Maple 6 - Ligninger\302\251 Erik Vestergaard 20131. IndledningEmnet ligninger er et af de mest centrale i matematik. Derfor f\303\245r det sit helt eget dokument. At l\303\270se ligninger er p\303\245 ingen m\303\245de let, generelt set. Nogle af de st\303\270rste problemer indenfor matematikken vedr\303\270rer ligninger, og flere af dem er ul\303\270ste. Derfor kan Maple heller ikke l\303\270se alle de ligninger, man m\303\245tte kaste efter den, men den er rigtig st\303\246rk!! Nogle typer ligninger kan l\303\270ses eksakt, mens langt de fleste ligninger ikke kan l\303\270ses eksakt - l\303\270sningerne kan simpelthen ikke skrives som et udtryk involverende de s\303\246dvanlige matematiske funktioner. I de tilf\303\246lde, hvor en eksakt l\303\270sning ikke kan findes, er der heldigvis h\303\245b for at man kan finde en tiln\303\246rmet l\303\270sning, ogs\303\245 kaldet en numerisk l\303\270sning. Vi skal kigge p\303\245 begge typer, dvs. b\303\245de de eksakte og de numeriske l\303\270sninger. Vi vil ogs\303\245 senere kigge p\303\245 systemer af ligninger og ogs\303\245 en smule p\303\245 uligheder. Der er en opgavesektion i slutningen af de fleste afsnit. L\303\270sninger til differentialligninger vil ikke blive omtalt i dette dokument. 2. De to grundl\303\246ggende kommandoer til ligningsl\303\270sningVi vil i dette afsnit kun kigge p\303\245 ligninger med \303\251n ubekendt. Alle tal i ligningen antages reelle. P\303\245 trods af at Maple indeholder nogle specielle metoder til s\303\246rlige ligninger, s\303\245 vil vi i dette afsnit af overskueligheds grunde is\303\246r fokusere p\303\245 de to grundl\303\246ggende kommandoer til ligningsl\303\270sning, nemlig solve og fsolve. I det f\303\270lgende vil vi kalde det for kommafidusen, hvis man skriver mindst en af tallene i ligningen som et kommatal.
solveKan benyttes til at l\303\270se ligninger eksakt med, men hvis man bruger kommafidusen, vil kommandoen regne numerisk. Den vil angive b\303\245de reelle og komplekse l\303\270sninger. Kommandoen vil i begge tilf\303\246lde fors\303\270ge at finde alle l\303\270sninger, hvis den kan. fsolveKan kun finde reelle numeriske l\303\270sninger. I tilf\303\246ldet med en n'te gradsligning giver kommandoen alle reelle l\303\270sninger. I andre typer ligninger vil kommandoen fors\303\270ge at finde \303\251n l\303\270sning ad gangen. Roots*Med optionen numeric kan kommandoen Roots v\303\246re god til at finde numeriske l\303\270sninger til komplicerede ligninger indenfor et givet (endeligt) interval. Den kr\303\246ver kald af pakken LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEoU3R1ZGVudEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYkLUYsNiVRKkNhbGN1bHVzMUYnRi9GMi9GM1Enbm9ybWFsRidGPS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Y9.
* Fra pakken LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlEoU3R1ZGVudEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYnLUYjNictRiw2JlEqQ2FsY3VsdXMxRidGL0YyRjVGLy8lK2V4ZWN1dGFibGVHRjQvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnL0Y2USdub3JtYWxGJ0YvRkUvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGL0ZARkJGRQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Den tredje kommando er medtaget, fordi den kan v\303\246re hensigtsm\303\246ssig i visse tilf\303\246lde med sv\303\246re ligninger, hvor man s\303\270ger efter numeriske l\303\270sninger. Den har den fordel frem for fsolve, at den kan finde flere numeriske l\303\270sninger p\303\245 \303\251n gang. Man kan dog i princippet n\303\270jes med fsolve. Her er en mulig strategi ved ligningsl\303\270sning:I de fleste tilf\303\246lde kan man med fordel benytte solve-kommandoen - med kommafidusen, hvis man \303\270nsker numeriske l\303\270sninger. Man kan overveje for en sikkerheds skyld at studere et plot, for at v\303\246re mere sikker p\303\245, at man har f\303\245et alle l\303\270sninger med. Det anbefales at sortere eventuelle komplekse l\303\270sninger fra i hovedet. Alternativt kan man kalde pakken RealDomain inden solve-kommandoen.Kommandoen fsolve er god i tilf\303\246ldet med polynomier med \303\251n variabel, da den giver samtlige reelle l\303\270sninger med kommatal. Til komplicerede ligninger er det bedst at kigge p\303\245 et plot, observere de omtrentlige grafiske l\303\270sninger og finde dem med stor pr\303\246cision \303\251n ad gangen ved hj\303\246lpe kommandoen fsolve og i Bem\303\246rkningHvad der menes med et plot i forbindelse med en ligning kan bedst illustreres med et par eksempler. Er ligningen LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0YyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEoJm1pbnVzO0YnRj4vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkkvJSlzdHJldGNoeUdGSS8lKnN5bW1ldHJpY0dGSS8lKGxhcmdlb3BHRkkvJS5tb3ZhYmxlbGltaXRzR0ZJLyUnYWNjZW50R0ZJLyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGWC1GLzYlUSNsbkYnL0YzRklGPi1JKG1mZW5jZWRHRiQ2JC1GIzYkRi5GPkY+RkMtRjs2JFEiNUYnRj4tRkQ2LVEiPUYnRj5GR0ZKRkxGTkZQRlJGVC9GV1EsMC4yNzc3Nzc4ZW1GJy9GWkZlby1GOzYkRkJGPkY+ plottes 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. Er ligningen 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, s\303\245 plottes 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. Man flytter alts\303\245 alt over p\303\245 venstre side, s\303\245 der st\303\245r 0 p\303\245 h\303\270jre side. Kig n\303\246rmere p\303\245 eksempel 10. Bem\303\246rkning om kontekstmenuenMan kan ogs\303\245 l\303\270se ligninger direkte ved at h\303\270jreklikke og bruge kontekstmenuen. I de to eksempler nedenfor er f\303\270lgende kontekstmenuer blevet brugt: Solve > Obtain Solutions for > x henholdvis Solve > Numerically Solve. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==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 svarer til henholdsvis at bruge solve og fsolve. Kontekstmenuerne er alts\303\245 en overbygning p\303\245 de allerede eksisterende kommandoer. Men da de ikke d\303\246kker alle de muligheder, som kommandoerne med deres options tilbyder, anbefales det generelt set at bruge kommandoerne. I nogle af de simple simplere tilf\303\246lde For at forst\303\245, hvordan de enkelte kommandoer fungerer, giver vi en r\303\246kke eksempler. Eksempel 1Lad os starte med at kigge p\303\245 en simpel 2. gradsligning: 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. Hvis vi \303\270nsker eksakte l\303\270sninger, kan vi blot bruge solve kommandoen: 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(); # input placeholderDet er p\303\246nt at skrive LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEiLEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1JI21pR0YkNiVRInhGJy8lJ2l0YWxpY0dGNy9GMFEnaXRhbGljRidGLw== efter ligningen for at fremh\303\246ve, at det er x, som skal findes. Det er ikke strengt n\303\270dvendig her, men det er det hvis der for eksempel i ligningen er flere bogstavst\303\270rrelser tilstede, for eksempel parametre. Ofte vil vi blot v\303\246re interesseret i at lave l\303\270sningerne i kommatal, alts\303\245 de numeriske l\303\270sninger. Da kan vi pr\303\270ve at bruger kommafidusen. Vi tilf\303\270jer et decimal-komma (punktum) til 0'et p\303\245 h\303\270jre side, hvorved vi tvinger solve-kommandoen til at t\303\246nke numerik: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(); # input placeholderVi kunne faktisk ogs\303\245 have benyttet fsolve kommandoen her: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(); # input placeholderJSFHJSFHEksempel 2Denne gang vil vi kigge p\303\245 en 4. gradsligning: 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. JSFHLad os kigge efter eksakte l\303\270sninger med solve kommandoen: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(); # input placeholderJSFHDet indirekte RootOf svar, som Maple giver, kan vi ikke direkte bruge til noget. Undertiden kan man dog f\303\245 noget fornuftigt ud af det ved at h\303\270jreklikke p\303\245 svaret og v\303\246lge All Values fra kontekstmenuen. I dette tilf\303\246lde vil vi faktisk f\303\245 alle fire eksakte l\303\270sninger, men vi vil undlade at udf\303\270re det her, da udtrykkene fylder uhyggeligt meget. Du kan eventuelt pr\303\270ve det af selv. Det er meget imponerende, at programmet kan angive eksakte l\303\270sninger, som ser s\303\245 komplicerede ud! I andre tilf\303\246lde vil man ikke f\303\245 noget ud af at bruge All Values, enten fordi l\303\270sningerne ikke kan angives eksakt (fx for n'te gradsligninger, hvor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjRGJ0Y5Rjk=), eller fordi Maple ikke kan finde ud af det. I det f\303\270lgende vil vi pr\303\270ve at finde alle de numeriske l\303\270sninger ved at benytte solve sammen med kommafidusen.