Parte 3

[size=100][b]INTRODUÇÃO[br][/b][br][b]1.[/b] Nesta construção, oberve o controle deslizante " x̅ " que representa um ponto x̅ pertencente ao intervalo [a,b]. E além disso, está representado também o retângulo em cor azul, cuja altura é dada por f( x̅ ) e cuja base coincide com o comprimento do intervalo [a,b].[/size]
[b][b][i][I[sub]i [/sub]- CP] [/i][/b]a) [/b]Ajuste os controles deslizantes para [b]a = 0,[/b] [b]b = 8 e [b][b]x̅ = 4 [/b][/b][/b]. Determine a área do retângulo ABCD.
[b][b][i][I[sub]i [/sub]- CP] [/i][/b]b) [/b]Agora ajuste os controles deslizantes para [b]a = 1,[/b] [b]b = 5 e [b]x̅ = 3[/b][/b]. Determine a área do retângulo ABCD.
[b][b][i][I[sub]i [/sub]- CP] [/i][/b]c) [/b]De modo geral, considerando um intervalo qualquer [a, b] e [b][b]x̅ [/b][/b][math]\in[/math] [a,b], qual a expressão que representa a área do retângulo ?
[i][b][I[sub]e[/sub]][/b] [/i][b]d) [/b]Posicione o controle deslizante em a = 0 e b =8 e observe o valor da integral.
[i][b][I[/b][sub][b]e[/b][/sub][/i][b][i]][/i] e) [/b]Posicione o controle deslizante em a = 1 e b = 5 e observe o valor da integral.
[b][b][i][I[sub]r[/sub]] [/i][/b]f) [/b][size=150]Com base nos resultados dos itens (a) e (b), o que você observa em relação ao valor da integral nos respectivos intervalos?[/size]
[justify][size=100][size=150][b][/b][/size][/size][/justify][size=150][size=100][justify][/justify][/size][/size][justify][b][/b][/justify][size=150][justify][b][/b][/justify][/size][size=200][size=150][justify][b][/b][/justify][/size][size=150][justify][b][b][i][I[sub]f[/sub]] [/i][/b]FORMALIZANDO O PENSAMENTO[/b][/justify][size=100][justify][b][/b][/justify][/size][/size][size=150][b]Teorema do Valor Médio para Integrais[/b][br]Seja f uma função contínua em um intervalo fechado [a,b].[br]Então [b]existe[/b] pelo menos um número [b]x̅[/b] em [a,b] tal que[/size][size=150][size=100][justify][br][img]data:image/png;base64,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[/img][br][/justify][/size][/size][size=150]Em outras palavras, existe um ponto  x̅  no intervalo [a,b] de modo que o valor da integral nesse intervalo é igual a área do retângulo cuja altura é[b] f(x̅)[/b] e a base o comprimento do intervalo.[br][/size][size=150][size=100][justify][/justify][/size][/size][/size][size=150][size=100][justify][/justify][/size][/size][size=150][size=100][justify][/justify][/size][/size][size=150][size=100][justify][/justify][/size][/size][size=150]Dessa forma, podemos interpretar [b]f(x̅)[/b] como o valor médio da função no intervalo [a,b]. Em[br]consequência dessa proposição, esse valor médio pode ser calculado da seguinte forma:[br][img]data:image/png;base64,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[/img][/size][br]
[size=150][b]2[/b]. Observe a construção a seguir e perceba que o intervalo mudou para [x, x + Δx].[/size]
[size=150][b][i][I[sub]e[/sub]][/i] a)[/b] Com base na construção acima qual seria a expressão que define a área do retângulo ABCD ?[/size]
[size=150][b][b][i][I[sub]e[/sub]] [/i][/b]b)[/b] Da mesma forma, qual expressão que define, em termos de integral, a área do trapézio ABFE?[/size]
[size=150][b][b][i][I[sub]r[/sub]] [/i][/b]c)[/b] Considerando que na construção o valor de [b]f([/b][b]x̅)[/b] é o [b]valor médio[/b] da função neste intervalo [x, x + Δx], qual a relação que podemos concluir entre as expressões dos itens (a) e (b)?[/size]
[b][i][I[sub]f[/sub]] [/i][/b][b]FORMALIZANDO O PENSAMENTO[br][/b]Na construção realizada, o ponto [b]x̅[/b] foi escolhido dentro do intervalo [x, x + Δx] de modo que a área do retângulo construído seja exatamente igual à área sob o gráfico da função nesse mesmo intervalo. Assim, temos que:[br][br][img]data:image/png;base64,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[/img]
[size=150][b]3.[/b] A construção mostra o intervalo [x, x+Δx], a região correspondente à integral nesse pequeno trecho e o ponto [b] [b]x̅[/b][/b], cuja altura [b] f(x̅)[/b] define o retângulo ABCD associado. [/size]
[size=150][b][b][i][I[sub]e[/sub]] [/i][/b]a)[/b] Movimente o controle deslizante lentamente Δx de modo que ele fique bem próximo de zero, para qual valor [b]x̅[/b] parece tender dentro do intervalo [x, x+Δx]?[/size]
[b][size=150][b][i][I[sub]r[/sub]] [/i][/b]b)[/size][/b] [size=150]Utilizando a construção dada podemos afirmar que 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[/img]? Justifique.[/size]
[b][i][I[sub]f[/sub]] [/i][/b][b]FORMALIZANDO O PENSAMENTO[/b][br]Em cada posição do controle deslizante , o ponto [b]x̅[/b] permanece contido no intervalo [x, x + Δx]. Isso garante as desigualdades[br][img]data:image/png;base64,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[/img][br]e, equivalentemente,[br][img]data:image/png;base64,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[/img][br]Quando o intervalo é reduzido e Δx se aproxima de zero, a distância entre x̅e x também se aproxima de zero. Assim,[br][br][img]data:image/png;base64,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[/img][br]
Schließen

Information: Parte 3