(x)+beta      %
  %%%%%%%%%%%%%%%%%%%%%%%%%
  u:=0.7cm; v=0.4cm;
  %figure(-3.2u,-1.6u,3.2u,4.8u);
  pair O,I,J,M,N;
  path p[];
  numeric a;
  O=(0,0);
  I=(u,0);
  J=(0,v);
  a=2;
  M=(a*u,a*a*v);
  N=M-2*(J-O);
  %repere(O,I,J);
  Xmin:=-3;
  Xmax:=3;
  Ymin:=-3;
  Ymax:=9;
 %Quadrillage en croix
  c:=0.07;
  p0:=(-c,0)*u--(c,0)*u--(0,0)*u--(0,c)*u--(0,-c)*u; % CROIX
  p0:=p0 shifted (floor(Xmin)*u,floor(Ymin)*v); %mise dans le coin SO
 for i=0 upto floor(Ymax-Ymin):
    for j=0 upto floor(Xmax-Xmin):
      draw p0 shifted (j*u,0) withpen pencircle scaled 0.2bp withcolor 0.6white;
    endfor ;
    p0:=p0 shifted (0,v);
 endfor ;
 %--
  drawarrow (Xmin*u,0)--(Xmax*u,0);
  drawarrow (0,Ymin*v)--(0,Ymax*v);
 drawarrow O--I withpen pencircle scaled 1.13pt;
 drawarrow O--J withpen pencircle scaled 1.13pt;
 label.bot(btex $\vec{\imath}$ etex, (0.5u,-0.1v));
 label.lft(btex $\vec{\jmath}$ etex, (-0.1u,0.5v));
  %--
  Xmin:=-3;
  Xmax:=3;
  Ymin:=-1.5;
  Ymax:=4.8;
  numeric Npts;
  Npts:=50;
   vardef f(expr x) = x*x enddef;
   vardef g(expr x) = x*x-2 enddef;
 p1= ( ( Xmin*u, (f(Xmin))*v )
         for i=1 upto Npts:
     ..( (Xmin + (i/Npts)*(Xmax - Xmin))*u, (f( Xmin + (i/Npts)*(Xmax - Xmin) ))*v)
   endfor ) ;
 %Xmin:=0.6;  Xmax:=5;
 p2= ( ( Xmin*u, (g(Xmin))*v )
         for i=1 upto Npts:
     ..( (Xmin + (i/Npts)*(Xmax - Xmin))*u, (g( Xmin + (i/Npts)*(Xmax - Xmin) ))*v)
   endfor ) ;
 draw p1;
 draw p2 dashed evenly;

 drawarrow M--N withcolor red withpen pencircle scaled 1bp;
 drawarrow ((M--N) shifted (-M+(u,v))) withcolor red withpen pencircle scaled 1bp;
 drawarrow ((M--N) shifted (-M+(-3u,9v))) withcolor red withpen pencircle scaled 1bp;
 label.rt(btex $-2\vec{\jmath}$ etex, .5*(M+N)) withcolor red;
  label.rt(btex $C_g$ etex, (-3u,2v));
  label.rt(btex $C_f$ etex, (-2u,4v));
  label.rt(btex $g(x)=f(x)-2$ etex, (-2.8u,8.5v));
  dotlabel(btex $$ etex,(0,-2v));
endfig;


beginfig(4)
  %%%%%%%%%%%%%%%%%%%%%%%%%
  % fonctions associées : %
  % g(x) = f(x+beta)      %
  %%%%%%%%%%%%%%%%%%%%%%%%%
  %u:=1cm; v:=0.5cm;
  %figure(-3.2u,-1.6u,3.2u,4.8u);
  pair O,I,J,M,N;
  path p[];
  numeric a, b;
  O=(0,0);
  I=(u,0);
  J=(0,v);