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(); # input placeholderVi f\303\245r naturligvis fire l\303\270sninger, da et n'te gradspolynomium som bekendt altid har pr\303\246cist n l\303\270sninger. De to er komplekse; det er dem, hvori der figurerer et stort I. Hvis vi ikke har brug for dem, kan de bare sorteres fra i hovedet. Dermed f\303\245s de to reelle l\303\270sninger: 8.515841973 og -11.92650835. Kommandoen fsolve giver derimod straks alle de reelle l\303\270sninger. Det kan man ikke regne med, at fsolve g\303\270r i alle tilf\303\246lde, som n\303\246vnt i tabellen ovenfor!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print(); # input placeholderJSFHEksempel 3Vi skal se, hvad Maple siger til en ligning, som har uendeligt mange l\303\270sninger: 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.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print(); # input placeholderDen svarer alts\303\245, at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTEYrRjk=. Det er det samme som at sige, at alle x duer i ligningen!Eksempel 4Man kan ogs\303\245 bruge kommandoen solve til at isolere en st\303\270rrelse i en ligning, hvori der figurerer andre symboler end den st\303\270rrelse, som man fors\303\270ger at isolere. Det er der ikke noget i vejen for, og Maple klarer ofte let et s\303\245dant problem. Man kan for eksempel fint benytte solve til at isolere v i udtrykket 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. Det g\303\270res s\303\245ledes: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print(); # input placeholderLUkmbW92ZXJHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JS1JI21vR0YkNi5RJyZyYXJyO0YnLyUwZm9udF9zdHlsZV9uYW1lR1EoMkR+TWF0aEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R1EldHJ1ZUYnLyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUkmbXRleHRHRiQ2JVEyc2ltcGxpZnl+c3ltYm9saWNGJ0YvRjJGQw==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For det f\303\270rste ser man, at der er to l\303\270sninger. Det skyldes selvf\303\270lgelig at en ligning af formen LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0YyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEiPUYnRj4vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkkvJSlzdHJldGNoeUdGSS8lKnN5bW1ldHJpY0dGSS8lKGxhcmdlb3BHRkkvJS5tb3ZhYmxlbGltaXRzR0ZJLyUnYWNjZW50R0ZJLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGWC1GLzYlUSJhRidGMkY1Rj4=, hvor a er positiv, har to l\303\270sninger, en positiv og en negativ. Men derudover er der opskrivningen af udtrykket. En gammeldags matematiker (som undertegnede selv), vil nok sige, at det kan skrives p\303\246nere, nemlig som 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. Men man kan desv\303\246rre ikke altid opn\303\245 den opskrivning, som man selv anser for p\303\246nest. Man kan fors\303\270ge at h\303\270jreklikke p\303\245 Maples svar og v\303\246lge Simplify > Symbolic, som jeg har gjort ovenfor. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Eksempel 5Man kan sagtens f\303\245 Maple til at l\303\270se ligninger med parametre. Et godt eksempel er det generelle udseende af en andengradsligning med parametrene a, b og c. JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEmc29sdmVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2MC1GLDYlUSJhRidGL0YyLUkjbW9HRiQ2LVEnJnNkb3Q7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlQtSSVtc3VwR0YkNiUtRiw2JVEieEYnRi9GMi1GIzYkLUkjbW5HRiQ2JFEiMkYnRkFGQS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRj42LVEiK0YnRkFGQ0ZGRkhGSkZMRk5GUC9GU1EsMC4yMjIyMjIyZW1GJy9GVkZkby1GLDYlUSJiRidGL0YyRj1GWkZgby1GLDYlUSJjRidGL0YyLUY+Ni1RIj1GJ0ZBRkNGRkZIRkpGTEZORlAvRlNRLDAuMjc3Nzc3OGVtRicvRlZGYHAtRmpuNiRGX29GQS1GPjYtUSIsRidGQUZDL0ZHRjFGSEZKRkxGTkZQRlIvRlZRLDAuMzMzMzMzM2VtRidGWkZBRkFGQQ==print(); # input placeholderVi ser til vores begejstring, at vi f\303\245r den velkendte generelle formel for l\303\270sninger til andengradsligningen! I dette eksempel er det vigtigt, at man i solve kommandoen husker at anf\303\270re hvilken st\303\270rrelse man \303\270nsker at finde, her x. Eksempel 6Maple kan naturligvis ogs\303\245 l\303\270se ligninger, som ikke blot involverer polynomier. Nogle af dem med transcendente funktioner s\303\245som LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEkY29zRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJ0YyRjJGMg==, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEkbG9nRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbW5HRiQ2JFEjMTBGJ0Y1L0YzUSV0cnVlRicvRjZRJ2l0YWxpY0YnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLzYlUSJ4RidGPkZARjVGNUY1, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRInhGJ0YyRjVGMkY1LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy9GNlEnbm9ybWFsRic= og LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEkZXhwRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJ0YyRjJGMg== kan l\303\270ses med solve kommandoen og/eller fsolve kommandoen. Det er ligninger, som ofte optr\303\246der i gymnasiet. Lad os kigge p\303\245 nogle eksempler. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEmc29sdmVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Ky1JI21uR0YkNiRRIjVGJy9GM1Enbm9ybWFsRictSSNtb0dGJDYtUScmc2RvdDtGJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZGLyUpc3RyZXRjaHlHRkYvJSpzeW1tZXRyaWNHRkYvJShsYXJnZW9wR0ZGLyUubW92YWJsZWxpbWl0c0dGRi8lJ2FjY2VudEdGRi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlUtSSVtc3VwR0YkNiUtRjs2JFElMS4yNUYnRj4tRiM2Jy1GLDYlUSJ4RidGL0YyRi8vJStleGVjdXRhYmxlR0ZGLyUwZm9udF9zdHlsZV9uYW1lR1EoMkR+TWF0aEYnRjIvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUZBNi1RIj1GJ0Y+RkRGR0ZJRktGTUZPRlEvRlRRLDAuMjc3Nzc3OGVtRicvRldGaW8tRjs2JFElMzQuN0YnRj4tRkE2LVEiLEYnRj5GRC9GSEYxRklGS0ZNRk9GUUZTL0ZXUSwwLjMzMzMzMzNlbUYnRmpuRl1vRj5GPkZdb0Y+print(); # input 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print(); # input placeholderI den sidste ligning f\303\245r vi udover den enlige reelle l\303\270sning ogs\303\245 en r\303\246kke komplekse. Du kan eventuelt sortere dem fra i hovedet. Hvis du som her ved, at der kun er en reel l\303\270sning, s\303\245 kan du ogs\303\245 v\303\246lge at bruge fsolve kommandoen:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEnZnNvbHZlRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiotSSNtbkdGJDYkUSIyRicvRjNRJ25vcm1hbEYnLUkjbW9HRiQ2LVEnJnNkb3Q7RidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRi8lKXN0cmV0Y2h5R0ZGLyUqc3ltbWV0cmljR0ZGLyUobGFyZ2VvcEdGRi8lLm1vdmFibGVsaW1pdHNHRkYvJSdhY2NlbnRHRkYvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZVLUklbXN1cEdGJDYlLUYsNiVRInhGJ0YvRjItRiM2JC1GOzYkUSUzLjY4RidGPkY+LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1GQTYtUSI9RidGPkZERkdGSUZLRk1GT0ZRL0ZUUSwwLjI3Nzc3NzhlbUYnL0ZXRmRvLUY7NiRRIzQ4RidGPi1GQTYtUSIsRidGPkZEL0ZIRjFGSUZLRk1GT0ZRRlMvRldRLDAuMzMzMzMzM2VtRidGZW5GPkY+Rj4=print(); # input 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print(); # input placeholderSidstn\303\246vnte med kommafidusen for at finde numeriske l\303\270sninger: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(); # input placeholderNB! Bem\303\246rk at 10-tals logaritmen skal skrives LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEkbG9nRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbW5HRiQ2JFEjMTBGJ0Y1L0YzUSV0cnVlRicvRjZRJ2l0YWxpY0YnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLzYlUSJ4RidGPkZARjVGNUY1 med et standard index. Benyt Ctrl+Shift+- til at lave indekset. Som det er international kotyme, bruges LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEkbG9nRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJ0YyRjJGMg== for den naturlige logaritmefunktion, som ogs\303\245 kaldes LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEjbG5GJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkobWZlbmNlZEdGJDYkLUYjNiQtRiw2JVEieEYnL0YwUSV0cnVlRicvRjNRJ2l0YWxpY0YnRjJGMkYy. Begge betegnelser kan benyttes i Maple!Eksempel 7En kapital p\303\245 4500 kr. inds\303\246ttes p\303\245 en bankkonto og bliver til 12000 kr. p\303\245 21 \303\245r. Hvor stor har den gennemsnitlige \303\245rlige rente v\303\246ret? Det er klart, at vi skal benytte renteformlen 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. 