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Expans\303\265es em S\303\251rie
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Introdu\303\247\303\243o</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Maple tem a capacidade de fazer v\303\241rias expans\303\265es em s\303\251ries e seus truncamentos, bem como a s\303\251rie formal completa para uma variedade de fun\303\247\303\265es elementares e especiais. No artigo deste m\303\252s, examinamos os comandos relevantes e dispositivos de interface que acessam essas funcionalidades. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">A Constru\303\247\303\243o das S\303\251ries </Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= No Maple, a sa\303\255da do comando taylor parece ser um polin\303\264mio em que um termo com um "O" foi anexado. O comando series produz uma expans\303\243o de s\303\251rie generalizada que poderia ser uma s\303\251rie de Taylor ou de Laurent, ou uma s\303\251rie mais geral. Em particular, os resultados destes comandos podem ser vistos na Tabela 1. 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder KytJInhHNiIiIiJGJSMhIiIiIiciIiQjRiUiJD8iIiImLUkiT0clKnByb3RlY3RlZEc2I0YlRig= JSFH 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LCgqKCkiIiMjIiIiRiVGJylJI1BpRyUqcHJvdGVjdGVkR0YmISIiKUkieEc2IkYmRidGJyoqI0YnIiInRidGJEYnRihGKylGLSMiIiZGJUYnRistSSJPR0YqNiMqJClGLSMiIipGJUYnRic= Tabela 1 Aplica\303\247\303\243o dos comandos taylor e series para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEkc2luRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJ0YyRjJGMg==
Na Tabela 1, a sa\303\255da do comando taylor n\303\243o \303\251 apenas um polin\303\264mio em que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiT0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiQtRiM2JC1JJW1zdXBHRiQ2JS1GLDYlUSJ4RicvRjBRJXRydWVGJy9GM1EnaXRhbGljRictRiM2JS1JI21uR0YkNiRRIjZGJ0YyRkBGQi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGMkYyRjI= foi adicionado. \303\211 uma constru\303\247\303\243o de s\303\251rie especial que pode ser convertida para um polin\303\264mio com o comando convert, como no LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYuLUkjbWlHRiQ2JVEicUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSomY29sb25lcTtGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjc3Nzc3OGVtRicvRk5GUy1GLDYlUSd0YXlsb3JGJ0YvRjItSShtZmVuY2VkR0YkNiQtRiM2KC1GLDYlUSRzaW5GJy9GMEY9RjktRlk2JC1GIzYlLUYsNiVRInhGJ0YvRjIvJStleGVjdXRhYmxlR0Y9RjlGOS1GNjYtUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIRkovRk5RLDAuMzMzMzMzM2VtRidGX29GYm9GOUY5LUY2Ni1RIjpGJ0Y5RjtGPkZARkJGREZGRkhGUkZULUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHRkwvJSZkZXB0aEdGYnAvJSpsaW5lYnJlYWtHUShuZXdsaW5lRidGNS1GLDYlUShjb252ZXJ0RidGL0YyLUZZNiQtRiM2J0YrRmRvLUYsNiVRKHBvbHlub21GJ0YvRjJGYm9GOUY5RmJvRjk= LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LChJInhHNiIiIiIqJiNGJSIiJ0YlKUYjIiIkRiUhIiIqJiNGJSIkPyJGJSlGIyIiJkYlRiU= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= O valor padr\303\243o da vari\303\241vel Order no Maple \303\251 6. Ele pode ser alterado, atribuindo-lhe outro valor inteiro. No entanto, ele tamb\303\251m pode ser temporariamente (ou seja, localmente) trocado dentro de um dos comandos taylor ou series simplesmente incluindo um inteiro como um terceiro argumento. Por exemplo, Order pode ser definido temporariamente para 7 como se segue. JSFH 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder KytJInhHNiIiIiJGJSMhIiIiIiciIiQjRiUiJD8iIiImLUkiT0clKnByb3RlY3RlZEc2I0YlIiIo Esta sa\303\255da sugere que cuidados devem ser tomados na interpreta\303\247\303\243o do termo "O" produzidos por esses comandos. As sa\303\255das na Tabela 1 s\303\243o tecnicamente corretas em que eles indicam o restante termo que \303\251 "O" de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= para a pot\303\252ncia de Order. Na verdade, os restantes termos na Tabela 1 s\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEib0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiQtRiM2JC1JJW1zdXBHRiQ2JS1GLDYlUSJ4RicvRjBRJXRydWVGJy9GM1EnaXRhbGljRictRiM2JC1JI21uR0YkNiRRIjZGJ0YyRjIvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjJGMkYy, que \303\251, "o" de