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Guia de Estudo de C\303\241lculo \302\251 Maplesoft, a division of Waterloo Maple Inc., 2005 Cap\303\255tulo 3: Leis de Limite
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Introdu\303\247\303\243o</Font></Text-field> Se todos os limites ( limits ) tivessem de ser avaliados( evaluated ) usando a defini\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkMtRiM2Ji1JI21pR0YkNiVRJyYjOTQ5O0YnLyUnaXRhbGljR0Y0Ri8tRiw2LVEoJm1pbnVzO0YnRi9GMkY1RjdGOUY7Rj1GP0ZBRkQtRkk2JVEnJiM5NDg7RidGTEYvRi9GK0Yv, os limites ( limits ) seriam computa\303\247\303\265es extremamentes tediosas. Felizmente, existem algumas regras gerais, chamadas as Leis de Limite, para avalia\303\247\303\243o de limites. Estas leis nos permitem evitar a aplica\303\247\303\243o da defini\303\247\303\243o para cada limite encontrado. A qualidade mais importante a se desenvolver ao longo deste cap\303\255tulo \303\251 a habilidade para avaliar um limite aplicando as Leis de Limite numa ordem apropriada. O Limite maplet ( Limit maplet ) fornece um excelente ferramenta para aprender os nomes das leis de limites e como elas podem ser aplicadas para avaliar um limite. Isto ser\303\241 demonstrado com tr\303\252s exemplos. O Teorema do Confronto \303\251 uma lei de limite que \303\251 bastante diferente de todas as outras. Ela depende das informa\303\247\303\265es que se tenha de duas fun\303\247\303\265es ( functions ) relacionadas. Por causa do tipo diferente deste resultado, ela \303\251 apresentada em separado das outras leis. Um exemplo de sua aplica\303\247\303\243o ser\303\241 dado neste cap\303\255tulo; exemplos adicionais ser\303\243o dados no cap\303\255tulo 4.
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Cap\303\255tulo Gloss\303\241rio </Font></Text-field> Os seguintes termos, neste cap\303\255tulo, t\303\252m conex\303\243o com o Dicion\303\241rio de Matem\303\241tica Maple ( Maple Math Dictionary). . upperbound bound constant denominator difference evaluate function graph hypothesis inequality limit multiple one-sided positive exponent product proof quotientrule quotient sine sandwichresult tables trigonometricfunction two-sided value zero
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Inicializa\303\247\303\243o</Font></Text-field> restart;
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">As Leis de Limite </Text-field> Em geral, os limites podem ser avaliados tomando o limite de termos individuais dentro de uma express\303\243o e depois combinando esses resultados usando as opera\303\247\303\265es matem\303\241ticas apropriadas. Por exemplo, o limite de uma soma \303\251 a soma dos limites. Tabela 3.1 resume as propriedades fundamentais de limites. Nome F\303\263rmula Condi\303\247\303\265es Extra Constante (Constant) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkMtRiM2KEYrLUknbXVuZGVyR0YkNiUtRiw2LVEkbGltRidGL0YyRjVGN0Y5RjsvRj5RJXRydWVGJ0Y/RkEvRkVRLDAuMTY2NjY2N2VtRictRiM2Ji1JI21pR0YkNidRInhGJy8lJ2l0YWxpY0dGTy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvRjBRJ2l0YWxpY0YnL0krbXNlbWFudGljc0dGJFEkZXhwRictRiw2LVEnJnJhcnI7RidGL0YyRjVGN0Y5RjtGPUY/RkFGRC1GVTYnUSJhRidGWEZaRmduRmluRi8vJSxhY2NlbnR1bmRlckdGNEYrLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHUSYwLjRlbUYnLyUmZGVwdGhHRmlvLyUqbGluZWJyZWFrR1ElYXV0b0YnLUZVNidRImNGJ0ZYRlpGZ25GaW5GLy1GLDYtUSI9RidGL0YyRjVGN0Y5RjtGPUY/L0ZCUSwwLjI3Nzc3NzhlbUYnL0ZFRmlwRmJwRi8= Identidade (Identity) 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 Multiplicado por Constante (Constant Multiple) 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existe Soma (Sum) 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exist Diferen\303\247a (Difference) 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existe, e se n for par, 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Tabela 3.1 Propriedades fundamentais de limites
Note as condi\303\247\303\265es listadas na terceira coluna. Se as condi\303\247\303\265es para uma regra n\303\243o forem satisfeitas, a regra n\303\243o pode ser usada para justificar a avalia\303\247\303\243o de um limite.
