tag:blogger.com,1999:blog-21079026266160814322024-03-13T22:34:07.668-07:00...::Blog do Prof. Deivison::...Anonymoushttp://www.blogger.com/profile/10465574769320496687noreply@blogger.comBlogger19125tag:blogger.com,1999:blog-2107902626616081432.post-60651530657046691162015-06-22T18:48:00.000-07:002015-06-22T19:02:00.609-07:00...::Coeficiente Angular e Linear de uma Função do 1º Grau::...<h2 style="text-align: center;">
<b>COEFICIENTE ANGULAR E LINEAR DE UMA FUNÇÃO DO 1º GRAU</b></h2>
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<b> </b>Prof. Esp. Deivison da Silva e Silva</div>
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e-mail:profdeivison2013@gmail.com</div>
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Definição: Uma função do 1º grau
é toda função da forma <b><i>f(x) = ax + b</i></b>, onde <b><i>a</i></b>
e <b><i>b</i>
</b>são números reais e a≠0.<o:p></o:p></div>
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Observação: Observe que
as únicas restrições para os valores de <b><i>a</i></b><i>,</i>
é que os mesmos sejam reais e diferentes de zero. Já os valores de <b><i>b</i></b>,
apenas basta que sejam reais.<o:p></o:p></div>
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Exemplos:<o:p></o:p></div>
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a)<span style="font-size: 7pt; font-stretch: normal;">
</span><!--[endif]-->f(x) = 2x -4 b) g(x) = -2x c) h(x) = -x+2 d)
t(x) = x<o:p></o:p></div>
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Escreva essas funções acima no seu
caderno e identifique em cada uma delas os valos de <b><i>a </i></b>e <b><i>b</i></b>.<o:p></o:p></div>
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O gráfico de uma função do 1º grau é representado por uma <b>reta</b>. <o:p></o:p></div>
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Numa função do primeiro grau temos dois coeficientes, <b>coeficiente angular e coeficiente Linear.<o:p></o:p></b></div>
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O <b><i>coeficiente angular</i></b> “<b><i>a”</i></b> está relacionado com o valor da
tangente do ângulo que a reta que representa o gráfico, forma com o eixo de x,
contado no sentido anti-horário.<o:p></o:p></div>
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Observe
a imagem:<o:p></o:p></div>
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De
acordo com o valor do coeficiente angular podemos classificar as funções do 1º
grau em <b><i>crescente </i></b>ou <b><i>decrescente</i></b>.<br />
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1º Caso: Se a > 0 teremos uma função que
chamamos de <b><i>Função Crescente</i></b>.<br />
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2º Caso: Se a < 0 teremos uma função que
chamamos de <b><i>Função decrescente</i></b>.<o:p></o:p></div>
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Exemplos de Funções Crescentes.<o:p></o:p></div>
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a)<span style="font-size: 7pt; font-stretch: normal;">
</span><!--[endif]-->f(x) = 2x + 4 b) g(x) = x – 1 c) h(x) = 3x + 5<o:p></o:p></div>
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Exemplos de funções decrescentes.<o:p></o:p></div>
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</span><!--[endif]-->f(x) = -4x + 4 b) g(x) = -x – 3 c) h(x) = -5x + 4<o:p></o:p></div>
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<b><i>Coeficiente
Linear “b”</i></b> está relacionado com o valor da ordenada do ponto de
intersecção do gráfico com o eixo de y.<o:p></o:p></div>
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Isto é, dada
uma função do tipo f(x) = ax + b, o ponto de intersecção do gráfico com o eixo
de y é o par ordenado (0,b). <o:p></o:p></div>
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Observe o
exemplo, dada função f(x) = 2x + 2. Observe o valor de b da função.<o:p></o:p></div>
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Bom pessoal, texto básico, simples mas com informações importantes para quem está estudando matemática. Até a próxima!!</div>
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Anonymoushttp://www.blogger.com/profile/10465574769320496687noreply@blogger.com10tag:blogger.com,1999:blog-2107902626616081432.post-15325249185237358142015-06-02T07:16:00.001-07:002015-06-02T07:20:29.399-07:00...::De volta o Blog do Professor Deivison da Silva::...<div class="separator" style="clear: both; text-align: center;">
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<span style="font-size: large;">Salve, salve pessoal! Em primeiro
lugar, bom dia todos e todos os leitores e leitoras do blog. Depois de um bom
tempo parado por motivos superiores, venho informar aos leitores do <i>blog do professor Deivison</i> que estamos
de volta com muitos projetos, informações, curiosidades, tutoriais, artigos
relacionados a essa área especial, muito temida por muitos: a Matemática. <o:p></o:p></span></div>
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<span style="font-size: large;"><br /></span></div>
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<span style="font-size: large;">Voltamos com várias ideias
interessantes para propor e auxiliar aos professores de Matemática e de áreas
afim, para os mesmos usarem como ferramenta de auxilio no processo de ensino e
Aprendizagem.<o:p></o:p></span></div>
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<span style="font-size: large;">Espero que possam curtir, compartilhar,
acessar e aproveitar o melhor do <i>blog do
professor Deivison.</i> Que Deus nos abençoe e nos dê sabedoria para
continuarmos nessa luta tão árdua, mas gratificante. Amém!<o:p></o:p></span></div>
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“<b><i>Ensinar não é transferir
conhecimento, mas criar as possibilidades para a sua própria produção ou a sua
construção</i></b>.” </div>
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<b style="text-indent: 47.2000007629395px;"><i>Paulo Freire</i></b></div>
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Anonymoushttp://www.blogger.com/profile/10465574769320496687noreply@blogger.com0Pedreiras - MA, Brasil-4.5719153 -44.600972000000013-5.0746303 -45.24641900000001 -4.0692002999999994 -43.955525000000016tag:blogger.com,1999:blog-2107902626616081432.post-14661918138555934322013-10-16T07:51:00.000-07:002015-06-22T18:57:26.839-07:00...::Transformação Linear 1ª Parte::...<div style="text-align: center;">
<span style="color: orange; font-size: large;"><b>TRANSFORMAÇÃO LINEAR</b></span></div>
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Prof. Esp. Deivison da Silva e Silva</div>
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e-mail:profdeivison2013@gmail.com<br />
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Introdução;</div>
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Situação: Se 1L de gasolina custa R$3,00, se uma pessoa abastecer <b>x</b> L de gasolina, pagaria R$ 3<b>x</b> de combustível. Escrevendo na forma de função, teremos:</div>
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V(x) = 3.x , onde V(x) é o valor a ser pago por <b>x </b>Litros de gasolina. Graficamente temos: </div>
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Vamos analisar nesta situação duas características simples porém muito interessante.</div>
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<ul>