  a:=2;
  b:=1.5;
  M:=(a*u,a*a*v);
  N:=M+b*(I-O);
  %repere(O,I,J);
  Xmin:=-3;
  Xmax:=4.5;
  Ymin:=-3;
  Ymax:=9;
   %Quadrillage en croix
  c:=0.07;
  p0:=(-c,0)*u--(c,0)*u--(0,0)*u--(0,c)*u--(0,-c)*u; % CROIX
  p0:=p0 shifted (floor(Xmin)*u,floor(Ymin)*v); %mise dans le coin SO
 for i=0 upto floor(Ymax-Ymin):
    for j=0 upto floor(Xmax-Xmin):
      draw p0 shifted (j*u,0) withpen pencircle scaled 0.2bp withcolor 0.6white;
    endfor ;
    p0:=p0 shifted (0,v);
 endfor ;
 %--
 drawarrow (Xmin*u,0)--(Xmax*u,0);
  drawarrow (0,Ymin*v)--(0,Ymax*v);
 drawarrow O--I withpen pencircle scaled 1.13pt;
 drawarrow O--J withpen pencircle scaled 1.13pt;
 label.bot(btex $\vec{\imath}$ etex, (0.5u,-0.1v));
 label.lft(btex $\vec{\jmath}$ etex, (-0.1u,0.5v));
  %--
  Xmin:=-3;
  Xmax:=2.8;
  Ymin:=-1.5;
  Ymax:=4.8;
  numeric Npts;
  Npts:=50;
   vardef f(expr x) = x*x enddef;
   vardef g(expr x) = (x-b)*(x-b) enddef;
 p1= ( ( Xmin*u, (f(Xmin))*v )
         for i=1 upto Npts:
     ..( (Xmin + (i/Npts)*(Xmax - Xmin))*u, (f( Xmin + (i/Npts)*(Xmax - Xmin) ))*v)
   endfor ) ;
 Xmin:=Xmin+b;  Xmax:=Xmax+b;
 p2= ( ( Xmin*u, (g(Xmin))*v )
         for i=1 upto Npts:
     ..( (Xmin + (i/Npts)*(Xmax - Xmin))*u, (g( Xmin + (i/Npts)*(Xmax - Xmin) ))*v)
   endfor ) ;
 draw p1;
 draw p2 dashed evenly;

 drawarrow M--N withcolor red withpen pencircle scaled 1bp;
 drawarrow ((M--N) shifted (-M+(u,v))) withcolor red withpen pencircle scaled 1bp;
 drawarrow ((M--N) shifted (-M+(-3u,9v))) withcolor red withpen pencircle scaled 1bp;
 %drawarrow M--N withcolor red withpen pencircle scaled 1bp shifted;
 label.top(btex $1,5\vec{\imath}$ etex, .5*(M+N)) withcolor red;

  label.rt(btex $C_g$ etex, (-1.5u,4v));
  label.rt(btex $C_f$ etex, (-2.7u,3v));
  label.rt(btex $g(x)=f(x-1,5)$ etex, (0u,8.5v));
dotlabel(btex $$ etex,(b,0)*u);
endfig;

beginfig(5)
  %%%%%%%%%%%%%%%%%%%%%%%%%
  % fonctions associées : %
  % g(x) = f(x-b)-a       %
  %%%%%%%%%%%%%%%%%%%%%%%%%
  %u:=1cm; v:=0.5cm;
  %figure(-3.2u,-1.6u,3.2u,4.8u);
  pair O,I,J,M,N,P,Q;
  path p[];
  numeric a, b,c;
  O=(0,0);
  I=(u,0);
  J=(0,v);
  a:=2;
  b:=1.5;
  M:=(a*u,a*a*v);
  N:=M+b*(I-O)-a*(J-O);
  P:=M+(b*u,0);
  Q:=P+(0,-a)*v;

  %repere(O,I,J);
  Xmin:=-3;
  Xmax:=4.5;
  Ymin:=-3;
  Ymax:=9;
 %Quadrillage en croix
  c:=0.07;
  p0:=(-c,0)*u--(c,0)*u--(0,0)*u--(0,c)*u--(0,-c)*u; % CROIX
  p0:=p0 shifted (floor(Xmin)*u,floor(Ymin)*v); %mise dans le coin SO
 for i=0 upto floor(Ymax-Ymin):
    for j=0 upto floor(Xmax-Xmin):
      draw p0 shifted (j*u,0) withpen pencircle scaled 0.2bp withcolor 0.6white;
    endfor ;
    p0:=p0 shifted (0,v);
 endfor ;
 %--
 %Axes et vect unit
  drawarrow (Xmin*u,0)--(Xmax*u,0);
  drawarrow (0,Ymin*v)--(0,Ymax*v);
 drawarrow O--I withpen pencircle scaled 1.13pt;
 drawarrow O--J withpen pencircle scaled 1.13pt;
 label.bot(btex $\vec{\imath}$ etex, (0.5u,-0.1v));
 label.lft(btex $\vec{\jmath}$ etex, (-0.1u,0.5v));
 %--
  Xmin:=-3;
  Xmax:=2.8;
  Ymin:=-1.5;
  Ymax:=4.8;
  numeric Npts;
  Npts:=50;
   vardef f(expr x) = x*x enddef;
   vardef g(expr x) = (x-b)*(x-b)-2 enddef;
 p1= ( ( Xmin*u, (f(Xmin))*v )
         for i=1 upto Npts:
     ..( (Xmin + (i/Npts)*(Xmax - Xmin))*u, (f( Xmin + (i/Npts)*(Xmax - Xmin) ))*v)
   endfor ) ;
 Xmin:=-1.8;  Xmax:=4.5;
 p2= ( ( Xmin*u, (g(Xmin))*v )
         for i=1 upto Npts:
     ..( (Xmin + (i/Npts)*(Xmax - Xmin))*u, (g( Xmin + (i/Npts)*(Xmax - Xmin) ))*v)
   endfor ) ;
 draw p1;
 draw p2 dashed evenly;


 drawarrow M--P withpen pencircle scaled 1pt;
 drawarrow P--Q withpen pencircle scaled 1pt;
 drawarrow O--(-a*J) withpen pencircle scaled 1pt shifted M shifted (b*I);
 drawarrow M--N withcolor red withpen pencircle scaled 1bp;
 drawarrow M--N withcolor red withpen pencircle scaled 1bp shifted (-M+(-3u,9v));
 label.top(btex $1,5\vec{\imath}$ etex, 0.5*(M+P));
 label.rt(btex $-2\vec{\jmath}$ etex,  0.5*(P+Q));
 label.rt(btex $1,5\vec{\imath}-2\vec{\jmath}$ etex, (0.6u,2.5v)) withcolor red;
  label.rt(btex $C_g$ etex, (-1u,5v));
  label.rt(btex $C_f$ etex, (-3u,3v));
  label.rt(btex $g(x)=f(x-1,5)-2$ etex, (0u,8.5v));
dotlabel(btex $$ etex,(b*u,-a*v));
endfig;

beginfig(6)
  %%%%%%%%%%%%%%%%%%%%%%%%%
  % fonctions associées : %
  % g(x) = f(-x)          %
  %%%%%%%%%%%%%%%%%%%%%%%%%
  u:=1cm; v:=1cm;
  %figure(-3.2u,-1.6u,3.2u,4.8u);
  pair M[],O,I,J;
  path p[];
  numeric a, b,c;
  O=(0,0);
  I=(u,0);
  J=(0,v);

  %repere(O,I,J);
  Xmin:=-2;
  Xmax:=2;
  Ymin:=-2;
  Ymax:=2;
 %Quadrillage en croix
  c:=0.07;
  p0:=(-c,0)*u--(c,0)*u--(0,0)*u--(0,c)*u--(0,-c)*u; % CROIX
  p0:=p0 shifted (floor(Xmin)*u,floor(Ymin)*v); %mise dans le coin SO
 for i=0 upto floor(Ymax-Ymin):
    for j=0 upto floor(Xmax-Xmin):
      draw p0 shifted (j*u,0) withpen pencircle scaled 0.2bp withcolor 0.6white;
    endfor ;
    p0:=p0 shifted (0,v);
 endfor ;
 %--
 %Axes et vect unit
  drawarrow (Xmin*u,0)--(Xmax*u,0);
  drawarrow (0,Ymin*v)--(0,Ymax*v);
 drawarrow O--I withpen pencircle scaled 1.13pt;
 drawarrow O--J withpen pencircle scaled 1.13pt;
 label.bot(btex $\vec{\imath}$ etex, (0.5u,-0.1v));
 label.lft(btex $\vec{\jmath}$ etex, (-0.1u,0.5v));
 %--
 M0:=(-2u,-1.8v);
 M1:=(0,-v);
 M2:=(u,0);
 M3:=(2u,1.5v);
 p1:=M0..M1..M2{dir 60}..M3{dir 30};
 draw p1;
draw p1 xscaled -1 dashed evenly;
  label.rt(btex $C_g$ etex, (-1.5u,1.5v));
  label.rt(btex $C_f$ etex, (-1.7u,-1.2v));
  label.rt(btex $g(x)=f(-x)$ etex, (0,1.7v));

