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1 }} {SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 317 37 "Merken Sie sich folgend e WWW-Adresse:" }{TEXT 317 0 "" }}{PARA 257 "" 0 "" {TEXT 318 47 "http ://www.mathematik.uni-ulm.de/sgm/baur/maple" }{TEXT 318 0 "" }}{PARA 258 "" 0 "" {TEXT 319 0 "" }}{PARA 258 "" 0 "" {TEXT 319 0 "" }}{PARA 258 "" 0 "" {TEXT 319 0 "" }}{PARA 259 "" 0 "" {TEXT 320 7 "Blatt 1" } {TEXT 320 0 "" }}{PARA 258 "" 0 "" {TEXT 319 0 "" }}{PARA 257 "" 0 "" {TEXT 318 18 "Aufgabenstellungen" }{TEXT 318 0 "" }}{PARA 258 "" 0 "" {TEXT 319 0 "" }}{PARA 258 "" 0 "" {TEXT 319 23 "Stand: 13. Oktober 20 06" }{TEXT 319 0 "" }}{PARA 258 "" 0 "" {TEXT 319 0 "" }}}{EXCHG {PARA 258 "" 0 "" {TEXT 319 0 "" }}{PARA 258 "" 0 "" {TEXT 319 77 "Die ersten beiden Aufgaben haben den Zweck, mit Maple etwas \"herumzuspie len\":" }{TEXT 319 0 "" }}{PARA 258 "" 0 "" {TEXT 319 0 "" }}}{EXCHG {PARA 258 "" 0 "" {TEXT 319 0 "" }}{PARA 260 "" 0 "" {TEXT 321 9 "Aufg abe 1" }{TEXT 321 0 "" }}{PARA 258 "" 0 "" {TEXT 319 0 "" }}{PARA 261 "" 0 "" {TEXT 322 11 "Teilen Sie " }{XPPEDIT 261 0 "3^175" "6#*$\"\"$ \"$v\"" }{TEXT 322 70 " durch 50!. Wie lautet der Z\344hler des gek\37 4rzten Bruches? (-> \"numer\")." }{TEXT 322 0 "" }{TEXT 322 59 "\nWie \+ oft ist der Faktor 3 darin enthalten? (-> \"ifactor\"). " }{TEXT 322 0 "" }{TEXT 322 53 "\nWieviel Dezimalstellen hat der Z\344hler? (-> \" length\")" }{TEXT 322 0 "" }}{PARA 258 "" 0 "" {TEXT 319 0 "" }}} {EXCHG {PARA 262 "> " 0 "" {MPLTEXT 1 323 0 "" }}}{EXCHG {PARA 258 "" 0 "" {TEXT 319 0 "" }}{PARA 263 "" 0 "" {TEXT 324 9 "Aufgabe 2" } {TEXT 324 0 "" }}{PARA 258 "" 0 "" {TEXT 319 0 "" }}{PARA 264 "" 0 "" {TEXT 325 71 "Bestimmen Sie die Primfaktorzerlegung von 98765432101234 56789 und 60! ." }{TEXT 325 0 "" }}{PARA 258 "" 0 "" {TEXT 319 0 "" }} }{EXCHG {PARA 262 "> " 0 "" {MPLTEXT 1 323 0 "" }}}{EXCHG {PARA 258 "" 0 "" {TEXT 319 0 "" }}{PARA 258 "" 0 "" {TEXT 319 107 "Das Vereinfach en von Ausdr\374cken --- denken Sie etwa an die Auswertung von Funktio nen oder deren Ableitungen" }{TEXT 319 0 "" }}{PARA 258 "" 0 "" {TEXT 319 113 "bei einer Kurvendiskussion --- ist eine h\344ufig auftretende Aufgabe. Wir lernen verschiedene \"Zauberworte\" kennen," }{TEXT 319 0 "" }}{PARA 258 "" 0 "" {TEXT 319 41 "die man hierzu mit Vorteil benu tzen kann:" }{TEXT 319 0 "" }}{PARA 258 "" 0 "" {TEXT 