LUklbXN1cEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JJW1yb3dHRiQ2JC1JI21uR0YkNiRRIjZGJy9GM1Enbm9ybWFsRidGPC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRic=. Assim, os comandos na Tabela 1 n\303\243o produzem o limite apertado LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiT0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiQtRiM2JC1JJW1zdXBHRiQ2JS1GLDYlUSJ4RicvRjBRJXRydWVGJy9GM1EnaXRhbGljRictRiM2JS1JI21uR0YkNiRRIjdGJ0YyRkBGQi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGMkYyRjI= que seria aplic\303\241vel se alguma forma dos restantes fossem analiticamente examinados para sua verdadeira ordem. A situa\303\247\303\243o \303\251 agravada pelo Maple "remember table," uma tabela interna que armazena certos c\303\241lculos para reduzir o tempo que levam para acessar novamente o c\303\241lculo. N\303\263s vemos o efeito desta tabela no c\303\241lculo a seguir. 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder KytJInhHNiIiIiJGJSMhIiIiIiciIiQjRiUiJD8iIiImLUkiT0clKnByb3RlY3RlZEc2I0YlIiIo A segunda vez que o comando \303\251 chamado com o valor padr\303\243o de Order, nomeadamente, seis, a tabela de lembrar entra em jogo, e agora, o Maple indica que o termo restante \303\251 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiT0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiQtRiM2JC1JJW1zdXBHRiQ2JS1GLDYlUSJ4RicvRjBRJXRydWVGJy9GM1EnaXRhbGljRictRiM2JC1JI21uR0YkNiRRIjdGJ0YyRjIvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjJGMkYy. O conte\303\272do da tabela de lembrar pode ser esvaziada com o comando forget, como na LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEnZm9yZ2V0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JVEnc2VyaWVzRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkBGPUZA 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder KytJInhHNiIiIiJGJSMhIiIiIiciIiQjRiUiJD8iIiImLUkiT0clKnByb3RlY3RlZEc2I0YlRig= Assim, \303\251 \303\272til pensar em termos de "series order" como um inteiro que o Maple usa para controlar o truncamento de uma s\303\251rie, e n\303\243o \303\251 necessariamente a ordem anal\303\255tica precisa do termo restante. Al\303\251m disso, n\303\243o \303\251 claramente o grau do polin\303\264mio truncado obtido ap\303\263s a convers\303\243o para um polin\303\264mio. \303\211 lament\303\241vel que o Maple usa "order" em muitos lugares onde "degree" seria o termo ou constru\303\247\303\243o mais apropriado. Quando a sa\303\255da do comando series cont\303\251m expoentes fracion\303\241rios, n\303\243o \303\251 a constru\303\247\303\243o de s\303\251rie especial, mas sim, uma express\303\243o na forma de uma soma de produtos em que o termo "big Oh" foi adicionado. O termo "big Oh" pode ser removido pela op\303\247\303\243o convert que trabalha para a sa\303\255da do comando taylor. JSFH
<Text-field style="Heading 1" layout="Heading 1">Interfaces para os Comandos <Font italic="true">taylor</Font> e <Font italic="true">series</Font> </Text-field> JSFH O comando series pode ser acessado diretamente, como na Tabela 1, ou a partir do Menu de Contexto. O comando taylor pode ser acessado diretamente, como na Tabela 1, a partir de v\303\241rios Modelos de Tarefas, ou a partir do comando TaylorApproximation no pacote Student Calculus 1. JSFH Figura 1 mostra a caixa de di\303\241logo que resulta da sele\303\247\303\243o Series\342\211\273Series\342\211\273LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== a partir do Menu de Contexto aplicado a uma express\303\243o como LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEkc2luRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJ0YyRjJGMg== ou 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jJCIjXSEiIi0lKUJPVU5EU19ZRzYjJCIiIUYqLSUtQk9VTkRTX1dJRFRIRzYjJCIlP0dGKi0lLkJPVU5EU19IRUlHSFRHNiMkIiUheiJGKi0lKUNISUxEUkVORzYi Figura 1 Op\303\247\303\243o de Series no Menu de Contexto