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Exemplos</Text-field> O tr\303\252s exemplos seguintes demonstram o uso destas leis de limite na avalia\303\247\303\243o de limites. Exemplos 3.1 e 3.2 foram tiradas do Cap\303\255tulo 2; Exemplo 3.3 \303\251 novo.
<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Exemplo 3.1: Use as Leis de Limite para avaliar <Equation executable="false" style="2D Math_2" input-equation="" 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</Text-field> Algebraic Manipulation Remarks 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original limit 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difference rule applied 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 constant rule applied 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 constant multiple rule applied 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 identity rule LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZDLUkjbW5HRiQ2JVEiMkYnLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJ0YvRi8= basic arithmetic \342\207\222 final answer
Table 3.2 Steps leading to computation of 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
Table 3.2 summarizes the steps leading to the conclusion that 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. Since each of the Limit Laws in Table 3.1 is actually a theorem about limits, correct application of these laws constitutes a valid proof that 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.
Em adi\303\247\303\243o \303\240 argumenta\303\247\303\243o embutida na lista de passos apresentada , voc\303\252 est\303\241 em condi\303\247\303\265es de repetir estes exemplos no ( Limit maplet ). Este maplet \303\251 na verdade o Tutor de Limite Passo-a-Passo ( Step-byStep Limit Tutor ) incorporado, acess\303\255vel do Ferramentas/Tutores/C\303\241culo-menu Uma Vari\303\241vel (Tools/Tutors/Calculus - Single Variable menu ) como M\303\251todos de Limite ( Limit Methods)... Para especificar um problema no Limit maplet, note que a linha superior deste maplet cont\303\251m campos para a fun\303\247\303\243o, vari\303\241vel, ponto de limite, e se o limite \303\251 lateral ( two-sided )(em branco) ou lateral \303\240 direita ou \303\240 esquerda ( one-sided )(direita ou esquerda). Pressione o bot\303\243o Start, depois aplique leis de limite clicando o bot\303\243o correspondente no Limit maplet. A barra de menus fornece um resumo de cada regra conhecida (Defini\303\247\303\243o da regra)(Rule Definition), ajuda, e um outro modo de aplicar as regras (Aplicar regra) (Apply the Rule). Note que a regra selecionada \303\251 geralmente aplicada para a primeira poss\303\255vel ocorr\303\252ncia; pode ser necess\303\241rio aplicar uma regra muitas vezes seguidas. Figura 3.1 mostra este Tutor inicializado para o exemplo 3.1 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Figure 3.1 O Limit maplet inicializado para Exemplo 3.1
<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Exemplo 3.2: Use as Leis de Limite para avaliar <Equation executable="false" style="2D Math_4" input-equation="" 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</Text-field> Coment\303\241rios 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limite original 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regras de diferen\303\247a e soma aplicadas 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regras de pot\303\252ncia e multiplica\303\247\303\243o por constante aplicadas 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 regras de identidade e constante aplicadas LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZDLUkjbW5HRiQ2JVEiNEYnLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJ0YvRi8= Aritm\303\251tica b\303\241sica => resposta answer Tabela 3.3 Principais passos para computa\303\247\303\243o de 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
Tabela 3.3 resume os passos principais para a conclus\303\243o de que 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Como cada uma das Leis de Limite na Tabela 3.1 \303\251 na verdade um teorema sobre limites, a aplica\303\247\303\243o correta destas leis constitui uma prova v\303\241lida de que 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 .
O exemplo final envolve a regra do quociente( quotient rule). Note que o Limit maplet( Limit maplet) aplica a regra selecionada sem checar nenhuma hip\303\263tese ( hypotheses ). Neste caso a regra do quociente \303\251 aplicada sem a verifica\303\247\303\243o de que o denominador ( denominator )n\303\243o \303\251 zero ( zero ).