<li>Para calcular o valor a ser pago por (x<span style="font-size: xx-small;">1 + </span>x<span style="font-size: xx-small;">2</span>) L de combustível.</li>
</ul>
1ª Forma: Multiplicar (x<span style="font-size: xx-small;">1+</span>x<span style="font-size: xx-small;">2</span>) por 3 assim: 3.(x<span style="font-size: xx-small;">1 + </span>x<span style="font-size: xx-small;">2</span>).<br />
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2ª Forma: Calcular V(x<span style="font-size: xx-small;">1</span>), V(x<span style="font-size: xx-small;">2</span>) e somá-los em seguida assim:</div>
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V(x<span style="font-size: xx-small;">1 + </span>x<span style="font-size: xx-small;">2</span>) = 3.(x<span style="font-size: xx-small;">1 + </span>x<span style="font-size: xx-small;">2</span>) = 3x<span style="font-size: xx-small;">1 +</span>3<span style="font-size: xx-small;"> </span>x<span style="font-size: xx-small;">2 </span>= V(x<span style="font-size: xx-small;">1</span>) +V(x<span style="font-size: xx-small;">2</span>).</div>
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<ul>
<li>Se a quantidade de litros de gasolina for multiplicada por um fator k o valor a ser pago será multiplicado por este mesmo fator k assim:</li>
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V(k.x) = k.(3.x) = k.(3.x) = k.V(x).<br />
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<b><span style="font-family: "Times New Roman","serif";">Definição:</span></b><span style="font-family: "Times New Roman","serif";"> Sejam V e W dois Espaços
Vetoriais. Uma Transformação Linear é uma função de V em W, </span></div>
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<li><span style="font-family: Times New Roman, serif;">F(u + v) = F(u) + F(v), para todo u,v pertencentes a V;</span></li>
<li><span style="font-family: Times New Roman, serif;">F(k.v) = k. F(v), para todo v pertencente a V e k pertencente ao Conjunto dos números Reais.</span></li>
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<b><span style="font-family: "Times New Roman","serif";">Observação:</span></b><span style="font-family: "Times New Roman","serif";"> No caso em que V = W, uma
Transformação Linear F: V-->V <span style="mso-text-raise: -3.0pt; position: relative; top: 3.0pt;"><v:shapetype coordsize="21600,21600" filled="f" id="_x0000_t75" o:preferrelative="t" o:spt="75" path="m@4@5l@4@11@9@11@9@5xe" stroked="f"><v:stroke joinstyle="miter"><v:formulas><v:f eqn="if lineDrawn pixelLineWidth 0"><v:f eqn="sum @0 1 0"><v:f eqn="sum 0 0 @1"><v:f eqn="prod @2 1 2"><v:f eqn="prod @3 21600 pixelWidth"><v:f eqn="prod @3 21600 pixelHeight"><v:f eqn="sum @0 0 1"><v:f eqn="prod @6 1 2"><v:f eqn="prod @7 21600 pixelWidth"><v:f eqn="sum @8 21600 0"><v:f eqn="prod @7 21600 pixelHeight"><v:f eqn="sum @10 21600 0"></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:formulas><v:path gradientshapeok="t" o:connecttype="rect" o:extrusionok="f"><o:lock aspectratio="t" v:ext="edit"></o:lock></v:path></v:stroke></v:shapetype><v:shape id="_x0000_i1025" o:ole="" style="height: 14.25pt; width: 48pt;" type="#_x0000_t75"><v:imagedata o:title="" src="file:///C:\Users\Deivison\AppData\Local\Temp\msohtmlclip1\01\clip_image001.wmz"></v:imagedata></v:shape><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025"
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Linear</b>.<o:p></o:p></span></div>
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<b><span style="font-family: "Times New Roman","serif";">EXEMPLOS<o:p></o:p></span></b></div>
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<span style="font-family: 'Times New Roman', serif;">Ex1: Verificar se a relação abaixo é ou não uma Transformação Linear:</span></div>
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Bom, pessoal que acompanha o blog em breve traremos a continuação desse artigo. Um forte abraço e bons estudos!!</div>
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Anonymoushttp://www.blogger.com/profile/10465574769320496687noreply@blogger.com2Pedreiras - MA, República Federativa do Brasil-4.574351 -44.598681700000043-30.0963855 -85.907275700000042 20.9476835 -3.2900877000000435tag:blogger.com,1999:blog-2107902626616081432.post-76004386016811679112013-06-26T17:29:00.000-07:002015-06-22T19:02:45.939-07:00...::Curso de Matemática Básica::...<div class="separator" style="clear: both; text-align: center;">
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Prof. Esp. Deivison da Silva e Silva</div>
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e-mail:profdeivison2013@gmail.com</div>
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<br />
<span style="font-size: 13.5pt; text-align: justify; text-indent: 35.4pt;">Olá leitores do Blog do Professor
Deivison, estou escrevendo este artigo para apresentar o curso que ministrarei
sobre <b><i>Matemática Básica</i></b>.</span><br />
<div style="margin: 0cm 0cm 13.5pt; text-indent: 35.4pt;">
<span style="font-size: 13.5pt;">Sou professor da Rede Pública Estadual e Municipal,
ministrei disciplinas na UEMA e em outras instituições de nível superior e
nesse contato com os alunos, ministrando aulas de matemática e física, percebi
que a maior dificuldade por parte dos alunos é na matemática básica. <o:p></o:p></span></div>
<div style="margin-bottom: 13.5pt; margin-left: 0cm; margin-right: 0cm; margin-top: 0cm; text-align: justify; text-indent: 35.4pt;">
<span style="font-size: 13.5pt;"><br />
Por esse motivo, decidi
ministrar esse curso para dirimir essas dificuldades que fazem da matemática o <b>“bicho papão"</b> para muitos e acabar
com essa imagem que muitos têm da mesma. Sem contar que em Concursos Públicos tem
uma importância muito grande, o Curso é ideal para quem quer prestar <b>Vestibular, Concurso Público, ENEM e também
como reforço escolar</b>.<o:p></o:p></span></div>
<div style="margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-indent: 35.4pt;">
<span style="font-size: 13.5pt;">Abordaremos vários temas importantes e
fundamentais para a compreensão da Matemática e garanto que os participantes
desse Curso terão outra visão depois de participarem desse curso. Não perca
tempo, garanta já a sua vaga, pois, são vagas limitadas!<o:p></o:p></span></div>
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<b><span style="font-size: 13.5pt;"><span style="color: red;">Para maiores informações:<o:p></o:p></span></span></b></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0cm; text-align: center; text-indent: 35.4pt;">
<b><span style="font-size: 13.5pt;"><span style="color: red;">Cel. (99)982605328<o:p></o:p></span></span></b></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0cm; text-align: center; text-indent: 35.4pt;">
<b><span style="font-size: 13.5pt;"><span style="color: red;">E-mail: </span><o:p></o:p></span></b><span style="text-align: right;"><b><span style="color: red;">profdeivison2013@gmail.com</span></b></span></div>
Anonymoushttp://www.blogger.com/profile/10465574769320496687noreply@blogger.com0Pedreiras - MA, República Federativa do Brasil-4.574351 -44.598681700000043-55.0701205 -127.21586920000004 45.9214185 38.018505799999957tag:blogger.com,1999:blog-2107902626616081432.post-73578631888490999602013-05-31T07:22:00.001-07:002013-05-31T07:32:26.850-07:00..::Enem 2013::...<div style="text-align: center;">
<b><span style="color: orange; font-size: large;">ENEM 2013</span></b></div>
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Prof. Esp. Deivison da Silva e Silva</div>
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e-mail:deivisonflp@hotmail.com</div>
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O prazo final para pagamento do Boleto Enem 2013 se encerra nesta quarta-feira (29/05). Neste artigo os estudantes que pretendem participar do Exame Nacional do Ensino Médio deste ano poderão obter informações gerais sobre a taxa de inscrição e também como imprimir e pagar o boleto do Enem 2013. Confira abaixo:</div>
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Foi divulgado pelo, INEP – Instituto Nacional de Estudos e Pesquisas Educacionais Anísio Teixeira, juntamente com o MEC – Ministério da Educação, o <a href="http://www.enem2013.org/edital-do-enem-2013-esta-previsto-para-maio.html" target="_blank">edital do Enem 2013</a>, que trás todas as regras e datas do exame.</div>
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Entre as informações mais importantes que o edital trás está o período de inscrições do <a href="http://www.enem2013.org/" target="_blank">Enem 2013</a>, que encerrou-se nesta segunda-feira, 27/05/2013.</div>
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Assim como aconteceu nas edições anteriores os estudantes que não possuem direito à isenção devem pagar a taxa de inscrição para participar do exame. O valor da taxa de inscrição é de R$ 35,00.</div>
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Os estudantes que completarão o ensino médio em 2013 são automaticamente isentos do pagamento desta taxa no ato da inscrição. Todos os outros participantes devem pagar a taxa de inscrição ou <a href="http://www.enem2013.org/isencao-enem-2013.html" target="_blank">declarar carência solicitando a isenção no Enem 2013</a>.</div>
<h2 style="text-align: justify;">
Isenção de Taxa de Inscrição no Enem 2013</h2>
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A isenção foi concedida apenas aos estudantes que realmente não têm condições de pagar a taxa de inscrição, sendo levados em conta os dados do grupo familiar informados pelo próprio candidato ao sistema.</div>
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Os pedidos foram analisados pelo INEP podendo ser deferidos ou indeferidos. Em caso de deferimento, o estudante mais nada precisou fazer. Em caso de indeferimento, é necessário <strong>imprimir o boleto do Enem 2013</strong> na Página de Acompanhamento de Inscrição e efetuar o pagamento do mesmo até a sua data de vencimento. O prazo final para pagamento do boleto do <a href="http://www.enem2013.org/" target="_blank">Enem 2013</a> termina nesta quarta-feira, 29/05/2013. Para acessar a Página de Acompanhamento de Inscrição do Enem 2013 siga o link a seguir: <a href="http://www.enem.inep.gov.br/" target="_blank">http://www.enem.inep.gov.br</a>. É necessário informar CPF e senha para entrar.</div>
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Quem não pagar o boleto até esta data estará excluído do Enem 2013. O pagamento poderá ser efetuado em qualquer agência bancária, casas lotéricas, postos de recebimento autorizados e Internet Banking.</div>
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Um questionamento enviado por muitos estudantes nos últimos dias foi se é necessário apresentar nos dias de aplicação das provas o boleto com comprovante de pagamento do mesmo ou algum documento relacionado ao deferimento do pedido de isenção. A resposta é não! No dia das provas leve apenas o Cartão de Confirmação de Inscrição, caneta esferográfica na cor preta e documento de identificação oficial com foto.</div>
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Fonte: <a href="http://www.enem2013.org/" style="text-align: justify;">http://www.enem2013.org/</a></div>
Anonymoushttp://www.blogger.com/profile/10465574769320496687noreply@blogger.com0Pedreiras - MA, República Federativa do Brasil-4.574351 -44.598681700000043-30.0963855 -85.907275700000042 20.9476835 -3.2900877000000435tag:blogger.com,1999:blog-2107902626616081432.post-72636222494149911392013-05-24T16:39:00.001-07:002015-06-22T19:00:04.338-07:00...::Introdução ao Estudo da Lógica Matemática::...<div style="text-align: center;">
<b><span style="color: orange; font-size: large;">LÓGICA MATEMÁTICA</span></b></div>
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Prof. Esp. Deivison da Silva e Silva</div>
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e-mail:profdeivison2013@gmail.com</div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Lógica Matemática</span></div>
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<br /><br /><br /><br /><br /><br />No estudo da Lógica Matemática o primeiro conceito que vamos tratar é o conceito de <b>Proposição.</b><br /><br /><br /><br /><br /><br /><br /><b><i>PROPOSIÇÃO:</i></b> é toda sentença, <i>expressa</i> em palavras ou símbolos, que <i>exprima um juízo</i> ao qual se possa atribuir um dos valores lógicos: <i>Verdadeiro ou Falso.</i><br /><br /><br /><br />Segundo Edgard [1], as proposições transmitem pensamentos, isto é, afirmam fatos ou exprimem juízos que formamos a respeito de determinados entes.<br /><br />São exemplos de proposições:<br /><br />1- A neve é branca.<br />2- São Luís é a capital do Maranhão.<br />3- π é irracional.<br />4- O número 6 é par.<br /><br />Observe que em todos esses exemplos, é possível atribuirmos um valor lógico ou <b><i>verdadeiro</i></b> ou <b><i>falso</i></b> para cada item.<br /><br />Não são exemplos de proposições:<br /><br />5-Pare!<br />6-Qual sua idade?<br />7-Volte para casa.<br /><br />Já nos itens acima, verifique que <i><b>não é possível julgá-los</b></i> como <b><i>verdadeiro</i></b> ou <b><i>falso</i></b>, ferindo assim o conceito de proposição. <br /><br /><br />No nosso estudo de Lógica Matemática, seguiremos os seguintes princípios, pois os mesmos norteiam a Lógica Proposicional:</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">1º) <b><i>Princípio da não contradição:</i></b> Uma proposição não pode ser verdadeira e falsa ao mesmo tempo.<br /><br /><br />2º) <b><i>Principio do Terceiro Excluído:</i></b> Uma proposição só pode assumir um de dois valores lógicos possíveis, ou verdadeiro ou falso.<br /><br />Devido o Princípio do Terceiro Excluído dizemos que a Lógica Matemática é uma <b><i>Lógica Bivalente.</i></b><br /></span><br />
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Valor Lógico das Proposições</span></div>
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<br /><b>Definição: </b>Dizemos que valor lógico de uma proposição é a <i><b>falsidade</b></i> se a proposição for falsa e <i><b>verdade</b></i> se a proposição for verdadeira.<br /><br />Usaremos as seguintes letras <b><i>V </i></b>e <i><b>F</b></i> para representar de forma abreviada a Falsidade e a Verdade respectivamente.</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br />Assim por exemplo:</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /> a) O fogo queima. </span><span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><i>“O valor lógico da proposição do item a é VERDADE (V).”</i></span><span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /></span><span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /> b) O quadrado tem 6 lados. </span><span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><i>“O valor lógico da proposição do item b é FALSO (F).”</i></span><span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /><br /></span><br />
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Proposições Simples e Proposições Compostas</span></div>
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<br />Segundo Edgard [1] as proposições podem ser classificadas sem proposições simples ou proposições atômicas e compostas ou moleculares.<br /><br />No nosso estudo, portanto usaremos a notação de <b><i>proposição simples</i></b> e <i><b>proposição compostas</b></i>.<br /><br /><br /><b>Definição:</b> Proposição Simples é aquela que <i><b>não contém</b></i> qualquer outra proposição como sua componente.<br /><br />Para representar as proposições simples, geralmente usaremos as letras latinas minúsculas m, p, t, q, r,..., <b><i>são as letras proposicionais.</i></b><br /><br />Exemplos de proposições simples:<br /><br />r: 4 é quadrado perfeito.<br />t: ⅔ é um número inteiro. <br />p: O número 6 é ímpar.<br /><br /><b>Definição:</b> Proposição Composta é aquela <i><b>que contém </b></i>outra proposição como sua componente.<br /><br />Para representar as proposições compostas, geralmente usaremos as letras latinas maiúsculas M, P, T, Q, R,..., <b><i>são as letras proposicionais.</i></b><br /><br />Exemplos de proposições compostas:<br /><br />P: João é rico e Paulo é estudante.<br />Q: Se eu estudar então serei aprovado.<br />B: Marcos é médico ou Flávia é escritora. <br /><br /><br />Ficamos por aqui, um forte abraço e até nosso próximo artigo.<br /><br />Bibliografia:</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><br /> [1] Iniciação à Lógica Matemática, Alencar Filho, Edgard.</span><br />
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Anonymoushttp://www.blogger.com/profile/10465574769320496687noreply@blogger.com1Pedreiras - MA, República Federativa do Brasil-4.574351 -44.598681700000043-30.0963855 -85.907275700000042 20.9476835 -3.2900877000000435tag:blogger.com,1999:blog-2107902626616081432.post-87549576845862376292013-05-10T08:57:00.000-07:002015-06-22T19:00:22.757-07:00...::Multiplicação de Matrizes::...<!--[if !mso]>
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<br />
<div align="center" class="MsoNormal" style="text-align: center;">
<b><span style="color: orange; font-size: medium; mso-bidi-font-weight: normal;">MULTIPLICAÇÃO DE MATRIZES</span></b><br />
<b><span style="color: orange; font-size: xx-small; mso-bidi-font-weight: normal;"><br /></span></b>
<b><span style="color: orange; font-size: xx-small; mso-bidi-font-weight: normal;"><br /></span></b>
<br />
<div align="right" class="MsoNormal" style="text-align: right;">
Prof. Esp. Deivison da Silva e Silva</div>
<div align="right" class="MsoNormal" style="text-align: right;">
e-mail:profdeivison2013@gmail.com</div>
<br />
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div class="MsoNormal">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6QdY7sESVHrFejFnp6SbTXnbeqeOYF6m5p_XNE-uTFZk1HhlhMkXvWz8UVlo_ay48h3DyeHUPbuiuAfqX7FYX1IL6VNyivyeUOe26gtkZRBwyzq6xzhJTQ5so3nY4r9WQzxreYd6e6flV/s1600/MATRIZES.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6QdY7sESVHrFejFnp6SbTXnbeqeOYF6m5p_XNE-uTFZk1HhlhMkXvWz8UVlo_ay48h3DyeHUPbuiuAfqX7FYX1IL6VNyivyeUOe26gtkZRBwyzq6xzhJTQ5so3nY4r9WQzxreYd6e6flV/s1600/MATRIZES.jpg" /></a></div>
<br /></div>
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<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="mso-tab-count: 1;"> </span><span style="line-height: 115%;">Seja uma matriz A de ordem <b>mxn</b><span style="mso-spacerun: yes;"><b> </b> </span>e uma matriz B de ordem nxk, definimos o
produto da matriz A pela matriz B a matriz C de ordem <b>mxk</b>, de forma que cada
elemento de C (cij) satisfaça a seguinte definição.</span></div>
<div class="MsoNormal">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
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src="data:image/png;base64,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<div align="center" class="MsoNormal" style="text-align: center;">
<br />
<span style="font-size: 14.0pt; line-height: 115%;"></span></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-indent: 35.4pt;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-indent: 35.4pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Observe que, cada elemento de C é obtido <span style="mso-spacerun: yes;"> </span>multiplicando-se ordenadamente os elementos da
linha i da matriz A pelos elementos correspondentes da coluna j da matriz B e ,
a seguir, somando-se os produtos obtidos.</span></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-indent: 35.4pt;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-indent: 35.4pt;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-indent: 35.4pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Bom, outra coisa interessante que observamos na
definição do produto da matriz A pela matriz B, é que, o produto de duas
matrizes, só é possível se, e somente se,</span> <span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">o número de colunas da matriz A for igual ao numero
de linhas da matriz B. Assim: </span></div>
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<span style="height: 40px; left: 0px; margin-left: 215px; margin-top: 19px; mso-ignore: vglayout; position: absolute; width: 62px; z-index: 1;"></span><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><span style="mso-tab-count: 3;"> </span><b> </b></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><b> A<span style="mso-bidi-font-weight: normal;"><sub>mxn</sub></span><span style="mso-spacerun: yes;"> </span>x<span style="mso-spacerun: yes;"> </span>B<span style="mso-bidi-font-weight: normal;"><sub>nxp</sub></span></b></span></div>
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<br /></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;"><b><span style="mso-bidi-font-weight: normal;"><sub><img alt="" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADwAAAAoCAIAAAAt2Q6oAAAAuUlEQVRYhe3QsRHDIBBE0Q0pgTLo0CVQHmUQXogDZBlbAkVenWf2RwQazbtFG6q1Nn8dVdhfZpZSMjMu6aJT1RudcwaQc6bDVp2qNrSZxRgBxBj9jD1Tbeh+UM/P2DMV2nBQz8nYCxXa50F+xl6o8HWQk7HXKpRSHq8A7O9Syo3otQrjpwAmP7mzo0ro3yQ0K6FZCc1KaFZCsxKaldCshGYlNCuhWQnNSmhWQrO6QIcQ4K8Qwgr9Lz0BBUUDepHgoeQAAAAASUVORK5CYII=" /> </sub></span></b></span></div>
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<br /></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR;">Vejamos a um exemplo prático de multiplicação de
matrizes:</span></div>
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<br /></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-indent: 35.4pt;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; text-indent: 35.4pt;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; text-align: center; text-indent: 35.4pt;">
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/> </span></div>
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<span style="mso-tab-count: 1;"> </span><span style="mso-text-raise: -89.0pt; position: relative; top: 89.0pt;"><br /></span></div>
<div class="MsoNormal">
<span style="font-size: 14.0pt; line-height: 115%;"><span style="mso-tab-count: 1;"> </span>Na multiplicação de matizes o
elemento neutro é a matriz identidade I. </span></div>
<div class="MsoNormal">
<br /></div>
