Fichier Cours-1S.mp (figure 6) — Modifié le 17 Septembre 2009 à 00 h 43
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