<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Exemplo 3.3: Use as Leis de Limite para avaliar <Equation executable="false" style="2D Math_6" input-equation="" display="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">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</Equation> </Text-field> Este problema usar\303\241 as regras de produto ( product ) e quociente ( quotient ). Seguindo os passos dos Exemplos 3.1 e 3.2, \303\251 f\303\241cil ver que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkMtRiM2KEYrLUYjNipGKy1JJ211bmRlckdGJDYlLUYsNi1RJGxpbUYnRi9GMkY1RjdGOUY7L0Y+USV0cnVlRidGP0ZBL0ZFUSwwLjE2NjY2NjdlbUYnLUYjNictSSNtaUdGJDYlUSJ0RicvJSdpdGFsaWNHRlEvRjBRJ2l0YWxpY0YnLUYsNi1RJyZyYXJyO0YnRi9GMkY1RjdGOUY7Rj1GP0ZBRkQtRiM2JS1GLDYtUSgmbWludXM7RidGL0YyRjVGN0Y5RjtGPUY/RkFGRC1JI21uR0YkNiRRIjJGJ0YvRi9GK0YvLyUsYWNjZW50dW5kZXJHRjRGKy1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR1EmMC40ZW1GJy8lJmRlcHRoR0ZbcC8lKmxpbmVicmVha0dRJWF1dG9GJ0YrLUYjNiYtRiw2LVEiKEYnRi8vRjNGUUY1L0Y4RlFGOUY7Rj1GP0ZBRkQtRiM2KEYrLUYjNiZGKy1JJW1zdXBHRiQ2JUZWRmBvLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrRi8tRiw2LVEiK0YnRi9GMkY1RjdGOUY7Rj1GPy9GQlEsMC4yMjIyMjIyZW1GJy9GRUZpcS1GIzYmLUZhbzYkUSI1RidGLy1GLDYtUTEmSW52aXNpYmxlVGltZXM7RidGL0YyRjVGN0Y5RjtGPUY/RkFGREZWRi9GK0YvLUYsNi1RIilGJ0YvRmlwRjVGanBGOUY7Rj1GP0ZBL0ZFUSwwLjExMTExMTFlbUYnRi9GK0YvLUYsNi1RIj1GJ0YvRjJGNUY3RjlGO0Y9Rj8vRkJRLDAuMjc3Nzc3OGVtRicvRkVGXHMtRiM2JUZdby1GYW82JFEiNkYnRi9GL0YrRi9GK0Yv 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Porque os dois primeiros limites existem, a Lei do Produto pode ser aplicada para obter 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 = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkMtRiM2Ji1GLDYtUSgmbWludXM7RidGL0YyRjVGN0Y5RjtGPUY/RkFGRC1GIzYmLUkjbW5HRiQ2JFEiNkYnRi8tRiw2LVExJkludmlzaWJsZVRpbWVzO0YnRi9GMkY1RjdGOUY7Rj1GP0ZBRkQtRk42JFElMTIxMkYnRi9GL0YrRi9GK0Yv Agora, porque este limite existe e porque 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 = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkMtRiM2Ji1JI21uR0YkNiRRIzM2RidGLy1GLDYtUSUmbmU7RidGL0YyRjVGN0Y5RjtGPUY/RkFGRC1GSTYkUSIwRidGL0YvRitGLw== a lei Lei do Quociente pode ser aplicada. O resultado \303\251 que 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 = 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 = 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
Quest\303\243o 3.1 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 Encontre `$fn1` Quest\303\243o 3.2 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 Se o limite n\303\243o existe, entre a sua resposta como dne.
