Exercice 2 restart: with(plots): ListePoints:=proc(f,u0,n)
local X,Y,l,i;
X:=u0;Y:=0;
l:=[X,Y]; point sur l'axe des abscissses [u0,0]
for i from 1 to n do
Y:=f(X);
l:=l,[X,Y]; on ajoute le point sur la courbe [un,f(un)]
X:=Y;
l:=l,[X,Y]; on ajoute le point sur la bissectrice [f(un),f(un)]
od;
[l]
end:
graphique:=proc(f,u0,n,a,b)
local l,Gf,Gs,diag;
diag:=plot(t,t=a..b,color=red): Graphe de la bissectrice
Gf:=plot(f,a..b,color=green,thickness=2): Graphe de la fonction f
l:=ListePoints(f,u0,n);
Gs:=plot(l,style=line,color=blue): Graphe constitu\351 des segments associ\351s \340 la suite u(n+1)=f(un)
display({Gf,Gs,diag},scaling=constrained);
end:
f:=t->1-t^2; NiM+SSJmRzYiZio2I0kidEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYiIiJGLSokOSQiIiMhIiJGJUYlRiU= a:=0:b:=1: u0:=0.7:n:=15: graphique(f,u0,n,a,b); 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