JSFH O termo "Series order" \303\251 o valor que ser\303\241 atribu\303\255do \303\240 op\303\247\303\243o Order ou vari\303\241vel. Se o checkbox "Truncate to polynomial" \303\251 marcado, um polin\303\264mio de grau pelo menos um, ir\303\241 resultar "Series order". 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 JSFH Figura 2 mostra o tutor do Taylor Approximation com suas configura\303\247\303\265es padr\303\243o. A fun\303\247\303\243o padr\303\243o \303\251 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEkc2luRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJ0YyRjJGMg== e o padr\303\243o "series order" \303\251 quatro. O comando TaylorApproximation mostrado na parte inferior do tutor fornece um polin\303\264mio de Taylor como uma aproxima\303\247\303\243o para a fun\303\247\303\243o de entrada, mas Maple declara esta aproxima\303\247\303\243o polinomial a ser de "order," isto \303\251, de "series order," ao inv\303\251s de "degree." O comando TaylorApproximation \303\251 apenas uma interface para o fundamental comando taylor. 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Figura 2 Tutor do Taylor Approximatiom acessando o comando TaylorApproximation
Tabela 2 fornece o caminho para um Modelo de Tarefas que chama o comando TaylorApproximation e/ou lan\303\247a o tutor do Taylor Approximatiom. A sintaxe para a execu\303\247\303\243o do comando TaylorApproximation \303\251 fornecida por este Modelo de Tarefa. Observe que a configura\303\247\303\243o local da vari\303\241vel Order deve ser feita sob a forma de uma equa\303\247\303\243o cujo lado esquerdo \303\251 a palavra "order". Como na Figura 2, "order" significa o grau do polin\303\263mio resultante, um uso que est\303\241 em conflito com a do fundamental comando taylor. Student[Calculus1][TaylorApproximationTutor](); Ferramentas\342\211\273Tarefas\342\211\273Pesquisa: C\303\241lculo\342\211\273 Aproxima\303\247\303\243o de Taylor de uma Fun\303\247\303\243o de Uma Vari\303\241vel
<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">Aproxima\303\247\303\243o de Taylor</Font></Text-field> Calcule a aproxima\303\247\303\243o de Taylor de um grau especificado para uma fun\303\247\303\243o de uma vari\303\241vel. Digite a fun\303\247\303\243o como uma express\303\243o. 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 LCYtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kmX194X19HRigiIiItSSRzaW5HRiVGKUYr Especifique a ordem, e ent\303\243o calcule a Aproxima\303\247\303\243o de Taylor. 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 LC4iIiJGI0kmX194X19HNiJGIyomI0YjIiIjRiMpRiRGKEYjISIiKiYjRiMiIidGIylGJCIiJEYjRioqJiNGIyIjQ0YjKUYkIiIlRiNGIyomI0YjIiQ/IkYjKUYkIiImRiNGIw== Alternativamente, voc\303\252 pode usar o tutor do Taylor Approximation, uma interface de apontar e clicar. H\303\241 duas maneiras de lan\303\247ar este tutor. A partir do menu Tools, selecione Tutors, Calculus - Single Variable, e em seguida Taylor Approximation. Digite abaixo a fun\303\247\303\243o em uma vari\303\241vel a ser aproximada, em seguida clique no seguinte bot\303\243o Taylor Approximation. try TaylorApproximation_temp := Student:-Calculus1:-TaylorApproximationTutor(DocumentTools:-Do(%TextArea0)); if TaylorApproximation_temp <> NULL then DocumentTools:-SetProperty('Plot0','visible','true'); DocumentTools:-SetProperty('Plot0','value',TaylorApproximation_temp); fi; catch: error end try;
Tabela 2 O Modelo de Tarefa de "Aproxima\303\247\303\243o de Taylor de uma Fun\303\247\303\243o de uma vari\303\241vel"
JSFH Pressionando o bot\303\243o "Taylor Approximation" ir\303\241 lan\303\247ar o tutor do Taylor Approximatiom pr\303\251-carregado com a fun\303\247\303\243o na caixa \303\240 direita do bot\303\243o. Alternativamente, se o pacote Student Calculus 1 \303\251 carregado primeiro na mem\303\263ria do Maple, o Menu de Contexto para uma express\303\243o conter\303\241 a op\303\247\303\243o "Tutors" da qual o tutor do Taylor Approximatiom pode ser selecionado. Isso seria mais direto do que acessando o tutor do Modelo de Tarefas. JSFH Tabela 3 fornece o caminho para um Modelo de Tarefas que chama o comando taylor e fornece uma ferramenta interativa para obten\303\247\303\243o de expans\303\265es e polin\303\264mios de Taylor. \303\211 poss\303\255vel ter acesso apenas a esta ferramenta, que por sua vez d\303\241 acesso ao tutor do Taylor Approximatiom. Ferramentas\342\211\273Tarefas\342\211\273Pesquisa: C\303\241lculo\342\211\273 Expans\303\265es e Polin\303\264mios de Taylor
