Exercice 9On d\351fnit la param\351trisation, restart;x:=t->1/t+ ln(2+t);y:=t->t+1/t;

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Calculons le vecteur vitesseVt:=[D(x)(t),D(y)(t)];

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Vt:=factor(Vt);

NiM+SSNWdEc2IjckKiosJkkidEdGJSIiIkYqRipGKiwmRilGKiEiI0YqRipGKUYsLCYiIiNGKkYpRiohIiIqKCwmRilGKkYvRipGKkYoRipGKUYs

V:=unapply(Vt,t);

NiM+SSJWRzYiZio2I0kidEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlNyQqKiwmOSQiIiJGMEYwRjAsJkYvRjAhIiNGMEYwRi9GMiwmIiIjRjBGL0YwISIiKigsJkYvRjBGNUYwRjBGLkYwRi9GMkYlRiVGJQ==

V(-1);

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Cette courbe n'est donc r\351guli\350re, le point de param\350tre -1 est stationaireTangente aux points A=M(-1)=(-1,-2), B=M(1)=(1+ln(3),0) et C=M(2)=(1/2,5/2)Les tangentes en B et C sont dirig\351es par les vecteurs

V(1);V(2);

NiM3JCMhIiMiIiQiIiE=NiM3JCIiISMiIiQiIiU=

D'o\371 les \351quations des tangentesXTB:=x(1)+t*op(1,V(1));YTB:=y(1)+t*op(2,V(1));

NiM+SSRYVEJHNiIsKCIiIkYnLUkjbG5HNiRJKnByb3RlY3RlZEdGK0koX3N5c2xpYkdGJTYjIiIkRidJInRHRiUjISIjRi4=NiM+SSRZVEJHNiIiIiM=

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

NiM+SSRYVENHNiIsJiMiIiIiIiNGKC1JI2xuRzYkSSpwcm90ZWN0ZWRHRi1JKF9zeXNsaWJHRiU2I0YpRik=NiM+SSRZVENHNiIsJiMiIiYiIiMiIiJJInRHRiUjIiIkIiIl

EqTB:=[XTB,YTB,t=-infinity..infinity]:EqTC:=[XTC,YTC,t=-infinity..infinity]:Tangente au point stationnaire ACalculons la limite du taux d'accroissement en -1Limit((y(t)-y(-1))/(x(t)-x(-1)),t=-1)=limit((y(t)-y(-1))/(x(t)-x(-1)),t=-1);

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On en d\351duit donc une tangente horizontale au point de A param\350tre -1XTA:=x(-1)+t;YTA:=y(-1)+2*t/3;

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EqTA:=[XTA,YTA,t=-infinity..infinity]:Branches Infinies \351ventuelles en -2, 0 et +infinityEtude en -2^+Limit('x'(t),t=-2,right)=limit(x(t),t=-2,right),Limit('y'(t),t=-2,right)=limit(y(t),t=-2,right) ;

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D'o\371 une branche infinie lorsque t->-2^+, il s'agit d'une asymptote horizontale d'\351quationXA1:=t;YA1:=-5/2;

NiM+SSRYQTFHNiJJInRHRiU=NiM+SSRZQTFHNiIjISImIiIj

EqA1:=[XA1,YA1,t=-infinity..infinity]:Position Relative: pour cela on \351tudie le signe de y(tau)+5/2 pour tau proche de -2 (par valeurs sup\351rieures)assume(tau>-2):is(y(tau)+5/2>0);

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#V\351rifions le \340 l'aide de son expression alg\351brique:factor(y(t)+5/2);

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On a donc l'arc est "en dessous" de cette asymptote.Etude en 0^-Limit('x'(t),t=0,left)=limit(x(t),t=0,left),Limit('y'(t),t=0,left)=limit(y(t),t=0,left) ;

NiQvLUkmTGltaXRHNiRJKnByb3RlY3RlZEdGJ0koX3N5c2xpYkc2IjYlLUkieEdGKTYjSSJ0R0YpL0YuIiIhSSVsZWZ0R0YpLCRJKWluZmluaXR5R0YnISIiLy1GJTYlLUkieUdGKUYtRi9GMUYy

D'o\371 une branche infinie lorsque t->0^-, Calculons la limite du taux y/xLimit('y'(t)/'x'(t),t=0,left)=limit(y(t)/x(t),t=0,left);

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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=0,left)=limit(y(t)-x(t),t=0,left);

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Donc la courbe admet une asymptote oblique d'\351quation y=x-ln(2)... d'o\371 son \351quation param\351triqueXA2:=t;YA2:=t-ln(2);