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<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 1"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 1"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 1"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 1"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="List Paragraph"/>
<w:LsdException Locked="false" Priority="29" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Quote"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 1"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 1"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 2"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 2"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 2"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 2"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 3"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 3"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 3"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 3"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 3"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 3"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 3"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 3"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 3"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 3"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 4"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 4"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 4"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 4"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 4"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 4"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 4"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 4"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 5"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 5"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 5"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 5"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 5"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 5"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 5"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 5"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 5"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 5"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 5"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 5"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Emphasis"/>
<w:LsdException Locked="false" Priority="21" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading"/>
</w:LatentStyles>
</xml><![endif]--><!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Tabela normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-qformat:yes;
mso-style-parent:"";
mso-padding-alt:0cm 5.4pt 0cm 5.4pt;
mso-para-margin-top:0cm;
mso-para-margin-right:0cm;
mso-para-margin-bottom:10.0pt;
mso-para-margin-left:0cm;
line-height:115%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri","sans-serif";
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:"Times New Roman";
mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;}
</style>
<![endif]--><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1027"/>
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1"/>
</o:shapelayout></xml><![endif]-->
</div>
<div class="MsoNormal">
<span style="height: 289px; margin-left: 143px; margin-top: 38px; mso-ignore: vglayout; position: absolute; width: 230px; z-index: 251663360;"></span><span style="font-size: 14.0pt; line-height: 115%;"> </span><span style="font-size: 14.0pt; line-height: 115%;">Exemplo:</span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal" style="text-align: center;">
<span style="font-size: 14.0pt; line-height: 115%;"> </span><img alt="" 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<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
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<br /></div>
<div class="MsoNormal" style="text-indent: 35.4pt;">
<br /></div>
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: 14.0pt; line-height: 115%;">Vimos então dois exemplos bem simples e práticos de
multiplicação de matrizes e deixarei aqui mais dois exemplos para você
praticar. </span></div>
<div class="MsoNormal" style="text-indent: 35.4pt;">
</div>
<b><span style="mso-ignore: vglayout;"><span style="font-size: 14.0pt; line-height: 115%;">Ex1:</span></span></b><span style="font-size: 14.0pt; line-height: 115%;"> </span><span style="mso-ignore: vglayout;"><span style="font-size: 14.0pt; line-height: 115%;"></span></span><br />
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</div>
<div class="MsoNormal" style="text-align: center; text-indent: 35.4pt;">
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<span style="mso-tab-count: 1;"> </span></div>
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<br /></div>
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<span style="mso-tab-count: 1;"><span style="mso-fareast-language: PT-BR;"><b>EX2:</b></span> </span></div>
<div style="text-align: center;">
<span style="mso-fareast-language: PT-BR;"><span style="mso-tab-count: 1;"></span><b> </b></span><img alt="" src="data:image/png;base64,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" /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="fr" style="text-indent: 35.4pt;">
“A matemática vista corretamente, possui
não apenas verdade, mas também suprema beleza - uma beleza fria e austera, como
a da escultura.”</div>
<div align="right" class="fr" style="text-align: right; text-indent: 35.4pt;">
<a href="http://pensador.uol.com.br/autor/bertrand_russell/"><span style="mso-bidi-font-weight: normal;"><span style="color: windowtext; text-decoration: none; text-underline: none;">Bertrand
Russell</span></span></a></div>
<br />
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</span>Anonymoushttp://www.blogger.com/profile/10465574769320496687noreply@blogger.com0tag:blogger.com,1999:blog-2107902626616081432.post-59714286507872657972013-04-07T19:08:00.000-07:002015-06-22T19:00:42.783-07:00..::Produtos Notáveis::..<!--[if !mso]>
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<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-size: large;"><span style="color: orange;"><b><span style="line-height: 115%;">PRODUTOS NOTÁVEIS</span></b></span></span><br />
<span style="font-size: large;"><span style="color: orange;"><b><span style="line-height: 115%;"><br /></span></b></span></span>
<br />
<div align="right" class="MsoNormal" style="text-align: right;">
Prof. Esp. Deivison da Silva e Silva</div>
<div align="right" class="MsoNormal" style="text-align: right;">
e-mail:profdeivison2013@gmail.com</div>
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDLm663ohn_tIMy0dul5HYbvLoYJn-s6MPw3MDQNCMfozfZfcxpN7ds_0kpfr_NQQBjiV_8YqWl2Q9ib6FZ_m2zBjSeuka-ZDeF78CiIR2xYBWopKnL9C3HVvESWvPm5Uie8xba9uBIk2J/s1600/prod+notavel2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDLm663ohn_tIMy0dul5HYbvLoYJn-s6MPw3MDQNCMfozfZfcxpN7ds_0kpfr_NQQBjiV_8YqWl2Q9ib6FZ_m2zBjSeuka-ZDeF78CiIR2xYBWopKnL9C3HVvESWvPm5Uie8xba9uBIk2J/s1600/prod+notavel2.JPG" /></a></div>
<br /></div>
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<span style="font-size: large;"><span style="line-height: 115%;">Olá! Estamos de volta com mais um artigo para o Blog do Prof.