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Polin\303\264mio de Taylor para uma Fun\303\247\303\243o de Uma Vari\303\241vel</Font></Text-field> Calcule a expans\303\243o de Taylor para uma fun\303\247\303\243o de uma vari\303\241vel sobre um ponto espec\303\255fico at\303\251 uma order espec\303\255fica. Digite a fun\303\247\303\243o com uma express\303\243o: 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 LCYqJiIiIyIiIi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSZfX3hfX0dGK0YlRiVGJUYl Especifique um ponto de expans\303\243o e uma ordem de expans\303\243o, e em seguida calcule a s\303\251rie de Taylor: 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 Ky9JJl9feF9fRzYiIiIkIiIhIiIjIiIiRihGJyNGKEYlRiUjRigiIzciIiUtSSJPRyUqcHJvdGVjdGVkRzYjRigiIiY= LUknbXN0eWxlRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YnNictSSNtaUdGJDYjUSFGJy1JJW1yb3dHRiQ2JUYrLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRitGMkY1 Alternativamente, voc\303\252 pode usar a interface a seguir para calcular a expans\303\243o de Taylor e o polin\303\264mio de Taylor:
Expans\303\243o e Polin\303\264mio de Taylor Digite a fun\303\247\303\243o: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tSSNtb0dGJDYtUSI9RidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZURj0= 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E&H!#:$!2NDc-@=Ll#!#:7$$"1ommY^*o-$!#:$!2B$pYK*zRu#!#:7$$"1baauX?7J!#:$!2ER(e!)zPKG!#:7$$"1ihh@**R#>$!#:$!2D5gI!yC(*G!#:7$$"2(444p1#=F$!#;$!2:d%GHi/TH!#:7$$"2ljjjf/8N$!#;$!2DA**4zU8'H!#:7$$"29444<tBV$!#;$!1:/*[!pGaH!#97$$"1#===]/$=N!#:$!2(=*y@!)o>"H!#:7$$"2%edd<^4(f$!#;$!2a(H!G%**ePG!#:7$$"2DDDDdr[n$!#;$!22;\`%\yEF!#:7$$"2LGGGK8!eP!#;$!2%)4Hn#4liD!#:7$$"273333u4%Q!#;$!2VxS0&QqYB!#:7$$"1pnn(GOa"R!#:$!1;%HysmR5#!#97$$"#S!""$!2dmmmmmmw"!#:-%&COLORG6&%$RGBG$""!!""$""!!""$"#5!""-%%VIEWG6$;$!#S!""$"#S!"";$!)Hp(>"!"($").z*>"!"(-&%&_AXISG6#"""6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#"""-%-TRANSPARENCYG6#$""!!""-&%&_AXISG6#""#6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#"""-%-TRANSPARENCYG6#$""!!""-%+AXESLABELSG6%Q"x6"Q"y6"-%%FONTG6%%(DEFAULTG%(DEFAULTG"#5-%*AXESSTYLEG6#%'NORMALG-%(SCALINGG6#%.UNCONSTRAINEDG-%%ROOTG6'-%)BOUNDS_XG6#$"$I"!""-%)BOUNDS_YG6#$"#]!""-%-BOUNDS_WIDTHG6#$"%S:!""-%.BOUNDS_HEIGHTG6#$"%g=!""-%)CHILDRENG6" use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # GetProperty( component_name, attribute_name ) # and # SetProperty( component_name, attribute_name, value ) # to access any of the attributes of the component. # See ?CustomizingComponents for more information. module() local f, a, F; Do(f = %MathContainer0); if nops(Typesetting:-Parse(Typesetting:-FromMathML(DocumentTools:-GetProperty('MathContainer2','value'))))=1 then a:=0 else a := eval(op(2,Typesetting:-Parse(Typesetting:-FromMathML(DocumentTools:-GetProperty('MathContainer2','value'))))); end if; F := Student:-Calculus1:-TaylorApproximationTutor(f,a); if F <> NULL then DocumentTools:-SetProperty('Plot1','visible','true'); DocumentTools:-SetProperty('Plot1','value', F); end if; end module; end use; Grau: Ponto base: use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # GetProperty( component_name, attribute_name ) # and # SetProperty( component_name, attribute_name, value ) # to access any of the attributes of the component. # See ?CustomizingComponents for more information. module() local f, q, a, F, Q; Do(f = %MathContainer0); q := op(2,Typesetting:-Parse(Typesetting:-FromMathML(DocumentTools:-GetProperty('MathContainer1','value')))); if is(q,posint) then Q:=q else Q:=5; end if; if nops(Typesetting:-Parse(Typesetting:-FromMathML(DocumentTools:-GetProperty('MathContainer2','value'))))=1 then a:=0 else a := eval(op(2,Typesetting:-Parse(Typesetting:-FromMathML(DocumentTools:-GetProperty('MathContainer2','value'))))); end if; F := taylor(f, x=a, Q+1); SetProperty('MathContainer3', 'value', F); end module; end use; use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # GetProperty( component_name, attribute_name ) # and # SetProperty( component_name, attribute_name, value ) # to access any of the attributes of the component. # See ?CustomizingComponents for more information. module() local f, q, Q, a, F; Do(f = %MathContainer0); q := op(2,Typesetting:-Parse(Typesetting:-FromMathML(DocumentTools:-GetProperty('MathContainer1','value')))); if is(q,posint) then Q:=q else Q:=5; end if; if nops(Typesetting:-Parse(Typesetting:-FromMathML(DocumentTools:-GetProperty('MathContainer2','value'))))=1 then a:=0 else a := eval(op(2,Typesetting:-Parse(Typesetting:-FromMathML(DocumentTools:-GetProperty('MathContainer2','value'))))); end if; F := convert(taylor(f, x=a, Q+1),polynom); SetProperty('MathContainer4', 'value', F); end module; end use; LUknbXN0eWxlRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YnNiYtSSNtaUdGJDYjUSFGJy1JJW1yb3dHRiQ2JEYrLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0YrRjI=use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # GetProperty( component_name, attribute_name ) # and # SetProperty( component_name, attribute_name, value ) # to access any of the attributes of the component. # See ?CustomizingComponents for more information. module() SetProperty('MathContainer0', 'value', NULL); SetProperty('MathContainer1', 'value', NULL); SetProperty('MathContainer3', 'value', NULL); SetProperty('MathContainer2', 'value', NULL); SetProperty('MathContainer4', 'value', NULL); Do(%Plot1=plots[display](plots[textplot]([0,0,""]),axes=none)); end module; end use;
Tabela 3 O Modelo de Tarefa "Expans\303\243o e Polin\303\264mio de Taylor" Para ambas as expans\303\265es em s\303\251rie e o polin\303\264mio de Taylor, o grau do polin\303\264mio \303\251 regido pelo op\303\247\303\243o "Degree". Se nenhum ponto base \303\251 fornecido, a ferramenta assume LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=. Lan\303\247ando do tutor a partir desta ferramenta, carrega a fun\303\247\303\243o e o ponto-base, mas n\303\243o o grau desejado. Fechando o tutor, coloca seu gr\303\241fico na janela de gr\303\241ficos da ferramenta. JSFH
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">S\303\251ries de Laurent</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= A s\303\251rie de Laurent 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 pode ser obtida com o comando series, ou com o comando laurent do pacote numapprox. O uso esta ilustrado na Tabela 4. 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder KytJInhHNiIiIiIhIiMjRiUiIiciIiEjIiIoIiRnJCIiIy1JIk9HJSpwcm90ZWN0ZWRHNiNGJSIiJA== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder KytJInhHNiIiIiIhIiMjRiUiIiciIiEjIiIoIiRnJCIiIy1JIk9HJSpwcm90ZWN0ZWRHNiNGJSIiJA== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Tabela 4 A s\303\251rie de Laurent atrav\303\251s dos comandos series e laurent
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">S\303\251ries Assint\303\263ticas</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= S\303\251ries de pot\303\252ncia assint\303\263ticas ,at\303\251 mesmo s\303\251rie com pot\303\252ncias fracion\303\241rias, podem ser obtidas em qualquer uma das quatro maneiras listadas na Tabela 5. 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LCgqKikiIiMjIiIiRiVGJylJI1BpRyUqcHJvdGVjdGVkR0YmISIiLUkkc2luRzYkRipJKF9zeXNsaWJHNiI2IywmSSJ4R0YwRicqJiNGJyIiJUYnRilGJ0YnRicpKiRGM0YrRiZGJ0YnKiwjRiciIilGJ0YkRidGKEYrLUkkY29zR0YuRjFGJylGOCMiIiRGJUYnRistSSJPR0YqNiMqJClGOCMiIiZGJUYnRic= 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LCgqKikiIiMjIiIiRiVGJylJI1BpRyUqcHJvdGVjdGVkR0YmISIiLUkkc2luRzYkRipJKF9zeXNsaWJHNiI2IywmSSJ4R0YwRicqJiNGJyIiJUYnRilGJ0YnRicpKiRGM0YrRiZGJ0YnKiwjRiciIilGJ0YkRidGKEYrLUkkY29zR0YuRjFGJylGOCMiIiRGJUYnRistSSJPR0YqNiMqJClGOCMiIiZGJUYnRic= 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LCgqKikiIiMjIiIiRiVGJylJI1BpRyUqcHJvdGVjdGVkR0YmISIiLUkkc2luRzYkRipJKF9zeXNsaWJHNiI2IywmSSJ4R0YwRicqJiNGJyIiJUYnRilGJ0YnRicpKiRGM0YrRiZGJ0YnKiwjRiciIilGJ0YkRidGKEYrLUkkY29zR0YuRjFGJylGOCMiIiRGJUYnRistSSJPR0YqNiMqJClGOCMiIiZGJUYnRic= 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LCgqKikiIiMjIiIiRiVGJylJI1BpRyUqcHJvdGVjdGVkR0YmISIiLUkkc2luRzYkRipJKF9zeXNsaWJHNiI2IywmSSJ4R0YwRicqJiNGJyIiJUYnRilGJ0YnRicpKiRGM0YrRiZGJ0YnKiwjRiciIilGJ0YkRidGKEYrLUkkY29zR0YuRjFGJylGOCMiIiRGJUYnRistSSJPR0YqNiMqJClGOCMiIiZGJUYnRic= Tabela 5 S\303\251ries de pot\303\252ncia assint\303\263tica
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Da Tabela 5, vemos que os comandos series, taylor, e asympt podem ser usados para gerar s\303\251ries de pot\303\252ncia assint\303\263tica, at\303\251 mesmo s\303\251rie com pot\303\252ncias fracion\303\241rias. O comando asympt assume que o ponto de expans\303\243o \303\251 o ponto no infinito. Ambos os comandos taylor e series precisam ser informados de que a expans\303\243o \303\251 o ponto no infinito. \303\211 ainda poss\303\255vel obter uma expans\303\243o assint\303\263tica, alterando vari\303\241veis, de modo que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjFGJ0Y5LUY2Ni1RIi9GJ0Y5RjtGPi9GQUYxRkJGREZGRkgvRktRLDAuMTY2NjY2N2VtRicvRk5GWC1GLDYlUSJ6RidGL0YyRjk=, expandindo-se sobre LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=, e restaurando LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== via LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKCZzcmFycjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjFGJ0Y5LUY2Ni1RIi9GJ0Y5RjtGPi9GQUYxRkJGREZGRkgvRktRLDAuMTY2NjY2N2VtRicvRk5GWC1GLDYlUSJ4RidGL0YyRjk=. Uma s\303\251rie de pot\303\252ncia assint\303\263tica, mesmo uma com pot\303\252ncias fracion\303\241rias, est\303\241 dispon\303\255vel atrav\303\251s do Menu de Contexto, sob a op\303\247\303\243o Series\342\211\273Asymptotic Series\342\211\273LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. A caixa de di\303\241logo resultante, mostrado na Figura 3, sugere que \303\251 poss\303\255vel obter uma s\303\251rie de pot\303\252ncia assint\303\263tica de forma interativa, como uma contru\303\247\303\243o de s\303\251ries ou como uma expans\303\243o truncada. 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Figura 3 Caixa de di\303\241logo para op\303\247\303\243o do menu de contexto: Series\342\211\273Asymptotic Series
Infelizmente, o Maple n\303\243o tem uma fun\303\247\303\243o para gerar uma s\303\251rie assint\303\263tica em rela\303\247\303\243o a uma base assint\303\263tica arbitr\303\241ria. No entanto, se 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 \303\251 uma seq\303\274\303\252ncia assint\303\263tica como LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKCZzcmFycjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJhRidGL0YyRjk=, ent\303\243o os coeficientes na expans\303\243o 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= podem ser obtidas recursivamente atrav\303\251s de 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">S\303\251ries Multivariadas </Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= O comando mtaylor \303\251 usado para gerar um polin\303\264mio de Taylor para uma fun\303\247\303\243o multivariada. Por exemplo, a expans\303\243o de Taylor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRInhGJ0YvRjItSSNtb0dGJDYtUSIsRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiVRInlGJ0YvRjJGQUZBRkE=, tomadas sobre 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, seria da forma 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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
Tabela 6 cont\303\251m a expans\303\243o de 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 no ponto 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. 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LC4jIiImIiIlISIiKiYjIiIiRiVGKUkieEc2IkYpRikqJkYoRilJInlHRitGKUYpKiYjRikiIilGKSksJkYqRilGKUYmIiIjRilGJiooRihGKSwmRi1GKUYzRiZGKUYyRilGJiomRi9GKSlGNUYzRilGJg== Tabela 6 Expans\303\243o de Taylor Multivariada de 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
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Mesmo que o Maple n\303\243o tenha uma constru\303\247\303\243o de s\303\251rie para o caso multivariado, a no\303\247\303\243o de "series order" \303\251 usado para determinar o grau do polin\303\264mio resultante. Infelizmente, isso resulta em um polin\303\264mio de um grau total menor do que o "series order" utilizado como par\303\242metro no comando mtaylor. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Porque n\303\243o h\303\241 nenhum "constru\303\247\303\243o de s\303\251ries" para o caso multivariado, Maple n\303\243o alinha em um termo de ordem para expans\303\265es geradas pelo comando mtaylor. Devido a isso, Eu posso relembrar que os colegas na RHIT iria ensinar aos seus alunos apenas sobre o comando mtaylor, mesmo no c\303\241lculo de uma \303\272nica vari\303\241vel. Isso evitaria a necessidade de acompanhamento com a etapa "convert-to-polynom(converter para polin\303\264mio)", diminuindo assim a carga de sintaxe nos dias em que todos os c\303\241lculos de Maple eram dependentes do conhecimento dos comandos apropriados.
