{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 256 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 6 "Quelle" }}{PARA 0 "" 0 "" {TEXT -1 295 "Dateiname: interval.mws\nDateigr\366\337e: 6 KB\nName: Corinna K\374bler\nSchule : Isolde-Kurz-Gymnasium\nKlasse: 12\nDatum: 10.24.97\nFach: Mathematik \nThema: Intervallschachtelung\nStichw\366rter: Intervallschachtelung/ Intervallhalbierung\nKurzbeschreibung: 1.)Intervallschachtelung\n2.)In tervallhalbierung\n3.)HI-LO\n" }}}{EXCHG {PARA 259 "" 0 "" {TEXT -1 16 " Corinna K\374bler" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 256 24 " I ntervallschachtelung " }{TEXT -1 84 " \+ 16.10.1997" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart:with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "m:=(l+r)/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"mG,&%\"lG#\"\" \"\"\"#%\"rGF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "l:=1: r:= 2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "for i from 0 to 20 do " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "if m^2 > 2 then r:=m fi;" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "if m^2 < 2 then l:=m fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "m;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"*D,Df(\"*74(o`" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+iN@9 9!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "m:=(l,r)->(l+r)/2:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "l:=1: r:=2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "for i to 10 do " }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 30 "if m(l,r)^2 > 2 then r:=m(l,r)" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 18 "else l:=m(l,r) fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "print ([l,m(l,r),r]) od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\" \"\"#\"\"&\"\"%#\"\"$\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%#\"\"& \"\"%#\"#6\"\")#\"\"$\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%#\"#6 \"\")#\"#B\"#;#\"\"$\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%#\"#6\" \")#\"#X\"#K#\"#B\"#;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%#\"#X\"#K# \"#\"*\"#k#\"#B\"#;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%#\"#X\"#K#\"$ \"=\"$G\"#\"#\"*\"#k" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%#\"$\"=\"$G \"#\"$j$\"$c##\"#\"*\"#k" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%#\"$\"= \"$G\"#\"$D(\"$7&#\"$j$\"$c#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%#\"$ \"=\"$G\"#\"%\\9\"%C5#\"$D(\"$7&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7% #\"$\"=\"$G\"#\"%(*G\"%[?#\"%\\9\"%C5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+j!R] T\"!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "print (evalf([l, m(l,r),r]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%$\"++D199!\"*$\"+\"y ]XT\"F&$\"+j!R]T\"F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 257 "" 0 " " {TEXT -1 81 "Beweis,da\337 aus der Monotonie und Beschr\344nktheit e iner Folge dei Konvergenz folgt:" }}}{EXCHG {PARA 258 "" 0 "" {TEXT -1 22 "Intervallschachtelung:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 100 "W\344hle ein Intervallende aus der Menge der Schranken und das andere aus der Menge der Folgenglieder.." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 122 "Intervallhalbierung garantiert, da\337 die Intervalll\344ngen \+ eine Nullfolge bilden und da\337 eine Intervallschachtelung vorliegt: " }}{PARA 0 "" 0 "" {TEXT -1 85 "also gilt zu jedem noch so kleinen Ep silon gibt es ....(Definition des Grenzwertes): " }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 38 "Dezimalzahl->ganze Zahl trunc, round." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart:with(plots):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 257 8 " HI - LO" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 133 "Einer denkt sich eine Zahl zwischen 0 und 100.Der andere versucht durch Intervallschachtelung die gesuchte Zahl herauszufinden . HI-LO" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "m:=(l,r)->(l+r)/ 2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"mG:6$%\"lG%\"rG6\"6$%)operat orG%&arrowGF),&9$#\"\"\"\"\"#9%F/F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "l:=1: r:=100: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "zuf:=rand(0..100):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "z:=zuf();" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG\"#q" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "for i from 0 to 10 do " }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 29 "if m(l,r) > z then r:=m(l,r) " }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 18 "else l:=m(l,r) fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "print (evalf([l,m(l,r),r]))od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%$\"++++]]!\")$\"++++DvF&$\"$+\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%$\"++++]]!\")$\"+++](G'F&$\"++++DvF&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%$\"+++](G'!\")$\"+++D1pF&$\"++++DvF&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7%$\"+++D1p!\")$\"++]i:sF&$\"++++DvF& " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%$\"+++D1p!\")$\"++v$41(F&$\"++]i :sF&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%$\"+++D1p!\")$\"+]Pf$)pF&$\" ++v$41(F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%$\"+]Pf$)p!\")$\"+DcEAq F&$\"++v$41(F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%$\"+]Pf$)p!\")$\"+ )oHH+(F&$\"+DcEAqF&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%$\"+]Pf$)p!\" )$\"+> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "1" 0 }{VIEWOPTS 1 1 0 1 1 1803 }