endfig;

beginfig(7)
  %%%%%%%%%%%%%%%%%%%%%%%%%
  % fonctions associées : %
  % g(x) = |f(x)|          %
  %%%%%%%%%%%%%%%%%%%%%%%%%
  u:=1cm; v:=1cm;
  %figure(-3.2u,-1.6u,3.2u,4.8u);
  pair M[],O,I,J;
  path p[];
  numeric a, b,c;
  O=(0,0);
  I=(u,0);
  J=(0,v);

  %repere(O,I,J);
  Xmin:=-2;
  Xmax:=2;
  Ymin:=-2;
  Ymax:=2;
 %Quadrillage en croix
  c:=0.07;
  p0:=(-c,0)*u--(c,0)*u--(0,0)*u--(0,c)*u--(0,-c)*u; % CROIX
  p0:=p0 shifted (floor(Xmin)*u,floor(Ymin)*v); %mise dans le coin SO
 for i=0 upto floor(Ymax-Ymin):
    for j=0 upto floor(Xmax-Xmin):
      draw p0 shifted (j*u,0) withpen pencircle scaled 0.2bp withcolor 0.6white;
    endfor ;
    p0:=p0 shifted (0,v);
 endfor ;
 %--
 %Axes et vect unit
  drawarrow (Xmin*u,0)--(Xmax*u,0);
  drawarrow (0,Ymin*v)--(0,Ymax*v);
 drawarrow O--I withpen pencircle scaled 1.13pt;
 drawarrow O--J withpen pencircle scaled 1.13pt;
 label.bot(btex $\vec{\imath}$ etex, (0.5u,-0.1v));
 label.lft(btex $\vec{\jmath}$ etex, (-0.1u,0.5v));
 %--
 M0:=(-2u,-1.8v);
 M1:=(0,-v);
 M2:=(u,0);
 M3:=(2u,1.5v);
 p1:=M0..M1..M2{dir 60}..M3{dir 30};
%draw p1;
% draw p1 withpen pencircle scaled 1.13pt dashed withdots;
  p2:=M0..M1..M2{dir 60};
  draw p2 yscaled -1 withpen pencircle scaled 2.5pt dashed withdots;
  draw p2 yscaled -1 withpen pencircle scaled 1.7pt dashed withdots withcolor white;

  draw M2{dir 60}..M3{dir 30} withpen pencircle scaled 2.5pt dashed withdots;
  draw M2{dir 60}..M3{dir 30} withpen pencircle scaled 1.7pt dashed withdots withcolor white;

draw p1;
  label.rt(btex $C_g$ etex, (-1.7u,1.2v));
  label.rt(btex $C_f$ etex, (-1.7u,-1.2v));
  label.rt(btex $g(x)=|f(x)|$ etex, (0,1.7v));

endfig;

beginfig(8)
  %%%%%%%%%%%%%%%%%%%%%%%%%
  % fonctions associées : %
  % g(x) = -f(x)          %
  %%%%%%%%%%%%%%%%%%%%%%%%%
  u:=1cm; v:=1cm;
  %figure(-3.2u,-1.6u,3.2u,4.8u);
  pair M[],O,I,J;
  path p[];
  numeric a, b,c;
  O=(0,0);
  I=(u,0);
  J=(0,v);

  %repere(O,I,J);
  Xmin:=-2;
  Xmax:=2;
  Ymin:=-2;
  Ymax:=2;
 %Quadrillage en croix
  c:=0.07;
  p0:=(-c,0)*u--(c,0)*u--(0,0)*u--(0,c)*u--(0,-c)*u; % CROIX
  p0:=p0 shifted (floor(Xmin)*u,floor(Ymin)*v); %mise dans le coin SO
 for i=0 upto floor(Ymax-Ymin):
    for j=0 upto floor(Xmax-Xmin):
      draw p0 shifted (j*u,0) withpen pencircle scaled 0.2bp withcolor 0.6white;
    endfor ;
    p0:=p0 shifted (0,v);
 endfor ;
 %--
 %Axes et vect unit
  drawarrow (Xmin*u,0)--(Xmax*u,0);
  drawarrow (0,Ymin*v)--(0,Ymax*v);
 drawarrow O--I withpen pencircle scaled 1.13pt;
 drawarrow O--J withpen pencircle scaled 1.13pt;
 label.bot(btex $\vec{\imath}$ etex, (0.5u,-0.1v));
 label.lft(btex $\vec{\jmath}$ etex, (-0.1u,0.5v));
 %--
 M0:=(-2u,-1.8v);
 M1:=(0,-v);
 M2:=(u,0);
 M3:=(2u,1.5v);
 p1:=M0..M1..M2{dir 60}..M3{dir 30};
 draw p1;
 draw p1 yscaled -1 dashed evenly;
  label.rt(btex $C_g$ etex, (-1.7u,1.2v));
  label.rt(btex $C_f$ etex, (-1.7u,-1.2v));
  label.rt(btex $g(x)=-f(x)$ etex, (0,1.7v));

endfig;

beginfig(9)
  %%%%%%%%%%%%%%%%%%%%%%%%%
  % fonctions associées : %
  % g(x) = 2*sin(x)      %
  %%%%%%%%%%%%%%%%%%%%%%%%%
  u:=1cm; v:=1cm;
  %figure(-3.2u,-1.6u,3.2u,4.8u);
  pair O,I,J,M,N;
  path p[];
  numeric a, b;
  O=(0,0);
  I=(u,0);
  J=(0,v);

  a:=2;
  b:=1.5;
  M:=(a*u,a*a*v);
  N:=M+b*(I-O);
  %repere(O,I,J);
  Xmin:=-2;
  Xmax:=7;
  Ymin:=-2;
  Ymax:=2;
   %Quadrillage en croix
  c:=0.07;
  p0:=(-c,0)*u--(c,0)*u--(0,0)*u--(0,c)*u--(0,-c)*u; % CROIX
  p0:=p0 shifted (floor(Xmin)*u,floor(Ymin)*v); %mise dans le coin SO
 for i=0 upto floor(Ymax-Ymin):
    for j=0 upto floor(Xmax-Xmin):
      draw p0 shifted (j*u,0) withpen pencircle scaled 0.2bp withcolor 0.6white;
    endfor ;
    p0:=p0 shifted (0,v);
 endfor ;
 %--
 drawarrow (Xmin*u,0)--(Xmax*u,0);
 drawarrow (0,Ymin*v)--(0,Ymax*v);
 drawarrow O--I withpen pencircle scaled 1.13pt;
 drawarrow O--J withpen pencircle scaled 1.13pt;
 label.bot(btex $\vec{\imath}$ etex, (0.5u,-0.1v));
 label.lft(btex $\vec{\jmath}$ etex, (-0.1u,0.5v));
  %--

  numeric Npts;
  Npts:=200;
   vardef f(expr x) = sind(x*180/3.1416) enddef;
   vardef g(expr x) = 2*sind(x*180/3.1416) enddef;
 p1= ( ( Xmin*u, (f(Xmin))*v )
         for i=1 upto Npts:
     ..( (Xmin + (i/Npts)*(Xmax - Xmin))*u, (f( Xmin + (i/Npts)*(Xmax - Xmin) ))*v)
   endfor ) ;
 p2= ( ( Xmin*u, (g(Xmin))*v )
         for i=1 upto Npts:
     ..( (Xmin + (i/Npts)*(Xmax - Xmin))*u, (g( Xmin + (i/Npts)*(Xmax - Xmin) ))*v)
   endfor ) ;
 draw p1;
 draw p2 dashed evenly;

  label.rt(btex $C_g$ etex, (2.5u,1.5v));
  label.top(btex $C_f$ etex, (-1.5u,-v));
  label.rt(btex $g(x)=2\sin (x)$ etex, (4u,1.5v));

endfig;

beginfig(10)
  %%%%%%%%%%%%%%%%%%%%%%%%%
  % fonctions associées : %
  % g(x) = 2*sin(x)      %
  %%%%%%%%%%%%%%%%%%%%%%%%%
  u:=1cm; v:=1cm;
  %figure(-3.2u,-1.6u,3.2u,4.8u);
  pair O,I,J,M,N;
  path p[];
  numeric a, b;
  O=(0,0);
  I=(u,0);
  J=(0,v);

  a:=2;
  b:=1.5;
  M:=(a*u,a*a*v);
  N:=M+b*(I-O);
  %repere(O,I,J);
  Xmin:=-2;
  Xmax:=7;
  Ymin:=-1;
  Ymax:=1;
   %Quadrillage en croix
  c:=0.07;
  p0:=(-c,0)*u--(c,0)*u--(0,0)*u--(0,c)*u--(0,-c)*u; % CROIX
  p0:=p0 shifted (floor(Xmin)*u,floor(Ymin)*v); %mise dans le coin SO
 for i=0 upto floor(Ymax-Ymin):
    for j=0 upto floor(Xmax-Xmin):
      draw p0 shifted (j*u,0) withpen pencircle scaled 0.2bp withcolor 0.6white;
    endfor ;
    p0:=p0 shifted (0,v);
 endfor ;
 %--
 drawarrow (Xmin*u,0)--(Xmax*u,0);
 drawarrow (0,Ymin*v)--(0,Ymax*v);
 drawarrow O--I withpen pencircle scaled 1.13pt;
 drawarrow O--J withpen pencircle scaled 1.13pt;
 label.bot(btex $\vec{\imath}$ etex, (0.5u,-0.1v));
 label.lft(btex $\vec{\jmath}$ etex, (-0.1u,0.5v));
  %--

  numeric Npts;
  Npts:=200;
   vardef f(expr x) = sind(x*180/3.1416) enddef;
   vardef g(expr x) = sind(2*x*180/3.1416) enddef;
 p1= ( ( Xmin*u, (f(Xmin))*v )
         for i=1 upto Npts:
     ..( (Xmin + (i/Npts)*(Xmax - Xmin))*u, (f( Xmin + (i/Npts)*(Xmax - Xmin) ))*v)
   endfor ) ;
 p2= ( ( Xmin*u, (g(Xmin))*v )
         for i=1 upto Npts:
     ..( (Xmin + (i/Npts)*(Xmax - Xmin))*u, (g( Xmin + (i/Npts)*(Xmax - Xmin) ))*v)
   endfor ) ;
 draw p1;
 draw p2 dashed evenly;

  label.rt(btex $C_g$ etex, (-1.8u,0.6v));
  label.top(btex $C_f$ etex, (3.5u,-0.9v));
  label.rt(btex $g(x)=\sin (2x)$ etex, (4.3u,0.8v));

endfig;


beginfig(11)
  %%%%%%%%%%%%%%%%%%%%%%%%%
  % fonctions associées : %
  % g(x) = 2*sin(x)      %
  %%%%%%%%%%%%%%%%%%%%%%%%%
  u:=1cm; v:=1cm;
  %figure(-3.2u,-1.6u,3.2u,4.8u);
  pair O,I,J,M,N;
  path p[];
  numeric a, b;
  O=(0,0);
  I=(u,0);
  J=(0,v);

