Exercices 3 - Déterminer les éventuelles asymptotes des fonctions suivantes

q=0;
q+=1;
f[x_,q]:=Sqrt[x^2-4x];
Print[q,".  f(x) = ",f[x,q]];

q+=1;
f[x_,q]:=3+1/Sqrt[2x-1];
Print[q,".  f(x) = ",f[x,q]];

q+=1;
f[x_,q]:=Sqrt[x^2+2x+3];
Print[q,".  f(x) = ",f[x,q]];

q+=1;
f[x_,q]:=Sqrt[x^2-x-6]+x;
Print[q,".  f(x) = ",f[x,q]];

q+=1;
f[x_,q]:=(Sqrt[2x^2+1]-Sqrt[3x^2-1])/(1-2x);
Print[q,".  f(x) = ",f[x,q]];

q+=1;
f[x_,q]:=(1-5x)/Sqrt[3x^2-x+1];
Print[q,".  f(x) = ",f[x,q]];

q+=1;
f[x_,q]:=(Sqrt[x^3-1]-Sqrt[2x^2-1])/(1-3x);
Print[q,".  f(x) = ",f[x,q]];

q+=1;
f[x_,q]:=(3x+7)/(Sqrt[x^2-4]-1);
Print[q,".  f(x) = ",f[x,q]];


q+=1;
f[x_,q]:=Sqrt[x^2+1]-Sqrt[4+x^2];
Print[q,".  f(x) = ",f[x,q]];


q+=1;
f[x_,q]:=Sqrt[4x^2+1]-2Sqrt[x^2-4x];
Print[q,".  f(x) = ",f[x,q]];

q+=1;
f[x_,q]:=(x-Sqrt[x^2+2x+4])/(3x-Sqrt[9x^2+3x]);
Print[q,".  f(x) = ",f[x,q]];

q+=1;
f[x_,q]:=Sqrt[x^2+1]/Sqrt[4x^3-4];
Print[q,".  f(x) = ",f[x,q]];

q+=1;
f[x_,q]:=Sqrt[4x-1]-Sqrt[4x^2-4];
Print[q,".  f(x) = ",f[x,q]];

q+=1;
f[x_,q]:=Sqrt[x^2-3x+2]/(4x-1);
Print[q,".  f(x) = ",f[x,q]];

Solutions

q=0;
q+=1;

Print[q,".  Dom f = ",Domaine[f[x,q],x]];
AV[f[x,q],x];
AO[f[x,q],x];

q+=1;
Print[q,".  Dom f = ",Domaine[f[x,q],x]];
AV[f[x,q],x];
AO[f[x,q],x];


q+=1;
Print[q,".  Dom f = ",Domaine[f[x,q],x]];
AV[f[x,q],x];
AO[f[x,q],x];


q+=1;
Print[q,".  Dom f = ",Domaine[f[x,q],x]];
AV[f[x,q],x];
AO[f[x,q],x];


q+=1;
Print[q,".  Dom f = ",Domaine[f[x,q],x]];
AV[f[x,q],x];
AO[f[x,q],x];


q+=1;
Print[q,".  Dom f = ",Domaine[f[x,q],x]];
AV[f[x,q],x];
AO[f[x,q],x];


q+=1;
Print[q,".  Dom f = ",Domaine[f[x,q],x]];
AV[f[x,q],x];
AO[f[x,q],x];


q+=1;
Print[q,".  Dom f = ",Domaine[f[x,q],x]];
AV[f[x,q],x];
AO[f[x,q],x];


q+=1;
Print[q,".  Dom f = ",Domaine[f[x,q],x]];
AV[f[x,q],x];
AO[f[x,q],x];

q+=1;
Print[q,".  Dom f = ",Domaine[f[x,q],x]];
AV[f[x,q],x];
AO[f[x,q],x];

q+=1;
Print[q,".  Dom f = ",Domaine[f[x,q],x]];
AV[f[x,q],x];
AO[f[x,q],x];

q+=1;
Print[q,".  Dom f = ",Domaine[f[x,q],x]];
AV[f[x,q],x];
AO[f[x,q],x];

q+=1;
Print[q,".  Dom f = ",Domaine[f[x,q],x]];
AV[f[x,q],x];
AO[f[x,q],x];


q+=1;
Print[q,".  Dom f = ",Domaine[f[x,q],x]];
AV[f[x,q],x];
AO[f[x,q],x];