Deivison, e desta vez, vamos abordar o tema de <b><i>Produtos Notáveis. </i></b>É um
assunto estudado no 8ª Ano, que considero de fundamental importância seu
conhecimento e desenvolvimento.</span></span></div>
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<br /></div>
<div class="MsoNormal" style="text-indent: 35.4pt;">
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<span style="font-size: large;">
</span><br />
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<span style="font-size: large;"><span style="line-height: 115%;">É muito utilizado em várias situações no Ensino Fundamental e
também Ensino Médio como, por exemplo, na solução de algumas equações do
segundo grau e em Física também.</span></span></div>
<span style="font-size: large;">
</span><br />
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<span style="font-size: large;"><span style="line-height: 115%;">Podemos entender como <b><i>Produtos notáveis,</i></b> o produto de
expressões algébricas que possuem uma maneira geral para sua resolução. Os
produtos notáveis aparecem no cálculo algébrico. Esses produtos são conhecidos
pelo nome de produtos notáveis. </span></span></div>
<span style="font-size: large;">
</span><br />
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<br /></div>
<span style="font-size: large;">
</span><br />
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<span style="font-size: large;"><span style="line-height: 115%;">O termo “<b><i>Produto</i></b>” pode ser o resultado de uma
função de multiplicação e o termo “<b><i>Notável</i></b>” pode ser definido como
“importante”, ou aquilo que se destaca ou de fácil identificação.</span></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<br /></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: large;"><span style="line-height: 115%;">Vamos abordar neste artigo três casos de produtos notáveis
mais comuns um a um passo a passo e resolver alguns exemplos para fixação da
forma de resolução de cada um. Bom, iremos utilizar as letras <b><i>a</i></b>
e <b><i>b</i></b>
no nosso estudo para apresentar as formas de resoluções de produtos notáveis.</span></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<br /></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<br /></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<br /></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
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<span style="font-size: large;">
</span><br />
<div align="center" class="MsoNormal" style="text-align: center; text-indent: 35.4pt;">
<span style="font-size: large;"><b><i><span style="line-height: 115%;">QUADRADO DA SOMA DE DOIS TERMOS</span></i></b><span style="line-height: 115%;"></span></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal">
<br /></div>
<span style="font-size: large;">
</span><br />
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<span style="font-size: large;"><b><span style="line-height: 115%;">(a+b)<sup>2</sup> = (1º termo)<sup>2</sup>+2.(primeiro).(segundo)+(2º
termo)<sup>2</sup>.</span></b></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal">
<span style="font-size: large;"><span style="line-height: 115%;">Ficando assim:</span></span></div>
<span style="font-size: large;">
</span><br />
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-size: large;"><b><span style="line-height: 115%;">(a+b)<sup>2</sup> = a<sup>2</sup>+2ab+b<sup>2</sup></span></b></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: large;"><span style="line-height: 115%;">Vejamos agora a resolução de alguns exemplos de quadrado da
soma de dois termos:</span></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: large;"><span style="line-height: 115%;">Exemplo1: (2a+3b)<sup>2</sup>= (2a)<sup>2</sup>+2. (2a). (3b)
+ (3b)<sup>2</sup></span></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: large;"><span style="line-height: 115%;"> =4a<sup>2</sup>+12ab+9b<sup>2</sup></span></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<br /></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: large;"><span style="line-height: 115%;">Exemplo2: (-5a+2b)<sup>2</sup>=(-5a)<sup>2</sup>+2.(-5a).(2b)+(2b)<sup>2</sup></span></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: large;"><span style="line-height: 115%;">
=25a<sup>2</sup>-20ab+4b<sup>2</sup></span></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<br /></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: large;"><span style="line-height: 115%;">Exemplo3: (</span><span style="line-height: 115%;">½ </span><span style="line-height: 115%;">a + b) = ( </span><span style="line-height: 115%;">½ </span><span style="line-height: 115%;">a)<sup>2</sup>+2. (</span><span style="line-height: 115%;">½ </span><span style="line-height: 115%;">a). (b) +(b)<sup>2</sup></span></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: large;"><span style="line-height: 115%;"> =</span><span style="line-height: 115%;">¼</span><span style="line-height: 115%;">a<sup>2</sup>+ab+b<sup>2</sup>.</span></span></div>
<span style="font-size: large;">
</span><br />
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<br /></div>
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<br /></div>
<div class="MsoNormal" style="text-indent: 35.4pt;">
<br /></div>
<div class="MsoNormal" style="text-indent: 35.4pt;">
<br /></div>
<span style="font-size: large;">
</span><br />
<div align="center" class="MsoNormal" style="text-align: center; text-indent: 35.4pt;">
<span style="font-size: large;"><b><i><span style="line-height: 115%;">QUADRADO DA DIFERENÇA DE DOIS TERMOS</span></i></b></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<br /></div>
<span style="font-size: large;">
</span><br />
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-size: large;"><b><span style="line-height: 115%;">(a-b)<sup>2</sup> = (1º termo)<sup>2</sup>-2.(primeiro).(segundo)+(2º
termo)<sup>2</sup>.</span></b></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal">
<span style="font-size: large;"><span style="line-height: 115%;">Ficando assim:</span></span></div>
<span style="font-size: large;">
</span><br />
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-size: large;"><b><span style="line-height: 115%;">(a-b)<sup>2</sup> = a<sup>2</sup>-2ab+b<sup>2</sup></span></b></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal">
<br /></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: large;"><span style="line-height: 115%;">Vejamos agora a resolução de alguns exemplos de quadrado da diferença
de dois termos:</span></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: large;"><span style="line-height: 115%;">Exemplo1: (-a-3b)<sup>2</sup>= (-a)<sup>2</sup>-2. (-a). (3b)
+ (3b)<sup>2</sup></span></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: large;"><span style="line-height: 115%;"> =a<sup>2</sup>-6ab+9b<sup>2</sup></span></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<br /></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: large;"><span style="line-height: 115%;">Exemplo2: (-4a-b)<sup>2</sup>= (-4a)<sup>2</sup>-2. (-4a).