319 0 "" }}} {EXCHG {PARA 258 "" 0 "" {TEXT 319 0 "" }}{PARA 265 "" 0 "" {TEXT 326 9 "Aufgabe 3" }{TEXT 326 0 "" }}{PARA 258 "" 0 "" {TEXT 319 0 "" }} {PARA 261 "" 0 "" {TEXT 322 30 "Vereinfachen Sie den Ausdruck " } {XPPEDIT 266 0 "sqrt(2*sqrt(19549)+286)" "6#-%%sqrtG6#,&*&\"\"#\"\"\"- F$6#\"&\\&>F)F)\"$'GF)" }{TEXT 322 26 " . (Quadratwurzel: \"sqrt\")" } {TEXT 322 0 "" }}{PARA 266 "" 0 "" {TEXT 327 47 "Geben Sie hierf\374r \+ eine 50-stellige N\344herung an!" }{TEXT 327 0 "" }}{PARA 258 "" 0 "" {TEXT 319 0 "" }}}{EXCHG {PARA 262 "> " 0 "" {MPLTEXT 1 323 0 "" }}} {EXCHG {PARA 258 "" 0 "" {TEXT 319 0 "" }}{PARA 267 "" 0 "" {TEXT 328 9 "Aufgabe 4" }{TEXT 328 0 "" }}{PARA 258 "" 0 "" {TEXT 319 0 "" }} {PARA 268 "" 0 "" {TEXT 329 36 "Vereinfachen Sie folgende Ausdr\374cke :" }{TEXT 329 0 "" }}{PARA 269 "" 0 "" {TEXT 330 0 "" }}{PARA 261 "" 0 "" {TEXT 322 4 "a) " }{XPPEDIT 279 0 "1/sin(x)^2+1/cos(x)^2" "6#,&*& \"\"\"F%*$-%$sinG6#%\"xG\"\"#!\"\"F%*&F%F%*$-%$cosGF)F+F,F%" }{TEXT 322 39 " (-> \"simplify\", \"normal\")" }{TEXT 322 0 "" } }{PARA 261 "" 0 "" {TEXT 322 4 "b) " }{XPPEDIT 276 0 "sin(x+y)+sin(x- y)" "6#,&-%$sinG6#,&%\"xG\"\"\"%\"yGF)F)-F%6#,&F(F)F*!\"\"F)" }{TEXT 322 26 " (-> \"expand\")" }{TEXT 322 0 "" }}{PARA 261 "" 0 "" {TEXT 322 4 "c) " }{XPPEDIT 273 0 "cos(x)*cos(y)-sin(x)*sin(y)" " 6#,&*&-%$cosG6#%\"xG\"\"\"-F&6#%\"yGF)F)*&-%$sinGF'F)-F/F+F)!\"\"" } {TEXT 322 17 " (-> \"combine\")" }{TEXT 322 0 "" }}{PARA 261 "" 0 "" {TEXT 322 4 "d) " }{XPPEDIT 270 0 "sin(Pi/4)/(sqrt(3)*(1+sqrt(2))*(1 -sqrt(8)))" "6#*&-%$sinG6#*&%#PiG\"\"\"\"\"%!\"\"F)*(-%%sqrtG6#\"\"$F) ,&F)F)-F.6#\"\"#F)F),&F)F)-F.6#\"\")F+F)F+" }{TEXT 322 29 " \+ (-> \"rationalize\")" }{TEXT 322 0 "" }}{PARA 261 "" 0 "" {TEXT 322 4 "e) " }{XPPEDIT 287 0 "(7+5*sqrt(2))^(1/3)" "6#),&\"\"(\"\"\"*&\"\"&F &-%%sqrtG6#\"\"#F&F&*&F&F&\"\"$!\"\"" }{TEXT 322 36 " \+ (-> \"radnormal\")" }{TEXT 322 0 "" }}{PARA 258 "" 0 "" {TEXT 319 0 "" }}}{EXCHG {PARA 262 "> " 0 "" {MPLTEXT 1 323 0 "" }}}{EXCHG {PARA 258 "" 0 "" {TEXT 319 0 "" }}{PARA 270 "" 0 "" {TEXT 331 9 "Aufg abe 5" }{TEXT 331 0 "" }}{PARA 258 "" 0 "" {TEXT 319 0 "" }}{PARA 271 "" 0 "" {TEXT 332 69 "Untersuchen Sie (analog dem Beispiel, welches Si e im ersten Teil der " }{TEXT 332 0 "" }{TEXT 332 86 "\nheutigen Veran staltung kennengelernt haben) folgende Funktion bzw. 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