prologues:=2; verbatimtex %\input Modele% % \documentclass{article} % \usepackage[latin1]{inputenc} % \usepackage[frenchb]{babel} % \usepackage{amsmath} % \begin{document} etex %input constantes; %input papiers; % 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); u := 1cm; v=u; % Unité pi:=3.14159265859; % def axes(expr xmin,xmax,ymin,ymax) = pickup pencircle scaled 0.5pt; draw ( (xmin,0) -- (xmax,0) ) scaled u ; draw ( (0,ymin) -- (0,ymax) ) scaled v; enddef; def axesfleches(expr xmin,xmax,ymin,ymax) = pickup pencircle scaled 0.5pt; drawarrow ( (xmin,0) -- (xmax,0) ) scaled u ; drawarrow ( (0,ymin) -- (0,ymax) ) scaled v; enddef; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% def grad(expr xscl,yscl,xmin,xmax,ymin,ymax)= pickup pencircle scaled 0.5pt; %% grad sur Ox for i=0 step xscl until xmax: draw (i*u,1/15cm)--(i*u,-1/15cm); endfor; for i=0 step -xscl until xmin: draw (i*u,1/15cm)--(i*u,-1/15cm); endfor; %% grad sur Oy for i=0 step yscl until ymax: draw (1/15cm,i*v)--(-1/15cm,i*v); endfor; for i=0 step -yscl until ymin: draw (1/15cm,i*v)--(-1/15cm,i*v); endfor; enddef; %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% def vecunit = pickup pencircle scaled 1pt; ahangle:=30; %angle au sommet de la flèche ahlength:=0.9*ahlength; %longueur de la pointe de flèche drawarrow (( 0,0) -- (1,0) ) scaled u ; % vecteur i drawarrow (( 0,0) -- (0,1) ) scaled v ; % vecteurj label.llft(btex $O$ etex, (0,0)); % Place la lettre O en bas à gauche de (0,0) %label.bot(btex $\vec{\imath}$ etex, (0.35,0)*u); %label.lft(btex $\overrightarrow{j}$ etex, (-0.15,0.5)*v); label.bot(btex $i$ etex, (0.35,0)*u); label.lft(btex $j$ etex, (-0.15,0.5)*v); %On colle ensuite dans le .tex: %\psfrag{O}{$O$} \psfrag{i}{$\vi$} \psfrag{j}{$\vj$} enddef; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% def vecunitaire = %pareil mais sans les psfrag pickup pencircle scaled 0.7pt; ahangle:=30; %angle au sommet de la flèche ahlength:=0.8*ahlength; %longueur de la pointe de flèche drawarrow (( 0,0) -- (1,0) ) scaled u ; % vecteur i drawarrow (( 0,0) -- (0,1) ) scaled v ; % vecteurj label.llft(btex $O$ etex, (0,0)); % Place la lettre O en bas à gauche de (0,0) label.bot(btex $\vec{\imath}$ etex, (0.35,0)*u); label.lft(btex $\vec{\jmath}$ etex, (-0.15,0.5)*v); enddef; %%%%%%%%%%%%% def courbe(suffix f)(expr xmin, xmax, M) = draw ( ( xmin*u, (f(xmin))*v ) for i=1 upto M: ..( (xmin + (i/M)*(xmax - xmin))*u, (f( xmin + (i/M)*(xmax - xmin) ))*v) endfor ) ; enddef; %%%% %%% def relie_pts(suffix f)(expr xmin, xscl, N) = draw ( ( xmin*u, (f(xmin))*v )% for i=1 upto N:% --( (xmin + i*xscl)*u, (f( xmin + i*xscl) )*v) endfor ) dashed evenly ; for i=0 upto N:% dotlabel(btex $$ etex ,((xmin + i*xscl)*u, (f( xmin + i*xscl) )*v)); %(xmin + i*xscl)*u, (f( xmin + i*xscl) ))*v); endfor; enddef; %% %%########################################################### %% beginfig(1) %vardef est nécéssaire pour pouvoir passer f en argument %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% vardef f(expr x) = mexp(-256*x)-1 enddef; % Ici on définit f(x) vardef g(expr x) = cosd(x/pi*180) enddef; % Ici on définit g(x) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Def des fonctions usuelles en metapost %% %% %% %% mexp(x)=exp(x/256) %% %% mlog(x)=ln(x/256) %% %% cosd(x)=cos(x) x en degrés x/pi*180 %% %% sind(x)=sin(x) x en degrés %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % On règle la fenêtre ici % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% i=1; xmin=-2; % xmax=6.3; % xscl=1; % ymin=-1; % ymax=7; % yscl=1; % Nb_de_pts=50; % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% axes(xmin,xmax,ymin,ymax); grad(xscl,yscl,xmin,xmax,ymin,ymax); courbe(f,xmin,xmax,Nb_de_pts ); courbe(g,xmin,xmax,Nb_de_pts); vecunit; endfig; beginfig(1) % Illustre la convergence d'une suite vers l avec un tube l+/-epsilon %vardef est nécéssaire pour pouvoir passer f en argument %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %vardef g(expr x) = mexp(-256*x)-1 enddef; % Ici on définit f(x) vardef f(expr x) := 1.5*sind(x/pi*700)/x+0.7 enddef; % Ici on définit g(x) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Def des fonctions usuelles en metapost %% %% %% %% mexp(x)=exp(x/256) %% %% mlog(x)=ln(x/256) %% %% cosd(x)=cos(x) x en degrés x/pi*180 %% %% sind(x)=sin(x) x en degrés %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % On règle la fenêtre ici % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% u:=0.8cm; i:=1; xmin:=-0.2; % xmax:=8; % xscl:=0.3; % ymin:=-0.1; % ymax:=1.9; % yscl:=2; % Nb_de_pts:=10; % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% pair A[]; axesfleches(xmin,xmax+xscl,ymin,2); grad(xscl,yscl,xmin,xmax,ymin,ymax); %reliepts(f,0.1,xmax,Nb_de_pts ); % relie_pts(f,1,xscl,Nb_de_pts); relie_pts(f,3*xscl,xscl,((xmax-3*xscl)/xscl)); A0=(0,0.7*v); A1=(0.3*u,1.8*v); A2=(0.6*u,1.5*v); A8=(xmax*u,0.7*v); draw A1--A2--(0.9*u,(f(0.9))*v) dashed evenly ; dotlabel(btex $$ etex ,A1); dotlabel(btex $$ etex ,A2); draw A0--A8; draw ((A0--A8) shifted (0,0.28*v)) dashed evenly ; draw ((A0--A8) shifted (0,-0.28*v)) dashed evenly ; label.lft(btex $\ell+\varepsilon$ etex ,A0 shifted (0,0.28*v)); label.lft(btex $\ell$ etex ,A0); label.lft(btex $\ell-\varepsilon$ etex ,A0 shifted (0,-0.28*v)); draw (((0,0)--(0,0.98*v)) shifted (16*xscl*u,0)); label.bot(btex $p$ etex ,(16*xscl*u,0)); label.bot(btex $n$ etex ,(xmax*u,0)); label.lft(btex $u_n$ etex ,(0,ymax*v)); %courbe(f,xmin,xmax,Nb_de_pts); %vecunit; endfig; beginfig(2) % Illustre le th des gendarmes pour fct avec un tube l+/-epsilon %vardef est nécéssaire pour pouvoir passer f en argument %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% vardef g(expr x) = 1/(0.7*x)+0.72 enddef; % Ici on définit f(x) vardef f(expr x) := 70*sind(x/pi*700)/(12*x*x)+0.7 enddef; % Ici on définit g(x) vardef h(expr x) := -1/(1.5*x)+0.62 enddef; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Def des fonctions usuelles en metapost %% %% %% %% mexp(x)=exp(x/256) %% %% mlog(x)=ln(x/256) %% %% cosd(x)=cos(x) x en degrés x/pi*180 %% %% sind(x)=sin(x) x en degrés %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % On règle la fenêtre ici % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% u:=1.2cm; v:=1.8cm; i:=1; xmin:=-0.2; % xmax:=10; % xscl:=0.3; % ymin:=-0.1; % ymax:=1.9; % yscl:=2; % Nb_de_pts:=20; % M:=20; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% pair A[];path p[]; axesfleches(xmin,xmax+xscl,ymin,2.3); grad(xscl,yscl,xmin,xmax,ymin,ymax); %reliepts(f,0.1,xmax,Nb_de_pts ); % relie_pts(f,1,xscl,Nb_de_pts); %relie_pts(f,3*xscl,xscl,((xmax-3*xscl)/xscl)); % courbe(f,3*xscl,xscl,((xmax-3*xscl)/xscl)); courbe(f,1.8,xmax,100 ); %courbe(g,1.1,xmax,Nb_de_pts ); courbe(h,0.6,xmax,Nb_de_pts ); xmin:=2; p1=( (0.6u,0.6v){dir 60}..( 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; A0=(0,0.7*v); %A1=(0.3*u,1.8*v); %A2=(0.6*u,1.5*v); A8=(xmax*u,0.7*v); %draw A1--A2--(0.9*u,(f(0.9))*v) dashed evenly ; %dotlabel(btex $$ etex ,A1); %dotlabel(btex $$ etex ,A2); draw A0--A8; draw ((A0--A8) shifted (0,0.28*v)) dashed evenly ; draw ((A0--A8) shifted (0,-0.28*v)) dashed evenly ; label.lft(btex $\ell+\varepsilon$ etex ,A0 shifted (0,0.28*v)); label.lft(btex $\ell$ etex ,A0); label.lft(btex $\ell-\varepsilon$ etex ,A0 shifted (0,-0.28*v)); label.bot(btex $x$ etex ,(xmax*u,0)); label.lft(btex $y$ etex ,(0,ymax*v)); label.rt(btex $C_g$ etex ,(2.1*u,2v)); label.top(btex $C_f$ etex ,(0.9*u,1.2v)); label.lft(btex $C_h$ etex ,(0.7*u,-0.3v)); endfig; end