Fichier f012.mp (figure 44) — Modifié le 14 Avril 2008 à 15 h 20

Source

input newcourbes;
input couleur;
input geometriesyr16;
input TEX;

verbatimtex
%&latex
\documentclass{article}
\usepackage[upright]{fourier}
\usepackage{color}
\def\E{\mathrm{e}}
\let\ve\vec
\def\DR{\mathcal{D}}
\def\CR{\mathcal{C}}
\def\HR{\mathcal{H}}
\newcommand{\Mathbold}[1]{\mbox{\boldmath$#1$\unboldmath}}
\begin{document}
etex

%%%%%%%%%%%%%%%%%%%%%%%%%%%%ùù
%
% continuité
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%

beginfig( 44);

%%%%%%%%%%%%%%%%%%%%%%%
vardef fx(expr t)=
t
enddef;

vardef fy(expr t)=cos(1/t)
% c'est la seule ligne à changer
enddef;
%%%%%%%%%%%%%%%%%%%%%
repere(0,0,-1.5,1.5,-1.25,1.25,4cm,2cm);
r_axes;
r_origine;
r_unites;
r_labelxy;

draw f_courbe(fx,fy,0.05,1.5,1900)withpen pencircle scaled 1.5bp withcolor red;
draw f_courbe(fx,fy,0.04,0.05,1900)withpen pencircle scaled 1.5bp withcolor red;
draw f_courbe(fx,fy,-0.05,-0.04,1900)withpen pencircle scaled 1.5bp withcolor red;
draw f_courbe(fx,fy,-1.45,-0.05,1900)withpen pencircle scaled 1.5bp withcolor red;
draw f_courbe(fx,fy,0.03,0.04,1900)withpen pencircle scaled 1.5bp withcolor red;
draw f_courbe(fx,fy,-0.04,-0.03,1900)withpen pencircle scaled 1.5bp withcolor red;
draw f_courbe(fx,fy,0.02,0.03,1900)withpen pencircle scaled 1.5bp withcolor red;
draw f_courbe(fx,fy,-0.03,-0.02,1900)withpen pencircle scaled 1.5bp withcolor red;
r_fin;
endfig;

beginfig( 45)

%%%%%%%%%%%%%%%%%%%%%%%
vardef fx(expr t)=
t
enddef;

vardef fy(expr t)=
(sin(t))/t           % c'est la seule ligne à changer
enddef;
%%%%%%%%%%%%%%%%%%%%%
repere(0,0,-16,16,-.25,1.25,.25cm,4cm);
r_axes;
r_origine;
r_unites;
r_labelxy;

draw f_courbe(fx,fy,0.05,15,100)withpen pencircle scaled 1.5bp withcolor red;

draw f_courbe(fx,fy,-15,-0.05,100)withpen pencircle scaled 1.5bp withcolor red;

r_fin;
endfig;

%%%%
%
%       P ar t i e        entière
%
%%%%%%%%%%%%%%%%%%%

beginfig(46);

repere(0,0,-5,5,-5,5,1cm,.5cm);
r_axes;
r_origine;
r_unites;
r_labelxy;
path p,c,t;
c:=halfcircle scaled 0.15cm rotated 90 shifted r_p(-3.9,-5);
p:=fullcircle scaled 0.15cm shifted r_p(-5,-5);
t:=r_p(-5,-5)--r_p(-4,-5);

for j:=1 upto 9 :
fill p shifted r_p(j,j) withcolor 0.4white;
draw c shifted r_p(j,j) withcolor 0.4white withpen pencircle scaled 1.3bp;
draw t shifted r_p(j,j) withcolor 0.4white withpen pencircle scaled 1.5bp;
endfor;

endfig;

%%% 1/x

beginfig( 47)

%%%%%%%%%%%%%%%%%%%%%%%
vardef fx(expr t)=
t
enddef;

vardef fy(expr t)=
1/t         % c'est la seule ligne à changer
enddef;
%%%%%%%%%%%%%%%%%%%%%
repere(0,0,-4,4,-3,3,1cm,1cm);
r_axes;
r_origine;
r_unites;
r_labelxy;

draw f_courbe(fx,fy,-4,-0.1,100)withpen pencircle scaled 1.5bp withcolor red;

draw f_courbe(fx,fy,0.1,4,100)withpen pencircle scaled 1.5bp withcolor red;

r_fin;
endfig;

beginfig( 48)

%%%%%%%%%%%%%%%%%%%%%%%
vardef fx(expr t)=
t
enddef;

vardef fy(expr t)=
(t*t-3*t+1)/(t-2)                   % c'est la seule ligne à changer
enddef;
%%%%%%%%%%%%%%%%%%%%%
repere(0,0,-2,6,-6,6,1cm,.5cm);
r_axes;
r_origine;
r_unites;
r_labelxy;

draw f_courbe(fx,fy,-2,1.9,1000)withpen pencircle scaled 1.5bp withcolor red;

draw f_courbe(fx,fy,2.1,6,1000)withpen pencircle scaled 1.5bp withcolor red;

draw r_p(2,-6)--r_p(2,6) dashed evenly scaled 1.5 withpen pencircle scaled 1.3bp withcolor 0.4white;

r_fin;
endfig;

%%%%%%%%%%%%%

%
% T V I en 0
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%

beginfig( 49)

%%%%%%%%%%%%%%%%%%%%%%%
vardef fx(expr t)=
t
enddef;

vardef fy(expr t)=
% c'est la seule ligne à changer
enddef;
%%%%%%%%%%%%%%%%%%%%%
repere(0,0,-1,5,-2,3,1.3cm,0.8cm);
r_axes;
r_origine;
%r_unites;
r_labelxy;

%draw f_courbe(fx,fy,,,100)withpen pencircle scaled 1.5bp withcolor red;

pair a,o,b,xa,ya,xb,yb;
a:=r_p(1,-1);
o:=r_p(1.5,0);
b:=r_p(4,2);
xa:=r_p(1,0);
ya:=r_p(0,-1);
xb:=r_p(4,0);
yb:=r_p(0,2);

draw a..o..b withpen pencircle scaled 1.4bp withcolor 0.5white;
dotlabel(btex  etex,a );
dotlabel(btex  etex,b );

draw yb--b--xb dashed evenly;
draw ya--a--xa dashed evenly;
label.lft(btex $f(b)$ etex,yb );
label.lft(btex $f(a)$ etex,ya );
label.bot(btex $b$ etex,xb );
label.top(btex $a$ etex,xa );
r_fin;
endfig;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%
%
%       Fonction Cube
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

beginfig(50);

%%%%%%%%%%%%%%%%%%%%%%%
vardef fx(expr t)=
t
enddef;

vardef fy(expr t)=
t**3          % c'est la seule ligne à changer
enddef;
%%%%%%%%%%%%%%%%%%%%%
repere(0,0,-3,3,-10,10,2cm,.5cm);
r_axes;
r_origine;
r_unites;
r_labelxy;
label.rt(btex \textcolor{red}{$\Mathbold{y=x^3}$} etex,r_p(2,fy(2)) );
end