DERIVE for Windows version 5.04 DfW file saved on 14 Dec 2004  A():=- 2LN() + ^2/2 - + 4 - 7/2 N(x):=- LN(x) - 2(x^(3/2) - 1) f(x):=LN(x)/x - x + 1 u(n):=IF(n = 0, , LN(u(n))/(u(n)) + 1) x:epsilon Real (0, 1) :epsilon Real (0, 1) :epsilon Real [1, 2] hCross:=APPROX(10049115913555993/10000000000000000) vCross:=APPROX(37593984962406013/1000000000000000000) %CExpnObj8 0 Utilisateurf(x):=LN(x)/SQRT(x)+1-x8<` Der(#1,x)DIF(f(x):=LN(x)/SQRT(x)+1-x,x)lhSimp(Der(#1,x))Mb?-LN(x)/(2*x^(3/2))+1/x^(3/2)-1hFctr(#3)"-(LN(x)+2*(x^(3/2)-1))/(2*x^(3/2))8, Utilisateur4N(x):=(-(LN(x)+2*(x^(3/2)-1))/(2*x^(3/2)))*2*x^(3/2)8`PSimp(Utilisateur)-LN(x)-2*(x^(3/2)-1)8\Xh UtilisateurN(1)tSimp(Utilisateur)08 Utilisateur x:epsilonReal (0, 1)8x Utilisateur N(x)>08 Resol(#10,x) SOLVE(N(x)>0,x)XSimp(Resol(#10,x))Mb? +x<#e^2 AND LN(x)^2-4*LN(x)-4*x^3>-4 AND x>08X Utilisateur N(x) CDispOleObj< CDispItem!ࡱ> "  !"#$&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Root EntryFOle CONTENTS%>!CompObjrB F,Image (bitmap indpendante du priphrique) StaticDib9q      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~                           ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~                            ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~                            ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~                            ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~                            ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~        !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~BM>!B( >!Z!Z!Z!d%Z!d%d%d%d%d%d%d%)d%{J{J{J!9d%){J99)){J99J))){J9JJJ!9)))9JJs9J)))JJJJJ)JJ{9J{9ZZ!9J1JJƌJu6scscs1JJ1JƌJƌJ)cƌJƌJRs!9BZƌJks!s){91JBZs9jeƌJcscscs!sBZRskҾcs!s)csJkҾcs!scs!scsRskք!s)!s)k{Ҿcscscscskք!scscsks11csRsƌJƌJzRsRs8%X1 Utilisateurf(1)=ISimp(Utilisateur)08Ua Utilisateuralpha:epsilonReal (0, 1)8mXy Utilisateurf(x)8 Int(#17,x)INT(f(x),x,1,alpha)Simp(Int(#17,x))92*SQRT(alpha)*LN(alpha)-alpha^2/2+alpha-4*SQRT(alpha)+7/28x- Lim(#19,)HLIM(2*SQRT(alpha)*LN(alpha)-alpha^2/2+alpha-4*SQRT(alpha)+7/2,alpha,0,0)9]Simp(Lim(#19,))7/28i Utilisateur(u(n):=IF(n=0,beta,LN(u(n))/SQRT(u(n))+1)8 Utilisateurbeta:epsilonReal [1, 2]8 UtilisateurLN(beta)/SQRT(beta)>=08 Resol(#24,)"SOLVE(LN(beta)/SQRT(beta)>=0,beta) )Simp(Resol(#24,))beta>=185Y UtilisateurLN(beta)/SQRT(beta)<=18e Resol(#27,)'NSOLVE(LN(beta)/SQRT(beta)<=1,beta,2,1)xSimp(Resol(#27,))Mb?'NSOLVE(LN(beta)/SQRT(beta)<=1,beta,2,1)8 UtilisateurLN(beta)/SQRT(beta)-1<=08 UtilisateurLN(beta)/SQRT(beta)-1%8I Fctr(#31)  (LN(beta)-SQRT(beta))/SQRT(beta)8Ua Utilisateur!LN(beta)-beta<=08m(y Resol(#33,)"!NSOLVE(LN(beta)-beta<=0,beta,1,2)Simp(Resol(#33,))#!NSOLVE(LN(beta)-beta<=0,beta,1,2)8 Utilisateur$(u(n):=IF(n=0,beta,LN(u(n))/SQRT(u(n))+1)%