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Cálculo de volume de revolução - Histórico de revisões
2024-03-28T16:19:19Z
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Ist12543 em 21h07min de 23 de março de 2018
2018-03-23T21:07:29Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Revisão anterior</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revisão das 21h07min de 23 de março de 2018</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l4" >Linha 4:</td>
<td colspan="2" class="diff-lineno">Linha 4:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*CONTEXTO : Primeiro ciclo universitário</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*CONTEXTO : Primeiro ciclo universitário</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*AREA: Matemática</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*AREA: Matemática</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*DISCIPLINA: Calculo <del class="diffchange diffchange-inline">diferencial </del>e <del class="diffchange diffchange-inline">integral </del>2</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*DISCIPLINA: Calculo <ins class="diffchange diffchange-inline">Diferencial </ins>e <ins class="diffchange diffchange-inline">Integral </ins>2</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*ANO: 1</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*ANO: 1</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*LINGUA: pt</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*LINGUA: pt</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*AUTOR: <del class="diffchange diffchange-inline">Equipa Calculo diferencial </del>e <del class="diffchange diffchange-inline">integral 2</del></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*AUTOR: <ins class="diffchange diffchange-inline">Ana Moura Santos </ins>e <ins class="diffchange diffchange-inline">Miguel Dziergwa</ins></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*MATERIA PRINCIPAL: </div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*MATERIA PRINCIPAL: <ins class="diffchange diffchange-inline">Aplicações ao cálculo de grandezas físicas</ins></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*DESCRICAO: </div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*DESCRICAO: <ins class="diffchange diffchange-inline">Cálculo de volume de um sólido de revolução</ins></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*DIFICULDADE: <del class="diffchange diffchange-inline">easy</del></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*DIFICULDADE: <ins class="diffchange diffchange-inline">**</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*TEMPO MEDIO DE RESOLUCAO: 15 mn</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*TEMPO MEDIO DE RESOLUCAO: 15 mn</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*TEMPO MAXIMO DE RESOLUCAO: 30 mn</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*TEMPO MAXIMO DE RESOLUCAO: 30 mn</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*PALAVRAS CHAVE: </div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*PALAVRAS CHAVE: <ins class="diffchange diffchange-inline">função integrável à Riemann, integral como soma de áreas circulares</ins></div></td></tr>
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Ist12543
http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?title=C%C3%A1lculo_de_volume_de_revolu%C3%A7%C3%A3o&diff=2048&oldid=prev
Ist178052: Criou a página com "<div class="toccolours mw-collapsible mw-collapsed" style="width:420px"> '''Metadata''' <div class="mw-collapsible-content"> *CONTEXTO : Primeiro ciclo universitário *AREA:..."
2016-09-02T14:20:14Z
<p>Criou a página com "<div class="toccolours mw-collapsible mw-collapsed" style="width:420px"> '''Metadata''' <div class="mw-collapsible-content"> *CONTEXTO : Primeiro ciclo universitário *AREA:..."</p>
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*CONTEXTO : Primeiro ciclo universitário<br />
*AREA: Matemática<br />
*DISCIPLINA: Calculo diferencial e integral 2<br />
*ANO: 1<br />
*LINGUA: pt<br />
*AUTOR: Equipa Calculo diferencial e integral 2<br />
*MATERIA PRINCIPAL: <br />
*DESCRICAO: <br />
*DIFICULDADE: easy<br />
*TEMPO MEDIO DE RESOLUCAO: 15 mn<br />
*TEMPO MAXIMO DE RESOLUCAO: 30 mn<br />
*PALAVRAS CHAVE: <br />
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Na figura abaixo está representada a região compreendida entre os gráficos das funções \(f\) e \(g\), no intervalo \( [0,1] \), sendo as funções dadas por \(\pmb{\text{f(x)=}}\pmb{1-x}\) e \(\pmb{\text{g(x)=}}\pmb{\sinh\left(\frac{3x}{2}\right)+3}\).<br />
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[[File:VolRevo.gif]]<br />
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O volume do sólido obtido quando se faz a revolução desta região em torno do eixo dos xx é igual a:<br />
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A)\(\pmb{\frac{1}{6}\pi\left(25+\sinh(3)+24\cosh\left(\frac{3}{2}\right)\right)}\)<br />
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B)\(\pmb{\frac{1}{36}\pi^2\left(11+4\cosh\left(\frac{3}{2}\right)\right)^2}\)<br />
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C)\(\pmb{\frac{1}{6}\pi\left(29+\sinh(3)+24\cosh\left(\frac{3}{2}\right)\right)}\)<br />
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D)\(\pmb{\frac{1}{6}\left(11+4\cosh\left(\frac{3}{2}\right)\right)}\)<br />
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Para obter o zip que contém as instâncias deste exercício clique aqui(volumesRevolucao)<br />
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Se deseja obter o código fonte que gera os exercícios contacte miguel.dziergwa@ist.utl.pt</div>
Ist178052