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EqA2:=[XA2,YA2,t=-infinity..infinity]:Position Relative: pour cela on \351tudie le signe de y(tau)-x(tau)+ln(2) pour tau proche de -2 (par valeurs sup\351rieures)assume(tau<0 and tau>-1):is(combine(y(tau)-x(tau)+ln(2))>0);

NiNJJmZhbHNlR0kqcHJvdGVjdGVkR0Yk

V\351rifions le \340 l'aide de son expression alg\351brique:combine(y(t)-x(t)+ln(2));

NiMsJi1JI2xuRzYkSSpwcm90ZWN0ZWRHRidJKF9zeXNsaWJHNiI2IywmIiIiRixJInRHRikjRiwiIiMhIiJGLUYs

or ceci est du signe oppos\351 que la limite de (y(t)-x(t)+ln(2))/t en O^-Limit(('y'(t)-'x'(t)+ln(2))/t,t=0,left)=limit((y(t)-x(t)+ln(2))/t,t=0,left);

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On a donc l'arc est "au dessus" de cette asymptote.Etude en 0^+Limit('x'(t),t=0,right)=limit(x(t),t=0,right),Limit('y'(t),t=0,right)=limit(y(t),t=0,right) ;

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D'o\371 une branche infinie lorsque t->0^+,Calculons la limite du taux y/xLimit('y'(t)/'x'(t),t=0,right)=limit(y(t)/x(t),t=0,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=0,right)=limit(y(t)-x(t),t=0,right);

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Donc la courbe admet une asymptote oblique d'\351quation y=x-ln(2)... d'o\371 son \351quation param\351triquePosition Relative: pour cela on \351tudie le signe de y(tau)-x(tau)+ln(2) pour tau proche de -2 (par valeurs sup\351rieures)assume(tau>0 ):is(combine(y(tau)-x(tau)+ln(2))>0);

NiNJJXRydWVHSSpwcm90ZWN0ZWRHRiQ=

V\351rifions le \340 l'aide de son expression alg\351brique:combine(y(t)-x(t)+ln(2));

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or ceci est du m\352me que la limite de (y(t)-x(t)+ln(2))/t en O^+Limit(('y'(t)-'x'(t)+ln(2))/t,t=0,right)=limit((y(t)-x(t)+ln(2))/t,t=0,right);

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On a donc l'arc est "au dessus" de cette asymptote.Etude en infinityLimit('x'(t),t=infinity)=limit(x(t),t=infinity),Limit('y'(t),t=infinity)=limit(y(t),t=infinity) ;

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

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La courbe admet donc une branche parabolique dans la direction de l'axe des ordonn\351esEtude des variations de x et yplot(x,-2..infinity);