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font opaque="true" background="[255,255,255]">O Teorema do Confronto</Font></Text-field> O limite 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 envolve um produto, mas a Lei do Produto n\303\243o pode ser aplicada porque 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 n\303\243o existe (veja Exemplo 7 no Cap\303\255tulo 1, o cap\303\255tulo Interpreta\303\247\303\243o Conceitual de Limite). Isto \303\251 particularmente frustrante porque seria bom se pod\303\251ssemos argumentar que 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 e 0*(nada) = 0. Mas, isto \303\251 verdade somente se soubermos alguma coisa mais sobre "nada". O Teorema do Confronto ( Squeeze Theorem ) \303\251 uma Lei de Limite que pode ser usada neste tipo de situa\303\247\303\243o. O Teorema do Confronto Seja f, g, e h fun\303\247\303\265es que satisfa\303\247am LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkMtRiM2KEYrLUYjNictSSNtaUdGJDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnLUYsNi1RMCZBcHBseUZ1bmN0aW9uO0YnRi9GMkY1RjdGOUY7Rj1GP0ZBRkQtRiM2Ji1GLDYtUSIoRidGLy9GM0ZQRjUvRjhGUEY5RjtGPUY/RkFGRC1GIzYkLUZLNiVRInhGJ0ZORlFGLy1GLDYtUSIpRidGL0ZlbkY1RmZuRjlGO0Y9Rj9GQS9GRVEsMC4xMTExMTExZW1GJ0YvRitGLy1GLDYtUSUmbGU7RidGL0YyRjVGN0Y5RjtGPUY/RkFGRC1GIzYnLUZLNiVRImdGJ0ZORlFGU0ZWRitGL0YrRi9GK0YvLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkMtRiM2J0YrLUYsNi1RJSZsZTtGJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZELUYjNictSSNtaUdGJDYlUSJoRicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnLUYsNi1RMCZBcHBseUZ1bmN0aW9uO0YnRi9GMkY1RjdGOUY7Rj1GP0ZBRkQtRiM2Ji1GLDYtUSIoRidGLy9GM0ZTRjUvRjhGU0Y5RjtGPUY/RkFGRC1GIzYkLUZONiVRInhGJ0ZRRlRGLy1GLDYtUSIpRidGL0ZobkY1RmluRjlGO0Y9Rj9GQS9GRVEsMC4xMTExMTExZW1GJ0YvRitGL0YrRi9GK0Yv para qualquer LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= pr\303\263ximo de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= (exceto possivelmente em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkMtRiM2Ji1JI21pR0YkNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRictRiw2LVEiPUYnRi9GMkY1RjdGOUY7Rj1GPy9GQlEsMC4yNzc3Nzc4ZW1GJy9GRUZVLUZJNiVRImFGJ0ZMRk9GL0YrRi8=). Se 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 e 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 , ent\303\243o 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 .
A ideia por tr\303\241s do Teorema do Confronto \303\251 esta: se voc\303\252 sabe que os valores ( values ) de uma fun\303\247\303\243oest\303\243o limitados acima ( bounded above ) e abaixo por fun\303\247\303\265es com limites conhecidos em um ponto --- e estes limites t\303\252m o mesmo valor --- ent\303\243o o limite desconhecido existe e tem o mesmo dos outros limites.
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Exemplo 3.4: <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> </Text-field> Como visto no in\303\255cio deste cap\303\255tulo, porque 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 n\303\243o existe, este limite n\303\243o pode ser avaliado usando a Lei do Produto. Figura 3.2 sugere o que est\303\241 acontecendo para este limite. g := x^2*sin(1/x): plot(g, x=-1/2..1/2, color=blue); 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 Figura 3.2 Gr\303\241fico de 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 no intervalo 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
As oscila\303\247\303\265es no seno( sine ) s\303\243o a raz\303\243o de o 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 n\303\243o existir. As oscila\303\247\303\265es no gr\303\241fico ( graph ) acima realmente significam que 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 n\303\243o existe? Como todos os valores da fun\303\247\303\243o seno est\303\243o entre LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEoJm1pbnVzO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4wNTU1NTU2ZW1GJy1JI21uR0YkNiRRIjFGJ0YvRi8= e 1 (inclusive), as seguintes inequa\303\247\303\265es (inequalities) devem ser v\303\241lidas para todo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkMtRiM2Ji1JI21pR0YkNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRictRiw2LVElJm5lO0YnRi9GMkY1RjdGOUY7Rj1GP0ZBRkQtSSNtbkdGJDYkUSIwRidGL0YvRitGLw==. 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkMtRiM2JkYrLUYsNi1RJSZsZTtGJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZELUkjbW5HRiQ2JFEiMUYnRi9GL0YrRi8= (3.1)