(b) + (b)<sup>2</sup></span></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: large;"><span style="line-height: 115%;"> =16a<sup>2</sup>+8ab+b<sup>2</sup></span></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="line-height: normal; text-indent: 35.4pt;">
<br /></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: large;"><span style="line-height: 115%;">Exemplo3: (3a-2b)<sup>2</sup>= (3a)<sup>2</sup>-2. (3a). (2b)
+ (2b)<sup>2</sup></span></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: large;"><span style="line-height: 115%;"> =9a<sup>2</sup>-12ab+4b<sup>2</sup></span></span></div>
<div class="MsoNormal" style="text-indent: 35.4pt;">
<br /></div>
<div class="MsoNormal" style="text-indent: 35.4pt;">
<br /></div>
<div class="MsoNormal" style="text-indent: 35.4pt;">
<br /></div>
<div class="MsoNormal" style="text-indent: 35.4pt;">
<br /></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="line-height: normal;">
<br /></div>
<span style="font-size: large;">
</span><br />
<div align="center" class="MsoNormal" style="text-align: center; text-indent: 35.4pt;">
<span style="font-size: large;"><b><i><span style="line-height: 115%;">PRODUTO DA SOMA PELA DIFERENÇA </span></i></b></span></div>
<span style="font-size: large;">
</span><br />
<div align="center" class="MsoNormal" style="text-align: center; text-indent: 35.4pt;">
<br /></div>
<span style="font-size: large;">
</span><br />
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-size: large;"><b><span style="line-height: 115%;">(a+b).(a-b) = (1º termo)<sup>2 </sup>- (2º termo)<sup>2</sup>.</span></b></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal">
<span style="font-size: large;"><span style="line-height: 115%;">Ficando assim:</span></span></div>
<span style="font-size: large;">
</span><br />
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-size: large;"><b><span style="line-height: 115%;">(a+b).(a-b) = a<sup>2</sup>- b<sup>2</sup></span></b></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: large;"><span style="line-height: 115%;">Vejamos agora a resolução de alguns exemplos do produto da
soma pela diferença de dois termos:</span></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: large;"><span style="line-height: 115%;">Exemplo1: (2a+3b). (2a-3b)= (2a)<sup>2</sup>- (3b)<sup>2</sup></span></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: large;"><span style="line-height: 115%;"> =4a<sup>2</sup>-9b<sup>2</sup></span></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: large;"><span style="line-height: 115%;">Exemplo2: (-5a+2b). (-5a-2b)=(-5a)<sup>2</sup> - (2b)<sup>2</sup></span></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: large;"><span style="line-height: 115%;">
=25a<sup>2</sup>- 4b<sup>2</sup>. </span></span></div>
<span style="font-size: large;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: large;"><span style="line-height: 115%;">Bom, pessoal por hoje é só, ficamos por aqui um forte abraço
e até nosso próximo artigo.</span></span></div>
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<br /></div>
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<br /></div>
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<span style="font-size: large;"><span style="line-height: 115%;">Lembrem-se: “Matemática aprende-se
fazendo!”.</span></span></div>
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</span><br />
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Anonymoushttp://www.blogger.com/profile/10465574769320496687noreply@blogger.com0tag:blogger.com,1999:blog-2107902626616081432.post-15698778932771016862013-04-02T07:37:00.000-07:002015-06-22T19:01:05.402-07:00..::Curiosidade Matemática sobre Potências::..<!--[if gte mso 9]><xml>
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<span style="color: orange;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: large; line-height: 115%;">CURIOSIDADE MATEMÁTICA
SOBRE POTÊNCIAS</span></b></span><br />
<span style="color: orange;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: large; line-height: 115%;"><br /></span></b></span>
<span style="color: orange;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: large; line-height: 115%;"><br /></span></b></span>
<br />
<div align="right" class="MsoNormal" style="text-align: right;">
Prof. Esp. Deivison da Silva e Silva</div>
<div align="right" class="MsoNormal" style="text-align: right;">
e-mail:profdeivison2013@gmail.com</div>
</div>
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<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: 14.0pt; line-height: 115%;">Desde meus tempos de Ensino Fundamental, ouvia sempre dos meus
Professores de Matemática que <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">todo número elevado a zero dava como
resultado 1</i></b>, claro não deixando de levar em consideração as observações
com relação a essa base com o expoente. </span></div>
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<br /></div>
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: 14.0pt; line-height: 115%;">Eu sempre que indagava a respeito de como isso era possível?