<Text-field style="Heading 1" layout="Heading 1">Interfaces para o Comando <Font italic="true">mtaylor</Font> </Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Figura 4 mostra o tutor do Taylor Approximation do pacote Student Multivariate Calculus. 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Figura 4 Tutor do Taylor Approximation de C\303\241lculo Multivariado
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= O polin\303\264mio de Taylor de primeiro-grau para a fun\303\247\303\243o 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, tomada em 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 \303\251 obtido na Figura 4. Al\303\251m disso, um gr\303\241fico da fun\303\247\303\243o e do polin\303\264mio de Taylor \303\251 desenhado. O gr\303\241fico do polin\303\264mio de Taylor de primeiro grau \303\251 o gr\303\241fico do plano tangente. Na parte inferior do tutor, o comando TaylorApproximation pode ser visto. A sintaxe deste comando contrasta com a do comando mtaylor e ao comando de nome semelhante do pacote Calculus 1 . Note em particular como o ponto de expans\303\243o \303\251 expresso, e note que o uso expl\303\255cito da equa\303\247\303\243o "order = 1" n\303\243o \303\251 necess\303\241rio. Na aus\303\252ncia do par\303\242metro "output=plot", a express\303\243o para o polin\303\264mio de Taylor seria retornado. Finalmente, note que o comando e o tutor usa "Order" para significar "degree". Dado que n\303\243o h\303\241 "series construct" no caso de multivariada, e dado que o comando e o tutor especificamente referente a "Approximation", \303\251 not\303\241vel que a no\303\247\303\243o de "series order" \303\251 usado, e usado quando o "degree" seria mais apropriado. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Tabela 7 mostra o caminho para um Modelo de Tarefa que oferece acesso ao comando Taylor Approximation e tutor. Ferramentas\342\211\273Tarefas\342\211\273Pesquisa: C\303\241lculo Multivariado\342\211\273Aproxima\303\247\303\243o de Taylor de uma Fun\303\247\303\243o Multivariada
<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">Aproxima\303\247\303\243o de Taylor de uma Fun\303\247\303\243o Multivariada</Font></Text-field> Calcule a aproxima\303\247\303\243o de Taylor de grau especificado para uma fun\303\247\303\243o multivariada. Digite a fun\303\247\303\243o. LUknbXN0eWxlRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YnNictSSNtaUdGJDYjUSFGJy1JJW1yb3dHRiQ2Li1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2PlExJkludmlzaWJsZVRpbWVzO0YnLyUnZmFtaWx5R1Emc2VyaWZGJy8lJXNpemVHUSMxMkYnLyUlYm9sZEdRJmZhbHNlRicvRjZGRy8lKnVuZGVybGluZUdGRy8lKnN1YnNjcmlwdEdGRy8lLHN1cGVyc2NyaXB0R0ZHLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvJSdvcGFxdWVHRkcvJStleGVjdXRhYmxlR0ZHLyUpcmVhZG9ubHlHRkcvJSljb21wb3NlZEdGRy8lKmNvbnZlcnRlZEdGRy8lK2ltc2VsZWN0ZWRHRkcvJSxwbGFjZWhvbGRlckdGRy8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdGRy9GOVEnbm9ybWFsRicvJSZmZW5jZUdGRy8lKnNlcGFyYXRvckdGRy8lKXN0cmV0Y2h5R0ZHLyUqc3ltbWV0cmljR0ZHLyUobGFyZ2VvcEdGRy8lLm1vdmFibGVsaW1pdHNHRkcvJSdhY2NlbnRHRkcvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZhcC1GPDYtUSM6PUYnRl9vRmFvRmNvRmVvRmdvRmlvRltwRl1wRl9wRmJwRjstSShtZmVuY2VkR0YkNiQtRjA2KC1GLDYlUSJ4RidGNUY4LUY8Ni1RIixGJ0Zfb0Zhb0Zjb0Zlb0Znb0Zpb0ZbcEZdcEZfcEZicEY7LUYsNiVRInlGJ0Y1RjhGV0Zfb0Zfb0Y7LUY8Ni1RLSZSaWdodEFycm93O0YnRl9vRmFvRmNvRmVvRmdvRmlvRltwRl1wRl9wRmJwRjstRmhwNiQtRjA2J0YrLUkobWFjdGlvbkdGJDYkLUYwNihGKy1GMDYnRistRiM2LEYrLUklbXN1cEdGJDYlLUYsNihGXnFGNS9GUFErWzk1LDAsMjE3XUYnL0ZWRjcvJTBmb250X3N0eWxlX25hbWVHUThNYXBsZX5JbnB1dH5QbGFjZWhvbGRlckYnRjgtSSNtbkdGJDYnUSIzRidGanJGXHNGXXNGX28vJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjstRjw2MFEnJnBsdXM7RidGanJGXHNGXXNGX29GYW9GY29GZW9GZ29GaW9GW3BGXXBGX3BGYnBGOy1GMDYpLUYsNihRJHNpbkYnRjVGanJGXHNGXXNGOC1GPDY/UTAmQXBwbHlGdW5jdGlvbjtGJ0Y/RkIvRkZGN0ZIRklGS0ZNRk9GUkZVRldGWUZlbkZnbkZpbkZbb0Zdby9GOVElYm9sZEYnLyUrZm9udHdlaWdodEdGZHRGYW9GY29GZW9GZ29GaW9GW3BGXXBGX3BGYnAtRmhwNiUtRjA2Ji1GLDYoRmRxRjVGanJGXHNGXXNGOEZcc0ZXRl9vRlxzRl9vRitGXHNGV0Zfb0YrRlxzRldGX29GK0ZXRl9vRitGVy9GXG9GN0Zfby8lK2FjdGlvbnR5cGVHUTttYXBsZXNvZnQ6dGFzay1wbGFjZWhvbGRlckYnRitGV0Zfb0Zfb0YrRldGX29GK0ZXRl9v Zio2JEkmX194X19HNiJJJl9feV9fR0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUsJiokKUYkIiIkIiIiRi4tSSRzaW5HRiU2I0YmRi5GJUYlRiU= Especifique um ponto de expans\303\243o e ordem, e ent\303\243o calcule a aproxima\303\247\303\243o de Taylor. 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 LDAqJiMiIiIiJD8iRiUpSSZfX3lfX0c2IiIiJkYlRiUqJiNGJSIiJ0YlKUYoIiIkRiUhIiIqJkYvRiVJJl9feF9fR0YpRiVGJUYoRiUiIiNGMComRi9GJSksJkYyRiVGJUYwRjNGJUYlKiQpRjZGL0YlRiU= Alternativamente, voc\303\252 pode usar o tutor do Taylor Series, uma interface de apontar e clicar. H\303\241 duas maneiras de lan\303\247ar este tutor. Do menu Tools, selececione Tutors, Calculus - Multi-Variable e em seguida Taylor Series. Digite abaixo uma fun\303\247\303\243o multivariada, em seguida clique no seguinte bot\303\243o Taylor Series. try TaylorSeries_temp := Student:-MultivariateCalculus:-TaylorApproximationTutor(DocumentTools:-Do(%TextArea1)); if TaylorSeries_temp <> NULL then DocumentTools:-SetProperty('Plot2','visible','true'); DocumentTools:-SetProperty('Plot2','value',TaylorSeries_temp); fi; catch: error end try;
Tabela 7 O Modelo de Tarefa "Aproxima\303\247\303\243o de Taylor de uma Fun\303\247\303\243o Multivariada"
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Novamente, se o pacote Student Multivariate Calculus \303\251 carregado, o Menu de Contexto para uma express\303\243o ir\303\241 conter a op\303\247\303\243o "Tutors", do qual o tutor do Taylor Approximation pode ser selecionado. Isso prova ser uma conex\303\243o mais eficiente para o tutor do que o Modelo de Tarefa. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">S\303\251ries Formais de Pot\303\252ncias </Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Maple tem dois processos separados para a produ\303\247\303\243o de s\303\251ries de pot\303\252ncia formal completa para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ==. Cada uma \303\251 acessada como uma op\303\247\303\243o para o comando convert, mas mesmo que pare\303\247a que exista uma interface comum, as abordagens fundamentais para a obten\303\247\303\243o da s\303\251rie de pot\303\252ncia formal s\303\243o diferentes. Na maioria dos casos, o processo funcionar\303\241, mas h\303\241 fun\303\247\303\265es para as quais apenas uma ser\303\241 bem sucedida em encontrar a s\303\251rie desejada. Tabela 8 ilustra as duas funcionalidades relevantes. 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LUkkU3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQqKCkhIiJJImtHRiciIiItSSpmYWN0b3JpYWxHRiU2IywmKiYiIiNGLUYsRi1GLUYtRi1GKylJInhHRidGMUYtL0YsOyIiIUkpaW5maW5pdHlHRiU= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEoY29udmVydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYoLUYsNiVRJHNpbkYnL0YwUSZmYWxzZUYnL0YzUSdub3JtYWxGJy1GNjYkLUYjNiUtRiw2JVEieEYnRi9GMi8lK2V4ZWN1dGFibGVHRj5GP0Y/LUkjbW9HRiQ2LVEiLEYnRj8vJSZmZW5jZUdGPi8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0Y+LyUqc3ltbWV0cmljR0Y+LyUobGFyZ2VvcEdGPi8lLm1vdmFibGVsaW1pdHNHRj4vJSdhY2NlbnRHRj4vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSRTdW1GJ0YvRjJGSEY/Rj9GSEY/ LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LUkkU3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQqKCkhIiJJJF9rMUdGJyIiIilJInhHRicsJiomIiIjRi1GLEYtRi1GLUYtRi0tSSpmYWN0b3JpYWxHRiU2I0YwRisvRiw7IiIhSSlpbmZpbml0eUdGJQ== Tabela 8 Obten\303\247\303\243o de s\303\251ries de pot\303\252ncia formal completa no Maple
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Deve ser \303\263bvio a partir da Tabela 8, que duas diferentes funcionalidades foram ativadas. No resultado do lado direito, o \303\255ndice de somat\303\263rio pode ser declarado pelo o usu\303\241rio, como mostramos no seguinte c\303\241lculo. 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A janela de di\303\241logo que aparece \303\251 mostrada na Figura 5. 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Figura 5 Janela de di\303\241logo para a op\303\247\303\243o do Menu de Contexto: Series\342\211\273Formal Power Series
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Na Figura 5, deve estar claro que mesmo a partir do Menu de Contexto \303\251 poss\303\255vel declarar o \303\255ndice de somat\303\263rio na s\303\251rie de pot\303\252ncia formal retornado. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Finalmente, note que \303\251 poss\303\255vel obter uma s\303\251rie de pot\303\252ncia assint\303\263tica formal completa, como ilustrado na Tabela 9. 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LUkkU3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQqJikhIiJJImtHRiciIiIpKiRJInhHRidGKywmRixGLUYtRi1GLS9GLDsiIiFJKWluZmluaXR5R0Yl Tabela 9 S\303\251rie de pot\303\252ncia assint\303\263tica formal completa
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
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