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print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=S\303\245 den s\303\270gte rente er 4.8%. KommentarerBenyt fsolve her. Det ser mest overskueligt ud, hvis man f\303\270rst tildeler K, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYEtfXzBgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn og n de angivne v\303\246rdier og derefter l\303\270ser ligningen. Husk at anbringe alle tre tildelinger indenfor samme matematikfelt. Det kan kontrolleres ved at n\303\245r cursoren st\303\245r i en af tildelingerne, skal der vises en stiplet kasse om alle de tre tildelinger. Her er der et tilf\303\246lde, hvor der forekommer en variabel med og uden index: K og LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYEtfXzBgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn . Det er derfor vigtigt at bruge literal index med Shift+- - , s\303\245 der ikke opst\303\245r misforst\303\245elser. Hvis du benytter solve med kommafidusen f\303\245r du en masse komplekse r\303\270dder ogs\303\245! For folk, der kender til teorien for komplekse tal, kan det endda tilf\303\270jes, at det i bund og grund er den binome ligning p\303\245 formen LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRIm5GJ0YyRjVGMkY1LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi1RIj1GJy9GNlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkgvJSlzdHJldGNoeUdGSC8lKnN5bW1ldHJpY0dGSC8lKGxhcmdlb3BHRkgvJS5tb3ZhYmxlbGltaXRzR0ZILyUnYWNjZW50R0ZILyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVy1GLzYlUSJrRidGMkY1RkQ=, vi l\303\270ser her. De 21 l\303\270sninger for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjFGJ0Y5LUY2Ni1RIitGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GVy1GLDYlUSJyRidGL0YyRjk= vil ligge symmetrisk rundt p\303\245 en cirkel i den komplekse plan. Hvis n havde v\303\246ret et lige tal, ville der have v\303\246ret yderligere en reel l\303\270sning og den er mindre end LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSNtbkdGJDYkUSIxRidGL0Yv, svarende til at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIitGJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkctSSNtaUdGJDYlUSJyRicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnRi8= er negativ. Den skal blot sorteres fra som kunstig her. Eksempel 8Vi skal nu kigge p\303\245 den trigonometrisk ligning 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. 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print(); # input placeholderVi f\303\245r her den ene l\303\270sning, der ligger i standardintervallet 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, hvori sinus funktionen er injektiv. Men der er som bekendt principielt uendeligt mange l\303\270sninger. Man kan f\303\245 alle disse ved at tilf\303\270je en option i solve kommandoen, nemlig AllSolutions. Det er nok ikke noget du nogensinde f\303\245r brug for, men lad os tage den alligevel: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print(); # input placeholderDette ser meget underligt ud. Her skal det n\303\246vnes, at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEkX0IxRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEifGlyRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMTExMTExMWVtRicvJSdyc3BhY2VHRkxGOQ== er en variabel, som kan antage v\303\246rdierne 0 og 1, mens LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEkX1oxRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEifGlyRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMTExMTExMWVtRicvJSdyc3BhY2VHRkxGOQ== er en variabel, der kan antage alle heltallige v\303\246rdier. Tilden ~ hentyder til at der er tilf\303\270jet antagelser eller begr\303\246nsninger ang\303\245ende den variable. I gamle dage ville man skrive l\303\270sningerne p\303\245 formen 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. , hvor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZFbGVtZW50O0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRKCYjODQ4NDtGJy9GMEY9RjlGOQ==. Ovenst\303\245ende angiver pr\303\246cist de samme l\303\270sninger! I afsnittet Ligninger med betingelser vil vi kigge p\303\245, hvordan vi kan finde l\303\270sningerne til ligningen indenfor et givet brugervalgt interval. Eksempel 9Vi skal se, hvad Maple siger til en ligning, som har uendeligt mange l\303\270sninger: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYuLUkjbW5HRiQ2JFEiM0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIn5GJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkctSSNtaUdGJDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnLUYzNi1RKCZtaW51cztGJ0YvRjZGOUY7Rj1GP0ZBRkMvRkZRLDAuMjIyMjIyMmVtRicvRklGVy1GLDYkUSI1RidGLy1GMzYtUSI9RidGL0Y2RjlGO0Y9Rj9GQUZDL0ZGUSwwLjI3Nzc3NzhlbUYnL0ZJRmpuRistRjM2LVEnJnNkb3Q7RidGL0Y2RjlGO0Y9Rj9GQUZDRkVGSC1JKG1mZW5jZWRHRiQ2JC1GIzYmRkpGUy1GLDYkUSIyRidGL0YvRi8tRjM2LVEiK0YnRi9GNkY5RjtGPUY/RkFGQ0ZWRlgtRiw2JFEiMUYnRi9GLw==. 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print(); # input placeholderDen svarer alts\303\245, at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTEYrRjk=. Det er det samme som at sige, at alle x duer i ligningen!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print(); # input placeholderDen eneste reelle rod vises. Vi stiller tilbage til default indstillingen med komplekse l\303\270sninger igen ved at droppe pakken med kommandoen unwith:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEndW53aXRoRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiQtRiw2JVErUmVhbERvbWFpbkYnRi9GMi9GM1Enbm9ybWFsRidGPS1JI21vR0YkNi1RIjpGJ0Y9LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlQvJStleGVjdXRhYmxlR0ZFRj0=JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFHEksempel 10Vi er nu kommet til den type ligninger, som Maple og alle andre maskiner og programmer har sv\303\246rt ved at l\303\270se. Det g\303\246lder typisk for transcendente ligninger. Her skal vi kigge p\303\245 ligningen 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, som umiddelbart ser ret uskyldig ud. Problemet er, at der indg\303\245r b\303\245de et polynomie-element LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiM0YnL0Y2USdub3JtYWxGJ0YyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRj4= og en transcendent funktion LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnL0YzUSdpdGFsaWNGJ0Y7Rj4vJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjI=. Der findes ingen regler, hvorved man kan simplificere en s\303\245dan ligning. En eksakt l\303\270sning kan simpelthen ikke skrives ved hj\303\246lp af de s\303\246dvanlige funktionsudtryk. Tilbage er der kun muligheden med at finde numeriske l\303\270sninger, men selv det er sv\303\246rt, da et program ikke kan tage h\303\270jde for alle de uendeligt mange ligninger, der findes. Lad os lige afpr\303\270ve de to f\303\270rste metoder fra tabellen (solve kommandoen b\303\245de med og uden kommafidusen):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print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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print(); # input 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(); # input placeholderI virkeligheden er der fire l\303\270sninger. Vi ser, at ingen af metoderne leverer det \303\270nskede. Det hj\303\246lper i dette tilf\303\246lde ikke at h\303\270jreklikke p\303\245 RootOf kommandoen og v\303\246lge All Values. Hvis man i \303\270vrigt giver ligningen til for eksempel en Texas TI 89 Titanium grafregner, s\303\245 finder den tre af de fire l\303\270sninger, og det er jo heller ikke godt nok. Vi leder efter en metode, som med meget stor sandsynlighed finder alle l\303\270sninger. Jeg siger med meget stor sandsynlighed, for man kan faktisk aldrig v\303\246re fuldst\303\246ndig sikker p\303\245, at en l\303\270sning smutter igennem nettet - med mindre man foretager en besv\303\246rlig ad hoc analyse af den p\303\245g\303\246ldende funktion, og det vil vi ikke g\303\270re. Vi skal g\303\270re brug af et plot af grafen for den funktion, som h\303\270rer til ligningen og kigge p\303\245 nulpunkter for funktionen. Vi er n\303\270dt til at v\303\246lge et endeligt interval at tegne grafen i. Allerede her er faren for, at der kunne ligge l\303\270sninger udenfor dette interval. For at im\303\270deg\303\245 dette problem en smule, v\303\246lger vi et stort interval at tegne grafen i fra start, fx fra -200 til 200. Da du kun er interesseret i nulpunkter, s\303\245 er det hensigtsm\303\246ssigt kun at vise grafen for y-v\303\246rdier omkring 0, for eksempel mellem -1 og 1. Hvis du ikke foretager den begr\303\246nsning bliver grafen undertiden uoverskuelig. 