{VERSION 5 0 "IBM INTEL LINUX" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 0 1 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 2 6 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 2 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "M aple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 6 "" 1 "" {TEXT -1 45 "\nLimite quand t tend vers l'infini de ln(t)/t" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "Int(1/u,u=1..t) = Int(1/u,u =1..sqrt(t)) + Int(1/u,u=sqrt(t)..t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*$%\"uG!\"\"/F(;\"\"\"%\"tG,&-F%6$F'/F(;F,*$F-#F,\"\"#F,- F%6$F'/F(;F3F-F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "ln(t) = Int(1/u,u=1..sqrt(t) ) + Int(1/u,u=sqrt(t)..t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%#lnG6 #%\"tG,&-%$IntG6$*$%\"uG!\"\"/F-;\"\"\"*$F'#F1\"\"#F1-F*6$F,/F-;F2F'F1 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 34 "Int(1/u,u=1..sqrt(t)) = 1/2*ln(t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*$%\"uG!\"\"/F(;\"\"\"*$%\"tG#F,\" \"#,$-%#lnG6#F.F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "ln(t) = 2 * Int(1/u,u=sqrt(t )..t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%#lnG6#%\"tG,$-%$IntG6$*$% \"uG!\"\"/F-;*$F'#\"\"\"\"\"#F'F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "2 * int (0,u=sqrt(t)..t) <= ln(t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#1\"\"!-% #lnG6#%\"tG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "ln(t) <= expand(2/sqrt(t) * int(1,u =sqrt(t)..t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#1-%#lnG6#%\"tG,&*&\" \"#\"\"\"F'#F+F*F+F*!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "limit(ln(t)/t,t=infini ty);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 " " }{MPLTEXT 1 0 0 "" }{TEXT -1 2 " " }}{PARA 0 "" 0 " " {TEXT -1 1 " " }{MPLTEXT 1 0 2 " " }}{PARA 0 "" 0 "" {TEXT -1 1 " \+ " }{MPLTEXT 1 0 0 "" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }{MPLTEXT 1 0 0 "" }}{PARA 0 "" 0 "" {TEXT -1 11 "\n\n\n\n\n\n\n\n\n " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 6 "" 1 "" {TEXT -1 14 "\nAutre m\351thode" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "diff(ln(t)/t,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$%\"tG!\"#\"\"\"*&-%#lnG6#F%F'F%F&!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "diff(ln(t)/t,t);" }} {PARA 0 "" 0 "" {TEXT -1 66 "# Si t >= e Alors ln(t) >= 1, et donc l n(t)/t est d\351croissante " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\" \"\"F%*$)%\"tG\"\"#F%!\"\"F%*&-%#lnG6#F(F%F(!\"#F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "# Or pour t > 1" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 14 "0 <= ln(t)/t ;" }}{PARA 0 "" 0 "" {TEXT -1 16 "# et pour t >= e" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "ln(t)/t <= 1/e;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#1\"\"!*&-%#ln G6#%\"tG\"\"\"F)!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#1*&-%#lnG6#% \"tG\"\"\"F(!\"\"*&F)F)%\"eGF*" }}}{EXCHG {PARA 6 "" 1 "" {TEXT -1 66 "\n D\351croissante et born\351e donc convergente vers une limite fini e a." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "ln(t)/t + ln(t)/t = t * ( ln(t^2)/t^2 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,$*(\"\"#\" \"\"-%#lnG6#%\"tGF'F+!\"\"F'*&F+F,-F)6#*$)F+F&F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "a+a = t * a;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,$%\"aG\"\"#*&%\"tG\"\"\"F%F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "a = 0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"aG\"\"! " }}}}{MARK "17 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }