Exercice 12restart;a:='a':lambda:='lambda':rho:=theta->a*exp(lambda*theta);

NiM+SSRyaG9HNiJmKjYjSSZ0aGV0YUdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiZJImFHRiUiIiItSSRleHBHNiRJKnByb3RlY3RlZEdGMkkoX3N5c2xpYkdGJTYjKiZJJ2xhbWJkYUdGJUYuOSRGLkYuRiVGJUYl

Calcul de la direction de la tangenteDrho:=D(rho);

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cV:=Drho(theta)/rho(theta);

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V:=unapply(arccot(cV),theta);On en d\351duit V modulo Pi

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D'o\371 quelques tangentes sont de direction constante par rapport \340 la direction (OM) (qui elle ne l'est pas)Variations de rho et de Va:=1:lambda:=2:plot(rho,-infinity..infinity);

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plot(V);

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Supports pour diff\351rents param\350tres a et lambdatmin:=-30/lambda:tmax:=60/lambda:a:=0.1:lambda:=1:sp1:=[rho(t),t,t=tmin..tmax]:a:=0.2:lambda:=1:sp2:=[rho(t),t,t=tmin..tmax]:a:=0.1:lambda:=2:sp3:=[rho(t),t,t=tmin..tmax]:a:=-0.1:lambda:=4:sp4:=[rho(t),t,t=tmin..tmax]:plot([sp1,sp2,sp3,sp4],0..1,-1..3,color=[blue,red,green,black],coords=polar);

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