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%;Vi ser, at der kun sker noget t\303\246t p\303\245 0. Derfor indskr\303\246nker vi intervallet. N\303\245r du g\303\270r det i praksis, skal du blot lige \303\246ndre i x-gr\303\246nserne og trykke p\303\245 Enter, mens cursoren st\303\245r i plot kommandoen, s\303\245 vil du f\303\245 grafen i det mindre interval. Ingen grund til at aflevere flere grafer! Jeg er dog n\303\270dt til at g\303\270re det i denne demonstration: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%;JSFHNu kan vi for alvor se nulpunkterne. Der er klart fire. Vi har stadig ikke fundet nulpunkterne, kun gjort os klart, at der er fire, og at de ligger t\303\246t p\303\245 v\303\246rdierne -1, 0, 2 og 6. Der er to m\303\245der, hvorp\303\245 vi kan finde nulpunkterne med stor pr\303\246cision: Metode 1: For hvert nulpunkt bruges fsolve kommandoen med den omtrentlige v\303\246rdi for nulpunktet som startv\303\246rdiMetode 2: Bruger kommandoen Roots fra studenterpakken i et lille interval omkring alle de opdagede r\303\270dderLad os afpr\303\270ve dem begge:Metode 1Vi vil finde nulpunktet t\303\246t p\303\245 -1 ved at udskifte x med LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSomdW1pbnVzMDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GUy1JI21uR0YkNiRRIjFGJ0Y5Rjk=: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print(); # input placeholderSamme procedure gentages for de \303\270vrige tre nulpunkter ... Metode 2Vi skal bruge Roots kommandoen fra pakken LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEoU3R1ZGVudEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYmLUYsNiVRKkNhbGN1bHVzMUYnRi9GMi8lK2V4ZWN1dGFibGVHRjEvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnL0YzUSdub3JtYWxGJ0ZCLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRj1GP0ZC. Vi benytter "long form" af kommandoen: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(); # input placeholderHusk optionen numeric, s\303\245 kommandoen regner numerisk! Vi har til vores gl\303\246de f\303\245et alle fire l\303\270sninger. KommentarerMan kunne tro, at man blot kunne have brugt Roots kommandoen p\303\245 et meget stort interval, fx fra -1000 til 1000. Det g\303\245r desv\303\246rre ikke. Jo st\303\270rre interval der v\303\246lges, jo st\303\270rre tendens vil kommandoen have til at "glemme" l\303\270sninger - simpelthen fordi metoden er n\303\270dt til at begr\303\246nse de beregninger, den skal foretage, s\303\245 man f\303\245r svaret ret hurtigt!Hvis man har en ligning, hvor der ikke st\303\245r et 0 p\303\245 den ene side af lighedstegnet, s\303\245 plotter man blot den funktion, som svarer til venstresiden minus h\303\270jresiden. For ligningen 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 vil man s\303\245ledes plotte funktionen 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. Husk parentesen omkring h\303\270jresiden!Eksempel 11Nu skal vi kigge p\303\245 en rigtig ustyrlig ligning: 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. Man kan ret nemt argumentere for, at denne ligning selv i det lille lukkede interval 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 har uendeligt mange l\303\270sninger. N\303\245r x n\303\246rmer sig 0, vil LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIi9GJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHUSV0cnVlRicvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMTY2NjY2N2VtRicvJSdyc3BhY2VHRkgtSSNtaUdGJDYlUSJ4RicvJSdpdGFsaWNHRj0vRjBRJ2l0YWxpY0YnRi8= g\303\245 mod uendelig p\303\245 en kontinuert m\303\245de. Da funktionen sinus bliver ved med at svinge mellem LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSNtbkdGJDYkUSIxRidGL0Yv og 1, n\303\245r argumentet g\303\245r mod uendelig, s\303\245 vil LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEkc2luRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUkjbW5HRiQ2JFEiMUYnRjItSSNtb0dGJDYtUSIvRidGMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHUSV0cnVlRicvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRLDAuMTY2NjY2N2VtRicvJSdyc3BhY2VHRlMtRiw2JVEieEYnL0YwRkgvRjNRJ2l0YWxpY0YnRjJGMkYy blive ved med at svinge hurtigere og hurtigere, n\303\245r x n\303\246rmer sig til 0. Lad os kigge p\303\245 situationen grafisk, idet vi tegner grafen for den funktion, som er lig med venstresiden minus h\303\270rjresiden i ligningen, alts\303\245 teknikken omtalt i kommentaren ovenfor. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSVwbG90RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNi4tRiw2JVEkc2luRicvRjVRJmZhbHNlRicvRjhRJ25vcm1hbEYnLUY7NiQtRiM2JC1JJm1mcmFjR0YkNigtSSNtbkdGJDYkUSIxRidGRC1GIzYkLUYsNiVRInhGJ0Y0RjdGRC8lLmxpbmV0aGlja25lc3NHRlAvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGWi8lKWJldmVsbGVkR0ZDRkRGRC1JI21vR0YkNi1RKiZ1bWludXMwO0YnRkQvJSZmZW5jZUdGQy8lKnNlcGFyYXRvckdGQy8lKXN0cmV0Y2h5R0ZDLyUqc3ltbWV0cmljR0ZDLyUobGFyZ2VvcEdGQy8lLm1vdmFibGVsaW1pdHNHRkMvJSdhY2NlbnRHRkMvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZdcEZTLUZqbjYtUSIsRidGREZdby9GYG9GNkZhb0Zjb0Zlb0Znb0Zpby9GXHBRJjAuMGVtRicvRl9wUSwwLjMzMzMzMzNlbUYnRlMtRmpuNi1RIj1GJ0ZERl1vRl9vRmFvRmNvRmVvRmdvRmlvL0ZccFEsMC4yNzc3Nzc4ZW1GJy9GX3BGXHFGaW4tRk42JFEkMC4xRidGRC1Gam42LVEjLi5GJ0ZERl1vRl9vRmFvRmNvRmVvRmdvRmlvRltwL0ZfcEZlcEZecUZERkRGREYrLyUrZXhlY3V0YWJsZUdGQ0ZE%;Vi ser, at grafen svinger s\303\245 hurtigt, at vi slet ikke kan se hvad der sker t\303\246t p\303\245 nul. Sk\303\246rmens opl\303\270sning og vores eget syn forhindrer det. Man kan dog zoome ind p\303\245 omr\303\245det n\303\246r LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= ved at indsn\303\246vre intervallet, hvis man \303\270nsker. Lad os se, hvad kommandoen Roots siger til ligningen i omtalte interval.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(); # input placeholderMaple giver alts\303\245 lidt arbitr\303\246rt ca. 50 l\303\270sninger. Grafregneren Texas TI 89 Titanium giver i \303\270vrigt 4 l\303\270sninger. Men der er jo uendeligt mange l\303\270sninger, s\303\245 de vil aldrig kunne skrives op! Generelle kommentarer:
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LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIkIUdGKi0lLkJPVU5EU19IRUlHSFRHNiMkIiRnI0YqLSUpQ0hJTERSRU5HNiI=I s\303\246rlige tilf\303\246lde kan Maple tage lang tid om en beregning. Hvis man ikke vil vente p\303\245 at den bliver f\303\246rdig, kan man trykke p\303\245 viste ikon i v\303\246rkt\303\270jslinjen. Den siger: Interrupt the current operation. Ikonen er gr\303\245, n\303\245r Maple ikke arbejder. Hj\303\246lpemenuMan kan f\303\245 rigtig mange detaljer om de enkelte kommandoers funktion i hj\303\246lpemenuen. Pr\303\270v fx at skrive solve,details i hj\303\246lpemenuen og tryk ENTER. .
Opgaver 1Opgave 1L\303\270s f\303\270lgende ligninger eksakt ved hj\303\246lp af solve kommandoen:a) 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b) 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) 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d) 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NB! Den sidste ligning resulterer i en RootOf fra Maple. H\303\270jreklik p\303\245 svaret og v\303\246lg All Values i kontekstmenuen og se hvor vild en l\303\270sning man f\303\245r!Opgave 2L\303\270s nedenst\303\245ende ligninger numerisk ved hj\303\246lp af solve kommandoen. Brug kommafidusen, hvis det er n\303\270dvendig. a) 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b) 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) 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) 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NB! Husk at symbolerne for kvadratroden og den n'te rod kan findes i Expression paletten. Opgave 3Bestem kun de reelle numeriske l\303\270sninger til nedenst\303\245ende ligninger. a) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiM0YnL0Y2USdub3JtYWxGJ0YyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEiPUYnRj4vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkkvJSlzdHJldGNoeUdGSS8lKnN5bW1ldHJpY0dGSS8lKGxhcmdlb3BHRkkvJS5tb3ZhYmxlbGltaXRzR0ZJLyUnYWNjZW50R0ZJLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGWC1GOzYkUSM3MEYnRj5GPg==b) 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c) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiNEYnL0Y2USdub3JtYWxGJ0YyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEiPUYnRj4vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkkvJSlzdHJldGNoeUdGSS8lKnN5bW1ldHJpY0dGSS8lKGxhcmdlb3BHRkkvJS5tb3ZhYmxlbGltaXRzR0ZJLyUnYWNjZW50R0ZJLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGWC1GOzYkUSMxMEYnRj5GPg==Opgave 4Benyt solve kommandoen med og uden kommafidusen til at finde l\303\270sningerne til nedenst\303\245ende ligninger: a) 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) 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) 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d) 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 5Benyt solve kommandoen til at bestemme alle l\303\270sningerne til nedenst\303\245ende 2. gradsligninger, b\303\245de eksakt og med kommatal. Nogle af l\303\270sningerne er komplekse!a) 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) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYuLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYmLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJy8lK2V4ZWN1dGFibGVHRjQvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnRj4vJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEoJm1pbnVzO0YnRj4vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRk4vJSlzdHJldGNoeUdGTi8lKnN5bW1ldHJpY0dGTi8lKGxhcmdlb3BHRk4vJS5tb3ZhYmxlbGltaXRzR0ZOLyUnYWNjZW50R0ZOLyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGZ24tRjs2JFEjMTBGJ0Y+LUZJNi1RIn5GJ0Y+RkxGT0ZRRlNGVUZXRlkvRmZuUSYwLjBlbUYnL0ZpbkZhb0YuLUZJNi1RIitGJ0Y+RkxGT0ZRRlNGVUZXRllGZW5GaG4tRjs2JFEjMjVGJ0Y+LUZJNi1RIj1GJ0Y+RkxGT0ZRRlNGVUZXRlkvRmZuUSwwLjI3Nzc3NzhlbUYnL0ZpbkZdcC1GOzYkRkdGPkZARkJGPg==c) 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Opgave 6Bestem de reelle l\303\270sninger til nedenst\303\245ende ligninger b\303\245de eksakt og numerisk. a) 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b) 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) 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Opgave 7Nedenfor er der ligninger indeholdende potensfunktioner. Du skal finde de reelle numeriske l\303\270sninger. Benyt solve kommandoen med kommafidusen. Det giver i nogle af opgaverne ogs\303\245 komplekse l\303\270sning (dem med et stort I i). Sort\303\251r disse fra. a) 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b) 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) 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NB! Da disse ligninger viser sig kun at have \303\251n reel l\303\270sning, kunne man ogs\303\245 have benyttet fsolve ovenfor og f\303\245et svaret straks. Men husk, at fsolve kommandoen kun giver \303\251n rod ad gangen, undtagen hvis det er en polynomie-ligning, i hvilket tilf\303\246lde man f\303\245r samtlige reelle l\303\270sninger. S\303\245 v\303\246r varsom med den, hvis du ikke ved, om der er mere end 1 l\303\270sning og det ikke er en polynomie-ligning!Opgave 8Isoler den variable a i f\303\270lgende udtryk: a) 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) 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c) 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NB! I opgave b): Brug ikke et e fra tastaturet. Brug eventuelt 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 fra Expression paletten. Opgave 9Kurt s\303\246tter 1280 kr. ind p\303\245 en konto til en \303\245rlig rente p\303\245 3.75%. Hvor mange \303\245r g\303\245r der, f\303\270r bel\303\270bet er vokset til 5000 kr? Hj\303\246lp: Benyt renteformlen. Opgave 10Indbyggertallet i en bestemt by er p\303\245 8 \303\245r vokset fra 13000 til 17000. Hvor mange procent er indbyggertallet i gennemsnit vokset med pr. \303\245r? Hj\303\246lp: Benyt renteformlen. Da der kun er \303\251n l\303\270sning er det en fordel at benytte fsolve fremfor solve, fordi du s\303\245 slipper for at sortere komplekse l\303\270sninger fra. Opgave 11Benyt kommandoen fsolve til at bestemme alle reelle r\303\270dder i f\303\270lgende n'te gradsligninger: a) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYyLUkjbW5HRiQ2JFEkMC40RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEifkYnRi8vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRy1JJW1zdXBHRiQ2JS1JI21pR0YkNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRictRiM2JS1GLDYkUSIzRidGL0ZRRlQvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUYzNi1RIitGJ0YvRjZGOUY7Rj1GP0ZBRkMvRkZRLDAuMjIyMjIyMmVtRicvRklGXG8tRiw2JFEjMTJGJ0YvRjItRks2JUZNLUYjNiUtRiw2JFEiMkYnRi9GUUZURmVuLUYzNi1RKCZtaW51cztGJ0YvRjZGOUY7Rj1GP0ZBRkNGW29GXW8tRiw2JFEjNzFGJ0YvRjJGTUZobi1GLDYkUSM4OEYnRi8tRjM2LVEiPUYnRi9GNkY5RjtGPUY/RkFGQy9GRlEsMC4yNzc3Nzc4ZW1GJy9GSUZlcC1GLDYkRmduRi9GLw==b) 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c) 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Opgave 12L\303\270s f\303\270lgende ligninger numerisk:a) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkmbWZyYWNHRiQ2KC1GIzYmLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lK2V4ZWN1dGFibGVHUSV0cnVlRicvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnRjQtRiM2KC1JJW1zdXBHRiQ2JS1JI21pR0YkNiVRInhGJy8lJ2l0YWxpY0dGOS9GNVEnaXRhbGljRictRiM2Ji1GMTYkUSIyRidGNEY3RjpGNC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYtUSgmbWludXM7RidGNC8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGWC8lKXN0cmV0Y2h5R0ZYLyUqc3ltbWV0cmljR0ZYLyUobGFyZ2VvcEdGWC8lLm1vdmFibGVsaW1pdHNHRlgvJSdhY2NlbnRHRlgvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0Zhb0YwRjdGOkY0LyUubGluZXRoaWNrbmVzc0dGMy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zoby8lKWJldmVsbGVkR0ZYLUZTNi1RIj1GJ0Y0RlZGWUZlbkZnbkZpbkZbb0Zdby9GYG9RLDAuMjc3Nzc3OGVtRicvRmNvRmFwLUZANiVGQi1GIzYmLUYxNiRRIjNGJ0Y0RjdGOkY0Rk9GN0Y6RjQ=b) 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c) 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Opgave 13L\303\270s nedenst\303\245ende ligning ved at tegne grafen for funktionen p\303\245 venstre side for at skabe et overblik, og benyt dern\303\246st fsolve kommandoen til at finde r\303\270dderne \303\251n efter \303\251n, som beskrevet i eksempel 10. Afpr\303\270v ogs\303\245 metoden kommandoen Roots fra studenterpakken, ogs\303\245 omtalt i eksempel 10. 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 14Nedenst\303\245ende ligning er \303\246kvivalent med et fjerdegradspolynomium bortset fra singulariteten i LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjNGJ0Y5Rjk=, hvor venstresiden ikke er defineret. Derfor kunne man m\303\245ske h\303\245be p\303\245, at fsolve kunne give alle l\303\270sninger hertil, da fsolve som bekendt kan finde alle reelle l\303\270sninger til polynomier (der er skrevet op p\303\245 s\303\246dvanlig vis), men det er ikke tilf\303\246ldet her. Her overg\303\245r fsolve til kun at levere \303\251n l\303\270sning ad gangen. Plot grafen for 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. Benyt eventuelt optionen discont til plot kommandoen for at f\303\245 tegnet grafen p\303\246nere i n\303\246rheden af LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjNGJ0Y5Rjk=. Benyt dern\303\246st metoderne i eksempel 10 til at bestemme de reelle l\303\270sninger. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkmbWZyYWNHRiQ2KC1GIzYqLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JFEiNEYnL0Y7USdub3JtYWxGJ0ZDLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi1RKCZtaW51cztGJ0ZDLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZOLyUpc3RyZXRjaHlHRk4vJSpzeW1tZXRyaWNHRk4vJShsYXJnZW9wR0ZOLyUubW92YWJsZWxpbWl0c0dGTi8lJ2FjY2VudEdGTi8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRmduLUZANiRRIjVGJ0ZDLUZJNi1RIn5GJ0ZDRkxGT0ZRRlNGVUZXRlkvRmZuUSYwLjBlbUYnL0ZpbkZhby1GMTYlRjMtRiM2JC1GQDYkUSIzRidGQ0ZDRkUtRkk2LVEiK0YnRkNGTEZPRlFGU0ZVRldGWUZlbkZobi1GQDYkUSM2N0YnRkNGQy1GIzYmRjNGSEZnb0ZDLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZncC8lKWJldmVsbGVkR0ZOLUZJNi1RIj1GJ0ZDRkxGT0ZRRlNGVUZXRlkvRmZuUSwwLjI3Nzc3NzhlbUYnL0ZpbkZgcUYzRkM=NB! Ligningen kan imidlertid ogs\303\245 l\303\270ses via solve kommandoen med kommafidusen, da der trods alt her er tale om en algebraisk ligning. Afpr\303\270v det eventuelt. 3. Ligninger med betingelserMed udtrykket "ligninger med betingelser" menes for eksempel ligninger, hvor man kun \303\270nsker l\303\270sningerne i et n\303\246rmere angivet interval. Det kan ogs\303\245 v\303\246re, at man kun \303\270nsker de reelle l\303\270sninger, osv. Eksempel 1Vi vil finde de positive l\303\270sninger til andengradsligningen LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0YyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEoJm1pbnVzO0YnRj4vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkkvJSlzdHJldGNoeUdGSS8lKnN5bW1ldHJpY0dGSS8lKGxhcmdlb3BHRkkvJS5tb3ZhYmxlbGltaXRzR0ZJLyUnYWNjZW50R0ZJLyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGWC1GOzYkUSI0RidGPi1GRDYtUSJ+RidGPkZHRkpGTEZORlBGUkZUL0ZXUSYwLjBlbUYnL0ZaRlxvRi5GQy1GOzYkUSI3RidGPi1GRDYtUSI9RidGPkZHRkpGTEZORlBGUkZUL0ZXUSwwLjI3Nzc3NzhlbUYnL0ZaRmVvLUY7NiRGQkY+Rj4=. Her har vi at b\303\245de 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 og LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= skal opfyldes p\303\245 samme tid. Det opfattes som et system af ligninger/uligheder, og de anbringes altid i kr\303\270llede parenteser (eller firkantede parenteser). LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==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(); # input placeholderEksempel 2Vi \303\270nsker de l\303\270sninger til 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, som ligger mellem 0 og 5. Igen et system af ligninger/uligheder: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JSFHBem\303\246rk at Maple intet skriver, da der ingen l\303\270sninger er i dette interval. JSFHKommentarM\303\245ske er man usikker p\303\245 om der virkelig ikke er nogen l\303\270sninger eller Maple blot ikke kan finde ud af det. For at f\303\245 n\303\246rmere at vide om det, kan man h\303\246ve informations-niveauet i Maple: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Ved at udf\303\270re ovenst\303\245ende kommandlinje igen f\303\245s: 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%;Lad os s\303\246tte informationsniveauet tilbage til niveau 0: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Man kan naturligvis ogs\303\245 lige lave et plot, hvis man absolut vil sikre sig s\303\245 meget som muligt er. Eksempel 3N\303\245r man - som tilf\303\246ldet oftest er i gymnasiet - kun vil have de reelle l\303\270sninger til en ligning, s\303\245 er det nok nemmest blot i hovedet at kassere alle de l\303\270sninger, hvori der figurerer et "I". Hvis man ikke er tilfreds med det og vil have Maple til at g\303\270re det for \303\251n, kan man kalde en pakke, der hedder RealDomain. Husk, at Maple er case-sensitive, s\303\245 det er ikke ligegyldigt, hvad der skrives med sm\303\245t og stort!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print(); # input placeholderDen eneste reelle rod vises. Vi stiller tilbage til default indstillingen med komplekse l\303\270sninger igen ved at droppe pakken med kommandoen unwith:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEndW53aXRoRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiQtRiw2JVErUmVhbERvbWFpbkYnRi9GMi9GM1Enbm9ybWFsRidGPS1JI21vR0YkNi1RIjpGJ0Y9LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlQvJStleGVjdXRhYmxlR0ZFRj0=%;Eksempel 4Lad os kigge p\303\245 eksempel 8 fra afsnittet En oversigt, blot denne gang med den betingelse, at vi vil finde l\303\270sningerne i intervallet 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. Det kan g\303\270res s\303\245ledes: 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%;Igen s\303\270rger optionen AllSolutions for at vi ikke blot f\303\245r \303\251n l\303\270sning, men alle i det p\303\245g\303\246ldende interval. Optionen Explicit s\303\270rger for at de bliver udskrevet eksplicit, uden brug af variable med tilder, som vist tidligere i eksempel 8 i afsnittet En oversigt. KommentarHvis man skal l\303\270se mange trigonometriske ligninger af typen ovenfor, s\303\245 kan man undg\303\245 at skulle tilf\303\270je optionen AllSolutions i hver solve kommando, hvis man til geng\303\246ld tilf\303\270jer kommandoen LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVExX0VudkFsbFNvbHV0aW9uc0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVGMUYvRjIvJStleGVjdXRhYmxlR0YxLyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJ0Y5 f\303\270r solve kommandoerne. Husk underscoren i starten af kommandoen! En helt anden ting: Skal man l\303\270se komplicerede ligninger med trigonometriske funktioner i, s\303\245 kan det v\303\246re n\303\270dvendigt at regne numerisk. I s\303\245 fald kig p\303\245 Studenterpakken i afsnit 4! JSFHJSFHOpgaver 2Opgave 1Bestem l\303\270sningerne til f\303\270lgende ligning i intervallet 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: 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.Opgave 8Find alle l\303\270sninger til nedenst\303\245ende trigonometriske ligninger i intervallet 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: a) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEkY29zRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJ0YyRjItSSNtb0dGJDYtUSI9RidGMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlUtSSNtbkdGJDYkUSUwLjIzRidGMkYyb) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEkdGFuRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJ0YyRjItSSNtb0dGJDYtUSI9RidGMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlUtSSNtbkdGJDYkUSQyLjVGJ0YyRjI=c) 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Opgave 9L\303\270s f\303\270lgende trigonometriske ligning for 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: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Opgave 6Bestem den eksakte reelle l\303\270sning til ligningen 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 . Ligningen har ogs\303\245 en kompleks rod, men den skal du fjerne ved brug af pakken RealDomain. 4. LigningssystemerMaple kan naturligvis ogs\303\245 l\303\270se flere ligninger med flere ubekendte. Man har s\303\245 at g\303\270re med et system af ligninger.Eksempel 1Vi vil l\303\270se to ligninger med 2 ubekendte: 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 og 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. Det kan g\303\270res ved at skrive ligningerne med "m\303\246ngdetegn" udenomen, alts\303\245 kr\303\270llede parenteser. Da der er to ubekendte, skal de ogs\303\245 anbringes med kr\303\270llede parenteser om (eller firkantede): LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==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print(); # input placeholderEksempel 2Undertiden har man i fysik flere ligninger, hvor man \303\270nsker at eliminere (fjerne) en af st\303\270rrelserne. Et godt eksempel er de bev\303\246gelsesligninger, der g\303\246lder for bev\303\246gelser med konstant acceleration: 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 og 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. Man kan eliminere tiden t ved at udr\303\245be denne st\303\270rrelse som den ene variable i ligningssystemet. Den anden skal v\303\246re den st\303\270rrelse, som man \303\270nsker at finde et udtryk for. Lad os sige det er s. S\303\245 vi \303\270nsker alts\303\245 et udtryk for s, hvor tiden t ikke indg\303\245r, s\303\245 disse to st\303\270rrelser er de variable (ubekendte)! Vi anbringer kr\303\270llede parenteser rundt om begge ligninger og begge variable. 