  a:=2;
  b:=1.5;
  M:=(a*u,a*a*v);
  N:=M+b*(I-O);
  %repere(O,I,J);
  Xmin:=-2;
  Xmax:=7;
  Ymin:=-1;
  Ymax:=1;
   %Quadrillage en croix
  c:=0.07;
  p0:=(-c,0)*u--(c,0)*u--(0,0)*u--(0,c)*u--(0,-c)*u; % CROIX
  p0:=p0 shifted (floor(Xmin)*u,floor(Ymin)*v); %mise dans le coin SO
 for i=0 upto floor(Ymax-Ymin):
    for j=0 upto floor(Xmax-Xmin):
      draw p0 shifted (j*u,0) withpen pencircle scaled 0.2bp withcolor 0.6white;
    endfor ;
    p0:=p0 shifted (0,v);
 endfor ;
 %--
 drawarrow (Xmin*u,0)--(Xmax*u,0);
 drawarrow (0,Ymin*v)--(0,Ymax*v);
 drawarrow O--I withpen pencircle scaled 1.13pt;
 drawarrow O--J withpen pencircle scaled 1.13pt;
 label.bot(btex $\vec{\imath}$ etex, (0.5u,-0.1v));
 label.lft(btex $\vec{\jmath}$ etex, (-0.1u,0.5v));
  %--

  numeric Npts;
  Npts:=1000;
   vardef f(expr x) = sind(x*180/3.1416) enddef;
   vardef g(expr x) = sind(x*x*180/3.1416) enddef;
 p1= ( ( Xmin*u, (f(Xmin))*v )
         for i=1 upto Npts:
     ..( (Xmin + (i/Npts)*(Xmax - Xmin))*u, (f( Xmin + (i/Npts)*(Xmax - Xmin) ))*v)
   endfor ) ;
 p2= ( ( Xmin*u, (g(Xmin))*v )
         for i=1 upto Npts:
     ..( (Xmin + (i/Npts)*(Xmax - Xmin))*u, (g( Xmin + (i/Npts)*(Xmax - Xmin) ))*v)
   endfor ) ;
 draw p1;
 draw p2 dashed evenly;

  label.rt(btex $C_g$ etex, (-1.6u,0.5v));
  label.top(btex $C_f$ etex, (-1u,-0.8v));
  label.rt(btex $g(x)=\sin (x^2)$ etex, (-0.75u,-0.8v));

endfig;

beginfig(12)
  %%%%%%%%%%%%%%%%%%%%%%%%%
  % fonctions associées : %
  % g(x) = kx^2    %
  %%%%%%%%%%%%%%%%%%%%%%%%%
  u:=0.8cm; v:=0.43cm;
  %figure(-3.2u,-1.6u,3.2u,4.8u);
  pair O,I,J,M,N;
  path p[];
  numeric a;
  O=(0,0);
  I=(u,0);
  J=(0,v);
  a=2;
  M=(a*u,a*a*v);
  N=M-2*(J-O);
  %repere(O,I,J);
  Xmin:=-3;
  Xmax:=3;
  Ymin:=-4;
  Ymax:=9;
 %Quadrillage en croix
  c:=0.07;
  p0:=(-c,0)*u--(c,0)*u--(0,0)*u--(0,c)*u--(0,-c)*u; % CROIX
  p0:=p0 shifted (floor(Xmin)*u,floor(Ymin)*v); %mise dans le coin SO
 for i=0 upto floor(Ymax-Ymin):
    for j=0 upto floor(Xmax-Xmin):
      draw p0 shifted (j*u,0) withpen pencircle scaled 0.2bp withcolor 0.6white;
    endfor ;
    p0:=p0 shifted (0,v);
 endfor ;
 %--
  drawarrow (Xmin*u,0)--(Xmax*u,0);
  drawarrow (0,Ymin*v)--(0,Ymax*v);
 drawarrow O--I withpen pencircle scaled 1.13pt;
 drawarrow O--J withpen pencircle scaled 1.13pt;
% label.bot(btex $\vec{\imath}$ etex, (0.5u,-0.1v));
% label.lft(btex $\vec{\jmath}$ etex, (-0.1u,0.5v));
  %--
  Xmin:=-3;
  Xmax:=3;
  Ymin:=-2;
  Ymax:=4.8;
  numeric Npts;
  Npts:=50;
   vardef f(expr x) = x*x enddef;
   vardef g(expr x) = 2*x*x enddef;
   vardef h(expr x) = 5*x*x enddef;
   vardef k(expr x) = 0.5*x*x enddef;
   vardef l(expr x) = -0.5*x*x enddef;
  %f:
 p1= ( ( Xmin*u, (f(Xmin))*v )
         for i=1 upto Npts:
     ..( (Xmin + (i/Npts)*(Xmax - Xmin))*u, (f( Xmin + (i/Npts)*(Xmax - Xmin) ))*v)
   endfor ) ;
 %g:
Xmax:=2.12; Xmin:=-Xmax;
 p2= ( ( Xmin*u, (g(Xmin))*v )
         for i=1 upto Npts:
     ..( (Xmin + (i/Npts)*(Xmax - Xmin))*u, (g( Xmin + (i/Npts)*(Xmax - Xmin) ))*v)
   endfor ) ;
 %h:
 Xmax:=1.3416; Xmin:=-Xmax;
 p3= ( ( Xmin*u, (h(Xmin))*v )
         for i=1 upto Npts:
     ..( (Xmin + (i/Npts)*(Xmax - Xmin))*u, (h( Xmin + (i/Npts)*(Xmax - Xmin) ))*v)
   endfor ) ;
 %k:
 Xmax:=3; Xmin:=-Xmax;
 p4= ( ( Xmin*u, (k(Xmin))*v )
         for i=1 upto Npts:
     ..( (Xmin + (i/Npts)*(Xmax - Xmin))*u, (k( Xmin + (i/Npts)*(Xmax - Xmin) ))*v)
   endfor ) ;
 %l:
 Xmax:=3; Xmin:=-Xmax;
 p5= ( ( Xmin*u, (l(Xmin))*v )
         for i=1 upto Npts:
     ..( (Xmin + (i/Npts)*(Xmax - Xmin))*u, (l( Xmin + (i/Npts)*(Xmax - Xmin) ))*v)
   endfor ) ;
 draw p1;
 draw p2 dashed evenly;
 draw p3 dashed evenly scaled 2;
 draw p3 dashed withdots scaled 0.3;
 draw p4 dashed evenly scaled 0.5;
 draw p5 dashed evenly scaled 3;