Figura 3.3 demonstra estes limites ( bounds ) em 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. plot( [-1,sin(1/x),1], x=-1/2..1/2, color=[red,blue,red]); 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3s?6H!#;$"#5!""7$$"2&***\7`Wl7$!#<$"#5!""7$$"1nmmm*RRL$!#;$"#5!""7$$"2kmmTvJga$!#<$"#5!""7$$"1LLe9tOcP!#;$"#5!""7$$"*&Qk\R!"*$"#5!""7$$"1LL$3dg6<%!#;$"#5!""7$$"2jmmmw(GpV!#<$"#5!""7$$"-D"oK0e%!#7$"#5!""7$$"-v=5s#y%!#7$"#5!""7$$""&!""$"#5!""-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%%VIEWG6$;$!"&!""$""&!""%(DEFAULTG-%+AXESLABELSG6'Q"x6"Q!6"-%%FONTG6%%(DEFAULTG%(DEFAULTG"#5%+HORIZONTALG%+HORIZONTALG-%%ROOTG6'-%)BOUNDS_XG6#$"#q!""-%)BOUNDS_YG6#$"$?"!""-%-BOUNDS_WIDTHG6#$"%!)Q!""-%.BOUNDS_HEIGHTG6#$"%]P!""-%)CHILDRENG6" Figura 3.3 Representa\303\247\303\243o gr\303\241fica dos limites (bounds) em (3.1)
Multiplicando estas inequa\303\247\303\265es por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkMtRiM2JkYrLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy1JI21uR0YkNiRRIjJGJ0YvLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrRi9GK0Yv (uma quantidade positiva( positive )para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkMtRiM2Ji1JI21pR0YkNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRictRiw2LVElJm5lO0YnRi9GMkY1RjdGOUY7Rj1GP0ZBRkQtSSNtbkdGJDYkUSIwRidGL0YvRitGLw== ) fornece 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 (3.2)
que \303\251 v\303\241lida para todo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkMtRiM2Ji1JI21pR0YkNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRictRiw2LVElJm5lO0YnRi9GMkY1RjdGOUY7Rj1GP0ZBRkQtSSNtbkdGJDYkUSIwRidGL0YvRitGLw==. Figura 3.4 ilustra estes limites(bounds) em 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. plot( [-x^2,g,x^2], x=-1/2..1/2, color=[red,blue,red]); 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Figura 3.4 Gr\303\241fico mostrando que 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 pr\303\263ximo a 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
Agora, porque 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 e 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 --- note que ambos os limites existem e t\303\252m o mesmo limite --- oTeorema do Confronto nos permite concluir que 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 Maple pode confirmar este resultado por computa\303\247\303\243o direta, como se v\303\252 de q1 := Limit( x^2*sin(1/x), x=0 ): q1 = value( q1 ); Exemplos adicionais envolvendo Teorema do Confronto aparecer\303\243o no pr\303\263ximo cap\303\255tulo em limites trigonom\303\251tricos (trigonometric ).
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Cap\303\255tulo Resumo</Font></Text-field> Leis de Limite, incluindo o Teorema do Confronto, fornecem ferramentas rigorosas para avaliar limites sem ter de fornecer uma prova LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkMtRiM2Ji1JI21pR0YkNiVRJyYjOTQ5O0YnLyUnaXRhbGljR0Y0Ri8tRiw2LVEoJm1pbnVzO0YnRi9GMkY1RjdGOUY7Rj1GP0ZBRkQtRkk2JVEnJiM5NDg7RidGTEYvRi9GK0Yv para cada limite que encontrarmos. A qualidade mais importante a ser desenvolvida ao longo deste cap\303\255tulo \303\251 a habilidade para aplicar as leis de limite em uma ordem apropriada para avaliar um limite.
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7"><Font encoding="UTF-8">Qual \303\251 o Pr\303\263ximo?</Font></Text-field> O pr\303\263ximo cap\303\255tulo ser\303\241 nossa primeira aplica\303\247\303\243o extensiva das Leis de Limite.
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