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print(); # input placeholderVi har dermed den \303\270nskede formel: 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, og oveni har vi f\303\245et en formel for tiden t. Ret smart! Opgaver 3Opgave 1L\303\270s f\303\270lgende to ligninger med to ubekendte: 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 2L\303\270s f\303\270lgende tre ligninger med tre ubekendte (angiv l\303\270sningerne i kommatal): LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW9HRiQ2LVEifGZyRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSV0cnVlRicvJSpzZXBhcmF0b3JHUSZmYWxzZUYnLyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjcvJShsYXJnZW9wR0Y3LyUubW92YWJsZWxpbWl0c0dGNy8lJ2FjY2VudEdGNy8lJ2xzcGFjZUdRLDAuMTY2NjY2N2VtRicvJSdyc3BhY2VHRkQtSSdtdGFibGVHRiQ2Ny1JJG10ckdGJDYnLUkkbXRkR0YkNigtRiM2My1JI21uR0YkNiRRIzE3RidGLy1GLDYtUSJ+RidGLy9GM0Y3RjUvRjlGN0Y6RjxGPkZAL0ZDUSYwLjBlbUYnL0ZGRmZuLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR0Y0L0YwUSdpdGFsaWNGJy1GLDYtUSgmbWludXM7RidGL0ZZRjVGWkY6RjxGPkZAL0ZDUSwwLjIyMjIyMjJlbUYnL0ZGRmRvLUZTNiRRIzQxRidGL0ZWLUZpbjYlUSJ5RidGXG9GXm8tRiw2LVEiK0YnRi9GWUY1RlpGOkY8Rj5GQEZjb0Zlby1GUzYkUSMyOEYnRi9GVi1GaW42JVEiekYnRlxvRl5vLUYsNi1RIj1GJ0YvRllGNUZaRjpGPEY+RkAvRkNRLDAuMjc3Nzc3OGVtRicvRkZGaXAtRlM2JFEkMTk3RidGLy8lK2ZvcmVncm91bmRHUSpbMCwwLDI1NV1GJy8lKXJlYWRvbmx5R0Y0LyUwZm9udF9zdHlsZV9uYW1lR1EqMkR+T3V0cHV0RidGLy8lKXJvd2FsaWduR1EhRicvJSxjb2x1bW5hbGlnbkdGaHEvJStncm91cGFsaWduR0ZocS8lKHJvd3NwYW5HUSIxRicvJStjb2x1bW5zcGFuR0Zfci1GTjYoLUYjNictRmluNiNGaHFGXnFGYXFGY3FGL0ZmcUZpcUZbckZdckZgckZmcUZpcUZbci1GSzYnLUZONigtRiM2Mi1GLDYtUSomdW1pbnVzMDtGJ0YvRllGNUZaRjpGPEY+RkBGY29GZW8tRlM2JFEiNkYnRi9GVkZobkZccC1GUzYkUSMzM0YnRi9GVkZpb0Zgby1GUzYkUSM5N0YnRi9GVkZicEZlcC1GUzYkUSI1RidGL0Zcb0Zeb0ZmcUZpcUZbckZdckZgckZickZmcUZpcUZbci1GSzYnLUZONigtRiM2MS1GUzYkUSQxMDBGJ0YvRlZGaG5GYG8tRlM2JFEjNTBGJ0YvRlZGaW9GXHBGYnBGZXAtRlM2JFEkNTAwRidGL0ZecUZhcUZjcUYvRmZxRmlxRltyRl1yRmByRmJyRmZxRmlxRltyLyUmYWxpZ25HUSVheGlzRicvRmdxUSliYXNlbGluZUYnL0ZqcVEnY2VudGVyRicvRlxyUSd8ZnJsZWZ0fGhyRicvJS9hbGlnbm1lbnRzY29wZUdGNC8lLGNvbHVtbndpZHRoR1ElYXV0b0YnLyUmd2lkdGhHRml1LyUrcm93c3BhY2luZ0dRJjEuMGV4RicvJS5jb2x1bW5zcGFjaW5nR1EkMmVtRicvJSlyb3dsaW5lc0dRJW5vbmVGJy8lLGNvbHVtbmxpbmVzR0Zkdi8lJmZyYW1lR0Zkdi8lLWZyYW1lc3BhY2luZ0dRLDAuNGVtfjAuNWV4RicvJSplcXVhbHJvd3NHRjcvJS1lcXVhbGNvbHVtbnNHRjcvJS1kaXNwbGF5c3R5bGVHRjcvJSVzaWRlR1EmcmlnaHRGJy8lMG1pbmxhYmVsc3BhY2luZ0dRJjAuOGVtRidGXnFGYXFGY3FGLw==Opgave 3L\303\270s f\303\270lgende ligningssystem: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KEYrLUYjNidGKy1JKG1mZW5jZWRHRiQ2Ji1JJ210YWJsZUdGJDY2LUkkbXRyR0YkNictSSRtdGRHRiQ2KC1GIzYrLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGSi8lKXN0cmV0Y2h5R0ZKLyUqc3ltbWV0cmljR0ZKLyUobGFyZ2VvcEdGSi8lLm1vdmFibGVsaW1pdHNHRkovJSdhY2NlbnRHRkovJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZZLUYsNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy9GRlEnaXRhbGljRictRkI2LVEnJnNkb3Q7RidGRUZIRktGTUZPRlFGU0ZVRldGWi1GLDYlUSJ5RidGaW5GXG8tRkI2LVEiPUYnRkVGSEZLRk1GT0ZRRlNGVS9GWFEsMC4yNzc3Nzc4ZW1GJy9GZW5GaG8tSSNtbkdGJDYkUSI1RidGRS8lK2V4ZWN1dGFibGVHRltvLyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJ0ZFLyUpcm93YWxpZ25HRi4vJSxjb2x1bW5hbGlnbkdGLi8lK2dyb3VwYWxpZ25HRi4vJShyb3dzcGFuR1EiMUYnLyUrY29sdW1uc3BhbkdGW3EtRj02KC1GIzYmRitGXnBGYHBGRUZjcEZlcEZncEZpcEZccUZjcEZlcEZncC1GOjYnLUY9NigtRiM2L0ZBLUZbcDYkUSI3RidGRUZBLUklbXN1cEdGJDYlRmZuLUYjNiVGK0ZpbkZcby8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRkI2LVEqJnVtaW51czA7RidGRUZIRktGTUZPRlFGU0ZVL0ZYUSwwLjIyMjIyMjJlbUYnL0ZlbkZnci1GW3A2JFEiNEYnRkVGQUZhb0Zkby1GW3A2JFEjMTBGJ0ZFRl5wRmBwRkVGY3BGZXBGZ3BGaXBGXHFGXnFGY3BGZXBGZ3AvJSZhbGlnbkdRJWF4aXNGJy9GZHBRKWJhc2VsaW5lRicvRmZwUSdjZW50ZXJGJy9GaHBRJ3xmcmxlZnR8aHJGJy8lL2FsaWdubWVudHNjb3BlR0Zbby8lLGNvbHVtbndpZHRoR1ElYXV0b0YnLyUmd2lkdGhHRlx0LyUrcm93c3BhY2luZ0dRJjEuMGV4RicvJS5jb2x1bW5zcGFjaW5nR1EmMC44ZW1GJy8lKXJvd2xpbmVzR1Elbm9uZUYnLyUsY29sdW1ubGluZXNHRmd0LyUmZnJhbWVHRmd0LyUtZnJhbWVzcGFjaW5nR1EsMC40ZW1+MC41ZXhGJy8lKmVxdWFscm93c0dGSi8lLWVxdWFsY29sdW1uc0dGSi8lLWRpc3BsYXlzdHlsZUdGSi8lJXNpZGVHUSZyaWdodEYnLyUwbWlubGFiZWxzcGFjaW5nR0ZkdEZFLyUlb3BlbkdRInxmckYnLyUmY2xvc2VHRi5GXnBGYHBGRUYrRl5wRmBwRkVGK0ZFOpgave 4Idealgasligningen lyder: 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 , hvor p er trykket, V er volumenet, R er gaskonstanten, n er stofm\303\246ngden og T er temperaturen i kelvin. Sammenh\303\246ngen mellem stofm\303\246ngden, massen m og molarmassen M er: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEibUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJuRidGL0YyLUY2Ni1RJyZzZG90O0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZWLUYsNiVRIk1GJ0YvRjJGOQ==. Frembring en formel for trykket, hvori stofm\303\246ngden ikke indg\303\245r. Opgave 5I optikken har vi de to formler LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RJyZzZG90O0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZMLUYsNiVRJyYjOTU1O0YnL0YwRj1GOS1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjI3Nzc3NzhlbUYnL0ZORlctRiw2JVEiY0YnRi9GMkY5 og LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJoRidGL0YyLUY2Ni1RJyZzZG90O0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZWLUYsNiVRImZGJ0YvRjJGOQ==, hvor f er frekvensen, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy er b\303\270lgel\303\246ngden, c er lysets hastighed, E er energien og h er Plancks konstant. Find et udtryk for b\303\270lgel\303\246ngden, hvori frekvensen ikke indg\303\245r. Opgave 6Pr\303\270v i eksempel 2 at isolere hastigheden v i stedet for str\303\246kningen s, men stadig s\303\245 tiden t elimineres. Du f\303\245r et indirekte svar, men pr\303\270v at h\303\270jreklikke p\303\245 det og v\303\246lge All Values i kontekstmenuen. Hvilken formel f\303\245r du for v?5. UlighederVi skal kort ber\303\270re tilf\303\246ldet med uligheder ved et enkelt eksempel. Eksempel 1I denne opgave skal vi l\303\270se andengradsuligheden 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: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==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(); # input placeholderhvilket skal tolkes som intervallet 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. Hvis man vil have kommatal i intervalendepunkterne, s\303\245 er det nemmest at skrive et af tallene i uligheden som et kommatal, alts\303\245 benytte komma-fidusen, alts\303\245 skrive et af tallene i uligheden som et kommatal: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print(); # input placeholderalts\303\245 intervallet 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. JSFHJSFHOpgaver 4JSFHOpgave 1Bestem l\303\270sningsm\303\246ngden til f\303\270lgende uligheder - benyt kommatal!a) 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) 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c) 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JSFH6. Tildele navne til ligninger og l\303\270sningerEn rigtig fin ting i Maple er, at man kan tildele en ligning et navn og s\303\245 senere blot referere til det navn, n\303\245r man vil arbejde videre med ligningen. Man kan endda ogs\303\245 tildele l\303\270sningerne et navn. Huske at benytteLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkNGLw== (kolon lig med) ved tildelingen. Eksempel 1Lad os tildele navnet lign til ligningen LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkmbWZyYWNHRiQ2KC1JI21pR0YkNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2JS1JI21uR0YkNiRRIjNGJy9GNlEnbm9ybWFsRidGMkY1LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZFLyUpYmV2ZWxsZWRHUSZmYWxzZUYnLUkjbW9HRiQ2LVEiK0YnRj4vJSZmZW5jZUdGSi8lKnNlcGFyYXRvckdGSi8lKXN0cmV0Y2h5R0ZKLyUqc3ltbWV0cmljR0ZKLyUobGFyZ2VvcEdGSi8lLm1vdmFibGVsaW1pdHNHRkovJSdhY2NlbnRHRkovJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0Zpbi1JJW1zdXBHRiQ2JUYuLUYjNiUtRjs2JFEiMkYnRj5GMkY1LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1GTDYtUSgmbWludXM7RidGPkZPRlFGU0ZVRldGWUZlbkZnbkZqbkZhby1GTDYtUSI9RidGPkZPRlFGU0ZVRldGWUZlbi9GaG5RLDAuMjc3Nzc3OGVtRicvRltvRl5wLUY7NiRGQkY+Rj4=. Vi