Calcul de limites

Print[Limite[(1+1/x)^x,x,+Infinity]==E];
Print[Limite[(1+x)^(1/x),x,0]==E];
Print[Presente[Limite[Exp[x]/x,x,+Infinity]]];
Print[Presente[Limite[x Exp[x],x,-Infinity]]];
Print[Presente[Limite[(Exp[x]-1)/x,x,0]]];
Print[Presente[Limite[Log[x]/x,x,+Infinity]]];
Print[Presente[Limite[Log[x] x,x,0]]];

utiliser la règle de l'Hospital si nécessaire

n=0;
n++;l[n]=Limite[Log[x]/x^3,x,+Infinity];

n++;l[n]=Limite[x^2/Exp[-x],x,+Infinity];
n++;l[n]=Limite[(Exp[x]-Exp[-x])/Sin[x],x,0];
n++;l[n]=Limite[1/x Log[(1+x)/(1-x)],x,0];
n++;l[n]=Limite[Log[x]/Cot[x],x,0];
n++;l[n]= Limite[(1+1/x)^x,x,-Infinity];
n++;l[n]= Limite[(1+3/x)^x,x,+Infinity];
n++;l[n]= Limite[(1+1/x)^(5x),x,+Infinity];
n++;l[n]= Limite[(1+2/x)^(3x),x,+Infinity];
n++;l[n]= Limite[(1+1/x)^(x+5),x,+Infinity];
n++;l[n]= Limite[(1+2/x)^(2-x),x,+Infinity];
n++;l[n]= Limite[((x+2)/(x-3))^(3x-1),x,+Infinity];
n++;l[n]= Limite[(1-3x)^(-2/x),x,0];
n++;l[n]= Limite[(1+Sin[x])^(1/Sin[x]),x,0];
n++;l[n]= Limite[((x+1)/(2x+1))^(x^2),x,Infinity];
n++;l[n]= Limite[((x-1)/(x+1))^(x),x,Infinity];
n++;l[n]= Limite[((1/x^2)^((2x)/(x+1))),x,Infinity];
n++;l[n]= Limite[((x^2+2)/(2x^2+1))^(x^2),x,Infinity];

Do[Print[i,") ",l[i]],{i,1,10}]

Do[Print[i,") ",l[i]],{i,11,18}]

Solutions

Do[Print[i,") ",Presente[l[i]]],{i,1,n}]

Exercices :

Print["Sachant que ",Limite[(1+k/x)^x,x,Infinity],"= ",Exp[k]," calculer"]

n=0;
n++;l[n]=Limite[((2+x)/(3-x))^x,x,0];
n++;l[n]=Limite[((x-1)/(x^2-1))^(x+1),x,1];
n++;l[n]=Limite[(1/x^2)^(2x/(x+1)),x,Infinity];
n++;l[n]=Limite[((x^2-2x+3)/(x^2-3x+2))^(Sin[x]/x),x,0];
n++;l[n]=Limite[((x^2+2)/(2x^2+1))^(x^2),x,Infinity];
n++;l[n]= Limite[(1-1/m)^m,m,Infinity];
n++;l[n]= Limite[(1+2/x)^x,x,+Infinity];
n++;l[n]= Limite[(x/(x+1))^x,x,+Infinity];
n++;l[n]= Limite[((x+1)/(x+3))^(x+2),x,+Infinity];
n++;l[n]= Limite[(1+x/m)^m,m,+Infinity];
n++;l[n]= Limite[(1+Sin[x])^(1/x),x,0];

Do[Print[i,") ",l[i]],{i,1,n}]

Solutions

Do[Print[i,") ",Presente[l[i]]],{i,1,n}]