Exercice 7On d\351finit la param\351trisationrestart;x:=t->t/(1+t^3);y:=t->(t^2)/(1+t^3);

NiM+SSJ4RzYiZio2I0kidEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiY5JCIiIiwmRi5GLiokRi0iIiRGLiEiIkYlRiVGJQ==NiM+SSJ5RzYiZio2I0kidEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiY5JCIiIywmIiIiRjAqJEYtIiIkRjAhIiJGJUYlRiU=

Domaine d'EtudeR\351duisons l'intervalle d'\351tude \340 -1..1, En effet[x(1/t),y(1/t)]=[y(t),x(t)];

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simplify(%);

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evalb(%);

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Donc la partie de courbe correspondant aux autres param\351tres se d\351duira par sym\351trie / \340 la premi\350re bissectriceCalculons le vecteur vitesseVt:=[D(x)(t),D(y)(t)];

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Vt:=simplify(Vt);

NiM+SSNWdEc2IjckLCQqJiwmISIiIiIiKiRJInRHRiUiIiQiIiNGKywmRitGK0YsRishIiNGKiwkKihGLUYrLCZGMUYrRixGK0YrRjBGMUYq

V:=unapply(Vt,t);

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Cette courbe est donc r\351guli\350reTangente aux points A=M(0)=(0,0), B=M((1/2)^(1/3)) et C=M(1)=(1/2,1/2)Ces tangentes sont dirig\351es par les vecteurs

V(0);V((1/2)^(1/3));V(1);

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D'o\371 les \351quations param\351tr\351es des tangentes XTA:=x(0)+t*op(1,V(0));YTA:=y(0)+t*op(2,V(0));

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XTB:=x((1/2)^(1/3))+t*op(1,V((1/2)^(1/3)));YTB:=y((1/2)^(1/3))+t*op(2,V((1/2)^(1/3)));

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XTC:=x(1)+t*op(1,V(1));YTC:=y(1)+t*op(2,V(1));

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EqTA:=[XTA,YTA,t=-infinity..infinity]:EqTB:=[XTB,YTB,t=-infinity..infinity]:EqTC:=[XTC,YTC,t=-infinity..infinity]:Branches Infinies \351ventuellesLimit('x'(t),t=-1,right)=limit(x(t),t=-1,right),Limit('y'(t),t=-1,right)=limit(y(t),t=-1,right) ;

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D'o\371 une branche infinie lorsque t->-1^+, Calculons la limite du taux y/xLimit('y'(t)/'x'(t),t=-1,right)=limit(y(t)/x(t),t=-1,right);

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La courbe admet donc une direction asymptotique la droite d'\351quation y=-x. Calculons alors la limite suivanteLimit('y'(t)+'x'(t),t=-1,right)=limit(y(t)+x(t),t=-1,right);

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Donc la courbe admet une asymptote oblique d'\351quation y=-x-1/3... d'o\371 son \351quation param\351triqueXA:=t;YA:=-t-1/3;

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EqA:=[XA,YA,t=-infinity..infinity]:Position Relative: pour cela on \351tudie le signe de y(tau)+x(tau)+1/3 pour tau proche de -1 (par valeurs sup\351rieures)assume(tau>-1):is(y(tau)+x(tau)+1/3>0);

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#V\351rifions le \340 l'aide de son expression alg\351brique:factor(y(t)+x(t)+1/3);

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On a donc l'arc est "au dessus" de cette asymptote... Par sym\351trie / Ox on a la m\352me asymptote et la m\352me position relative pour t->infinityEtude des variations de x et yplot(x,-1..1,-5..1);

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plot(y,-1..1,-1..10);

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

varx:=D(x)(t)/abs(D(x)(t)):vary:=D(y)(t)/abs(D(y)(t))/2:On trace en rouge le signe x' et en vert le signe de y'plot([varx,vary],t=-1..1,discont=true,thickness=[3,3]);

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

support de la courbetotal:=[x(t),y(t),t=-infinity..infinity]: partiel:=[x(t),y(t),t=-1..1]:plot([total,partiel,EqTA,EqTB,EqTC,EqA],-0.6..0.6,-0.6..0.6,color=[blue,red,black,black,black,green],thickness=[1,2,2,2,2,2]);

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plot(total,-0.5..0.5,-0.5..0.5,axes=none);

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Attention MAPLE semble ajouter \340 la courbe son asymptote!!!De plus par manque de precision certains points de la courbe sont manquants ou approximatifs: car repr\351sent\351s en lignes bris\351es