benytter et kolon til slut for at undertrykke Maples svar. Dern\303\246st l\303\270ser vi ligningen med hensyn til x: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==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print(); # input placeholderMan kunne samtidigt have valgt at tildele et navn til l\303\270sningerne, fx. navnet l\303\270sn, ved i stedet for sidstn\303\246vnte linje at have skrevet: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print(); # input placeholderMan kan herefter referere til de to l\303\270sninger via LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEqbCYjMjQ4O3NuRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtSSNtbkdGJDYkUSIxRicvRjZRJ25vcm1hbEYnRjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUYvNiNRIUYnRj4= og LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEqbCYjMjQ4O3NuRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtSSNtbkdGJDYkUSIyRicvRjZRJ25vcm1hbEYnRjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUYvNiNRIUYnRj4= eller LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEqbCYjMjQ4O3NuRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYmLUYjNiQtSSNtbkdGJDYkUSIxRicvRjNRJ25vcm1hbEYnRj5GPi8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJy1GLDYjUSFGJ0Y+ og LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEqbCYjMjQ4O3NuRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYmLUYjNiQtSSNtbkdGJDYkUSIyRicvRjNRJ25vcm1hbEYnRj5GPi8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Y+. Man skal bruge standard indekser med Ctrl+Shift+- , literal indekser diuer ikke her! Den anden l\303\270sning kan for eksempel ses med:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JC1JJW1zdWJHRiQ2JS1GLDYlUSpsJiMyNDg7c25GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2JC1JI21uR0YkNiRRIjJGJy9GO1Enbm9ybWFsRidGQy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRkNGKy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRkM=print(); # input placeholderS\303\245 vi ser, at st\303\270rrelsen LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEqbCYjMjQ4O3NuRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtSSNtbkdGJDYkUSIyRicvRjZRJ25vcm1hbEYnRjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRj4= har f\303\245et tildelt v\303\246rdien for den anden l\303\270sning!Eksempel 2Den gode ting ved at benytte en kommando frem for en kontekstmenu er, at man kan referere til l\303\270sningerne i efterf\303\270lgende beregninger. Lad os sige, at vi i eksempel 1 i afsnittet En oversigt fik behov for at regne videre med den 2. l\303\270sning, for eksempel tilegne l\303\270sningen til en variabel a. G\303\270r f\303\270lgende:G\303\245 ned p\303\245 n\303\246ste linje og skift til Math modeSkriv LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMRjk= for at tildele a en v\303\246rdi og lad cursoren st\303\245 hvor den er nuBenyt tastekombinationen Ctrl+L, hvorved et vindue popper op. Man skriver nummeret p\303\245 Maples svar ude til h\303\270jre - uden brug af parenteser! I dette tilf\303\246lde er Maples svar nummeret med 6.4, som det ses p\303\245 figuren. Afslut med OK.
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at fort\303\246lle Maple, at man kun vil have fat i den anden l\303\270sning, skriver man et 2-tal som standard indeks med Ctrl+Shift+bindestreg. Tryk p\303\245 Enter tasten for at udf\303\270re kommandoen, mens cursoren st\303\245 i kommandoen. Det skulle gerne se s\303\245ledes ud: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print(); # input 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print(); # input placeholderHvis man gerne vil have undertrykt Maples svar p\303\245 tildelingen, s\303\245 skal man som s\303\246dvanlig blot s\303\246tte et semikolon i slutningen af kommandoen - husk indenfor kommandoen!! Tryk derefter p\303\245 Enter for at udf\303\270re kommandoen p\303\245ny. Det gode ved Labels er, at hvis man \303\246ndrer nogle tal i ligningen og genberegner, s\303\245 vil v\303\246rdien af a ogs\303\245 blive opdateret. Det sker jo ikke, hvis man blot havde copy & pasted den anden l\303\270sning fra Maples svar og sat a lig med tallet!Man kan ogs\303\245 lave et standard indeks p\303\245 2 lige i enden af solve kommandoen: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print(); # input placeholder7. L\303\270se ligninger med kontekstmenuenMan kan i mange tilf\303\246lde ogs\303\245 l\303\270se ligninger ved hj\303\246lp af kontekst menuen, alts\303\245 ved at h\303\270jreklikke p\303\245 ligningen og v\303\246lge relevante muligheder. Jeg vil n\303\270jes med at give et eksempel her, som indeholder flere pointer. Eksempel 1Lad os sige, at vi \303\270nsker at l\303\270se 3. gradsligningen LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYwLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiM0YnL0Y2USdub3JtYWxGJ0YyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEiK0YnRj4vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkkvJSlzdHJldGNoeUdGSS8lKnN5bW1ldHJpY0dGSS8lKGxhcmdlb3BHRkkvJS5tb3ZhYmxlbGltaXRzR0ZJLyUnYWNjZW50R0ZJLyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGWC1GOzYkUSM1NkYnRj4tRkQ2LVEifkYnRj5GR0ZKRkxGTkZQRlJGVC9GV1EmMC4wZW1GJy9GWkZcby1GLDYlRi4tRiM2JS1GOzYkUSIyRidGPkYyRjVGQC1GRDYtUSgmbWludXM7RidGPkZHRkpGTEZORlBGUkZURlZGWS1GOzYkUSMxOEYnRj5GaG5GLkZDLUY7NiRRIzM3RidGPi1GRDYtUSI9RidGPkZHRkpGTEZORlBGUkZUL0ZXUSwwLjI3Nzc3NzhlbUYnL0ZaRmJwLUY7NiRGQkY+Rj4= og tildele den ene reelle l\303\270sning til en variabel a. G\303\270r f\303\270lgende:Start med en restart. Indtast ligningen. Da vi \303\270nsker at regne med kommatal, bruger vi kommafidusen: Vi s\303\246tter et punktum efter et af tallene, her 37. H\303\270jreklik p\303\245 ligningen og v\303\246lg Solve > Obtain Solutions for > x i kontekstmenuen. Vi ser, at den reelle rod er l\303\270sning nr. 2. Derfor h\303\270jreklikkes p\303\245 Maples bl\303\245 svar og der v\303\246lges Select Element > 2. Nu vises kun den 2. l\303\270sning i bl\303\245. H\303\270jreklik p\303\245 denne og v\303\246lg Assign to a Name. Her kommer en boks frem, hvori man skriver den variable a og afslutter med OK.
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 f\303\245r derved nedenst\303\245ende. Man kan herefter regne videre med den 2. l\303\270sning, hvis man vil. a har f\303\245et tildelt denne v\303\246rdi.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUkjbW5HRiQ2JFEiM0YnL0Y2USdub3JtYWxGJy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYtUSIrRidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGSS8lKXN0cmV0Y2h5R0ZJLyUqc3ltbWV0cmljR0ZJLyUobGFyZ2VvcEdGSS8lLm1vdmFibGVsaW1pdHNHRkkvJSdhY2NlbnRHRkkvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZYLUY7NiRRIzU2RidGPi1GRDYtUSJ+RidGPkZHRkpGTEZORlBGUkZUL0ZXUSYwLjBlbUYnL0ZaRlxvLUYsNiVGLi1GIzYjLUY7NiRRIjJGJ0Y+RkAtRkQ2LVEoJm1pbnVzO0YnRj5GR0ZKRkxGTkZQRlJGVEZWRlktRjs2JFEjMThGJ0Y+RmhuRi5GQy1GOzYkUSQzNy5GJ0Y+LUZENi1RIj1GJ0Y+RkdGSkZMRk5GUEZSRlQvRldRLDAuMjc3Nzc3OGVtRicvRlpGYnAtRjs2JEZCRj4=LUkmbW92ZXJHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JS1JI21vR0YkNi5RJyZyYXJyO0YnLyUwZm9udF9zdHlsZV9uYW1lR1EoMkR+TWF0aEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R1EldHJ1ZUYnLyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUkmbXRleHRHRiQ2JVEwc29sdXRpb25zfmZvcn54RidGL0YyRkM=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LUkmbW92ZXJHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JS1JI21vR0YkNi5RJyZyYXJyO0YnLyUwZm9udF9zdHlsZV9uYW1lR1EoMkR+TWF0aEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R1EldHJ1ZUYnLyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUkmbXRleHRHRiQ2JVEvc2VsZWN0fmVudHJ5fjJGJ0YvRjJGQw==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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Der findes mange andre muligheder i kontekstmenuen. L\303\246seren opfordres til at pr\303\270ve ting af ...LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=