endfig;


beginfig(20)   %Aire entre courbes
  numeric M;
  vardef f(expr x) = 0.5*x*(3-x) enddef;
  vardef g(expr x) = x*x-6*x+6 enddef;
  path p[];
  u:=1cm;

  %---------
  v:=0.8cm;
  Xmin:=0;      %
  Xmax:=5;       %
  xscl:=1;         %
  Ymin:=-3.5;        %
  Ymax:=3;         %
  yscl:=1;         %
  M:=50;

  p3=(1u,v)..(1.5u,1.125v)..(3u,0)..(4u,-1.99v);
  p6=p3..(4u,-2v){dir 235}..(3u,-3v)..(2u,-2v)..(u,v)..cycle;
  fill p6 withcolor 0.7white;

  pickup pencircle scaled 0.5pt;
    drawarrow ( (Xmin,0) -- (Xmax,0) ) scaled u ;
    drawarrow ( (0,Ymin) -- (0,Ymax) ) scaled v;
  Xmax:=4.5;
  p1= ( ( Xmin*u, (f(Xmin))*v )
        for i=1 upto M:
    ..( (Xmin + (i/M)*(Xmax - Xmin))*u, (f( Xmin + (i/M)*(Xmax - Xmin) ))*v)
  endfor ) ;
Xmin:=0.6;  Xmax:=5;
p2= ( ( Xmin*u, (g(Xmin))*v )
        for i=1 upto M:
    ..( (Xmin + (i/M)*(Xmax - Xmin))*u, (g( Xmin + (i/M)*(Xmax - Xmin) ))*v)
  endfor ) ;
draw p1;
draw p2;
%p3=(1u,v)..(1.5u,1.125v)..(3u,0)..(4u,-1.99v);
%p4=(u,v)..(2u,-2v)..(3u,-3v)..(4u,-2v){dir 55};
%p6=p3..(4u,-2v){dir 235}..(3u,-3v)..(2u,-2v)..(u,v)..cycle;
%p5=buildcycle(p3,p4);
%draw p6;
%draw p3;
%draw p4;
%fill p6 withcolor 0.7white;
label.urt(btex $y= x(3-x)/2$ etex, (1.5u,1.2v));
label.urt(btex $y=x^2-6x+6$ etex, (0.5u,-3.6v));
endfig;



end