LSUlUExPVEc2Ji0lJ0NVUlZFU0c2JDdncDckJCEzNSsrKykqKioqKipcIyEjPSQhM19nKXolKjMnSE8hKkYsNyQkITNJM11sJVsmWyJcI0YsJCEzPXFdR11vY2RqRiw3JCQhMz87K0pyNChIWyNGLCQhM1dMV3ZZKT5HJGVGLDckJCEzU0NdJ3pYY1daI0YsJCEzJ1FrTCFlUTJdYUYsNyQkITNlSytpVz4lZlkjRiwkITNQMiYpb2InNE44JkYsNyQkITMnKlsrJHoiSCIqW0NGLCQhM0NiZW5jcnVNWUYsNyQkITNLbCtDIipRKT1WI0YsJCEzPzVRJHlQNyd6VUYsNyQkITMxKTRneSRlI3lSI0YsJCEzVVNiMSMpcCE+eSRGLDckJCEzIzM4IVsleW5QTyNGLCQhM1k1enZiTHBKTUYsNyQkITMtJz4/eG5eY0gjRiwkITNiUEp2YWNaV0hGLDckJCEzQmgtJzRkTnZBI0YsJCEzOFFCIVFHJ28wRUYsNyQkITNDNWpTXTErNEBGLCQhM1dgOjYhUjhPPiNGLDckJCEzJyplQiYpSGRZISo+RiwkITM1J1JjMUpXbiE+Riw3JCQhM18vIjRYIjM7ZD1GLCQhMyskeUxkSiRmcztGLDckJCEzISlcZTsqKmUmUXMiRiwkITM2JDRjXzAqNC06Riw3JCQhMy8/QkpfdG0qZSJGLCQhM1tTayF5KDRGejhGLDckJCEzKyF6ZWEhKXlhWCJGLCQhM0Ujby5oMzYhKUgiRiw3JCQhM1NUWk1MIUc+SyJGLCQhMytjVWJYaDFjN0YsNyQkITMzJHBJN0V4JCk9IkYsJCEzP1AzbDxpbWE3Riw3JCQhMyMzPCN6KmZlWDEiRiwkITNXNSFIUVRMW0giRiw3JCQhM2AmW09OUSpSMiUqISM+JCEzISlvMDA7PWYlUSJGLDckJCEzVyRHM0gnKUdgNylGW3IkITNTS0N1M0YqeWEiRiw3JCQhM00iMyFHVSRlSyVvRltyJCEzPi5zKkhXRm0iPUYsNyQkITMlKmZiI2U8UnReJkZbciQhM1kvNCpbdk5zRiNGLDckJCEzYVE1UDQrVSI+JUZbciQhMz80UzI4dyEzNCRGLDckJCEzZzBeJGZhJ2VJTkZbciQhM0slWypRUVdbXFBGLDckJCEzbXMiKlwjM2AocEdGW3IkITMnNE8weVkpcElaRiw3JCQhM3NSSzE+Jz4qM0FGW3IkITNlI0dbODteZy8nRiw3JCQhM3kxdGliaDNbOkZbciQhMzI4QEpUIUdQSihGLDckJCEzSylbY3M2eExvKSEjPyQhM2JAVSRIbExUYSlGLDckJCEzISkzKlIjeUUqZSk9Rml0JCEzY2dsPTpONSZwKkYsNyQkITNQT0dPQnI/TzVGaXQkITM4YzpsKlthSyQpKkYsNyQkITNHUncmW286Xyc9ISNAJCEzWzM5WCRvRCwoKipGLDckJCIzNiYzOFInKVI7aidGaXUkIjMnXCg0JlIrJUclKikqRiw3JCQiMyY0UW83YVxHXiJGaXQkIjN5ZXBWc14oKmYoKkYsNyQkIjMkZV9BNWw/QUAkRml0JCIzVXlTW1Y+PyZcKkYsNyQkIjNxcW14ZzxmNlxGaXQkIjN3IXosOCxdYkIqRiw3JCQiM1hnXEchKVJMNSQpRml0JCIzXndMTFpwYkooKUYsNyQkIjMtRCR6Kj53ITQ8IkZbciQiMytnYndfciN5QylGLDckJCIzX21ndT1LTm9CRltyJCIzOiIpZTohUk0wcSdGLDckJCIzLzNHXjwpKXpsTkZbciQiMy88JClIJ3AtS1EmRiw3JCQiM2ViYV1aKlFRIlxGW3IkIjMtKHlgdmdOMEYlRiw3JCQiMzkuIilceCF6PUUnRltyJCIzQEIwc3FlNFRPRiw3JCQiM2NHOnkqUWFhaChGW3IkIjMxWTsrcDNkXUtGLDckJCIzKVImXDEtKEghcCopRltyJCIzUzB3Xm1tdiIqSEYsNyQkIjMkW2kmb0tdTUY1RiwkIjM8RT09XUltPEdGLDckJCIzRWFaOyY0KHlkNkYsJCIzPzwrW3EycSJwI0YsNyQkIjMjPm9zUChbcCVSIkYsJCIzSkZxX2prITRhI0YsNyQkIjNXVSVbbjgsa24iRiwkIjNHcSI9bjRSKlJDRiw3JCQiMyMpZi0nSEhWXSI+RiwkIjMlb2cpPWU1RCRSI0YsNyQkIjNFeDsiRyYzayM+I0YsJCIzPyRwIzNaZjxtQkYsNyQkIjNWR2xQSTxPUUNGLCQiM2E3PkQ4PDtlQkYsNyQkIjNhRiNIeFpjenEjRiwkIjNLOTcnNE8zM08jRiw3JCQiM0lfSiIzVnVZJ0hGLCQiM0UtVThsMCo0UCNGLDckJCIza2hXUCRvS0RCJEYsJCIzM0kkSEpaTXJRI0YsNyQkIjNhMEVfdixeeU1GLCQiM0BGdD5vOFowQ0YsNyQkIjNIPyQ0NzhJUXUkRiwkIjNJPSZHWjk7elUjRiw3JCQiM0tFRk4pKkhVPlNGLCQiM106JCopSEghSGBDRiw3JCQiM28yZ04qUkYkZlVGLCQiMytgajdgbmN3Q0YsNyQkIjMqXFFOW3NJJT1YRiwkIjNPJSkpeT8tXkRdI0YsNyQkIjMjR0FNTCIpNGh5JUYsJCIzeiVcaiVIJCkqKkhERiw3JCQiM0NCdCIqeTopei8mRiwkIjNNJlsoZk4qW3NiI0YsNyQkIjN3JEc5dChmTixgRiwkIjNDI2ZRSyQzcSZlI0YsNyQkIjM/cTxlWl1vI2UmRiwkIjMvTGpEMSZRNmkjRiw3JCQiM2MhKkgkKUg8Wk5lRiwkIjN5Jio+WHAjKilvbCNGLDckJCIzLVRKUHBhUDBoRiwkIjMnXGAwUicqRygqcCNGLDckJCIzO1QpekhQWypcakYsJCIzVlZLSiNwOUx1I0YsNyQkIjNfRzd6YzZMPG1GLCQiMydIJHltZCwocHojRiw3JCQiMyEqUix0PXYiKm9vRiwkIjM5XCtNNDM4YUdGLDckJCIzOyhSciNleCo9OChGLCQiMy0wL0EmZm0/I0hGLDckJCIzSURXJDMsNCEqUShGLCQiMzcoW0hCYHAiKSpIRiw3JCQiMyEzPlBXbSE9ZXdGLCQiM2dXLCFbTHouNCRGLDckJCIzc1hsbWVcVTx6RiwkIjNVaUtHQ1JIJT4kRiw3JCQiM3dFIioqSHBSRD0pRiwkIjMlZTEoUSh5KD4/TEYsNyQkIjNpJCp5WlYiZmFXKUYsJCIzVzE7VEFjJzRaJEYsNyQkIjNHdCtyN1swKG8pRiwkIjMjKVtpI29jJ2VTT0YsNyQkIjMhZlYyUHJdUicqKUYsJCIza0dlYGp2UCkpUUYsNyQkIjM4dyVmJTMoNDtAKkYsJCIzcWNhJyo+IioqZj0lRiw3JCQiMz8kUlk7JmVtdiUqRiwkIjMteUYiKlIsTltZRiw3JCQiM051T2NpTi4tJypGLCQiMyM9KWUoKSo+YSsoXEYsNyQkIjNfYjRbdDdTRygqRiwkIjMhcC0rPiJmQCJSJkYsNyQkIjM9PDI2YjRJJ3oqRiwkIjNzeFZGISpbT29jRiw3JCQiM3d4L3VPMT9rKSpGLCQiM0VTOC9fWi81Z0YsNyQkIjNnZWBieC86KSopKkYsJCIzQTg2KUhhMUlBJ0YsNyQkIjNMUS1QPS41SyoqRiwkIjNnPz5meidHJilbJ0YsNyQkIjM/eXd4UV8yXCoqRiwkIjMhUV1TeW1YZmwnRiw3JCQiMzs+Xj1mLDBtKipGLCQiM29HeERUZSxub0YsNyQkIjM1UikpUT53YHUqKkYsJCIzLEUkR2AiXGEscUYsNyQkIjM5Z0Rmel0tJCkqKkYsJCIzPy0zQzNMJ0c8KEYsNyQkIjMxIUcnelJEXiIqKipGLCQiM0dPSFEoPUdaVShGLDckJCIiIiIiISQiM0F1aWhmISp6cioqRiwtJSZDT0xPUkc2JiUkUkdCRyQiIzUhIiIkRlxobEZlaGxGZmhsLSUqQVhFU1RJQ0tTRzYlNyUvJCEjNUZlaGxRKi1pbmZpbml0eTYiL0ZmaGxRIjBGX2lsL0ZjaGxRKWluZmluaXR5Rl9pbEZqaGwtJSVGT05URzYjJShERUZBVUxURy0lK0FYRVNMQUJFTFNHNiRRIUZfaWxGW2psLSUlVklFV0c2JDskISNEISIjRmNobDskITJpRkp5VCcqby4iISM7JCIyR3daYXZqcS4iRmZqbA==

plot(y,-2..infinity);

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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=-2..5,discont=true,thickness=[3,3]);

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Support de la courbetotal:=[x(t),y(t),t=-2..infinity]:plot([total,EqTA,EqTB,EqTC,EqA1,EqA2],-5..5,-10..10,color=[blue,black,black,black,green,green],thickness=[3,1,1,1,2,2,2]);

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Attention MAPLE semble ajouter \340 la courbe son asymptote!!!