Os livros de matemática sempre dizem a mesma coisa, <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">que é por definição</i></b> que
isso é verdade, ou seja, você tem que aceitar como verdade acabada.</span></div>
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<br /></div>
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: 14.0pt; line-height: 115%;">Resolvi escrever esse breve texto para trazer uma resposta
mais concreta para isso, simplesmente utilizando algumas propriedades das
potências, as quais são estudadas ao longo do Ensino Fundamental.</span></div>
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<br /></div>
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<span style="font-size: 14.0pt; line-height: 115%;">Dado um Número Real <b style="mso-bidi-font-weight: normal;">a </b></span><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">≠</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14.0pt; line-height: 115%;"> 0 </span></b><span style="font-size: 14.0pt; line-height: 115%;">temos que <b style="mso-bidi-font-weight: normal;">a<sup>0 </sup>= 1 </b>.</span></div>
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<br /></div>
<div class="MsoNormal">
<span style="font-size: 14.0pt; line-height: 115%;">Demostração:</span></div>
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<br /></div>
<div class="MsoNormal">
<span style="font-size: 14.0pt; line-height: 115%;"><span style="mso-tab-count: 1;"> </span>Bom, para nossa demostração iremos
utilizar três propriedades das potências:</span></div>
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<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
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<span style="font-size: 14.0pt; line-height: 115%;"> Agora
atribua valores para <b style="mso-bidi-font-weight: normal;">n</b> e observe que
<b style="mso-bidi-font-weight: normal;">a<sup>0</sup>= 1<sup>n</sup>=1</b>, o
que queríamos mostrar. </span></div>
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<br /></div>
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: 14.0pt; line-height: 115%;">Então fica aqui a minha sugestão aos Professores de
Matemática, utilizar as <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">propriedades das potências</i></b> para
mostrar a seus alunos de uma forma mais interessante esse fato. Também espero que esse
artigo sirva como material de apoio e como fonte de conhecimento para muitos. </span></div>
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<div class="MsoNormal" style="text-indent: 35.4pt;">
<br /></div>
<div class="MsoNormal" style="text-align: center; text-indent: 35.4pt;">
<span style="font-size: 14.0pt; line-height: 115%;">Lembrem-se: “Matemática aprende-se fazendo!!” . </span></div>
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<span style="font-size: 14.0pt; line-height: 115%;">Um forte
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Anonymoushttp://www.blogger.com/profile/10465574769320496687noreply@blogger.com0tag:blogger.com,1999:blog-2107902626616081432.post-48625608130222089302013-03-29T11:02:00.000-07:002015-06-22T19:01:28.357-07:00..::Goemetria Analítica: Distância entre dois pontos::..<!--[if !mso]>
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<br />
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="color: orange;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 20.0pt; line-height: 115%;">GEOMETRIA ANALÍTICA</span></b></span></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div align="right" class="MsoNormal" style="text-align: right;">
<div align="right" class="MsoNormal">
Prof. Esp. Deivison da Silva e Silva</div>
<div align="right" class="MsoNormal">
e-mail:profdeivison2013@gmail.com</div>
</div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<span style="color: lime;">
</span><br />
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="color: white;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 16.0pt; line-height: 115%;">Distância entre dois
Pontos</span></b></span></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: small;"><span style="line-height: 115%;">A Geometria foi criada pelos Gregos, porém, faltava para a
Geometria operacionalidade, que só seria conseguida, mediante a sua fusão com a
Álgebra que ocorreu em meados do Século XVII dando origem ao que temos hoje a <b>Geometria Analítica</b>.</span></span></div>
<div class="MsoNormal" style="text-indent: 35.4pt;">
<br /></div>
<span style="font-size: small;">
</span><br />
<div class="MsoNormal">
<span style="font-size: small;"><span style="line-height: 115%;"> Dois
grandes homens que até então não eram matemáticos, ambos graduados em Direito,
porém, movidos pelo amor a Matemática e também por razões filosóficas foram os
grandes precursores da descoberta da Geometria Analítica. </span></span></div>
<div class="MsoNormal">
<br /></div>
<span style="font-size: small;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: small;"><span style="line-height: 115%;">Um fato curioso, é que os dois realizaram várias descobertas
simultâneas, porém, não trabalharam juntos, o que mostra um caso, entres vários
existentes dentro da ciência, de descobertas simultâneas e independentes.</span></span></div>
<span style="font-size: small;">
</span><br />
<div class="MsoNormal">
<br /></div>
<span style="font-size: small;">
</span><br />
<div class="MsoNormal" style="text-indent: 35.4pt;">
<span style="font-size: small;"><span style="line-height: 115%;">Bom, então vamos ao que interessa! Hoje vamos abordar um tema muito interessante
dentro da Geometria Analítica: <b>Distância
entre dois pontos.</b></span></span></div>
<span style="font-size: small;">
</span><br />
<div class="MsoNormal">
<span style="font-size: small;"><span style="line-height: 115%;"> Consideremos
dois pontos <i><b>A(<span style="font-size: small;"><span style="font-size: small;">x</span><span style="font-size: xx-small;">a</span></span>,y<span style="font-size: xx-small;">a</span>) e B</b></i></span><span style="line-height: 115%;"><i><b><span style="line-height: 115%;">(x<span style="font-size: xx-small;">b</span>,y<span style="font-size: xx-small;">b</span>)</span></b></i> e
suponhamos sua representação no plano cartesiano. Observe a imagem abaixo:</span></span></div>
<span style="font-size: small;">
</span><br />
<div class="MsoNormal">
<span style="font-size: small;"><span style="line-height: 115%;">O problema será:
<i>Como determinar a distância entre os
pontos A e B</i>?</span></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<span style="font-size: small;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjejjK7rqpFI96Bd7qNe4kf3QGBj1tdsg35QKklNqQ74_N8-UK8l4MbxXHGy1UoVUfvtoRTZ4mO1sXroS9EllD6whPouDQCdW0fs_myGtROoc8GdsdUwg_V7KkU45o-xkg-rtgTHd7TYwaA/s1600/grafico1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjejjK7rqpFI96Bd7qNe4kf3QGBj1tdsg35QKklNqQ74_N8-UK8l4MbxXHGy1UoVUfvtoRTZ4mO1sXroS9EllD6whPouDQCdW0fs_myGtROoc8GdsdUwg_V7KkU45o-xkg-rtgTHd7TYwaA/s1600/grafico1.png" /></a></span></div>
<span style="font-size: small;">
</span><br />
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-size: small;">
</span></div>
<span style="font-size: small;">
</span><br />
<div class="MsoNormal">
<br /></div>
<span style="font-size: small;">
</span><br />
<div class="MsoNormal">
<span style="font-size: small;"><span style="line-height: 115%;">Observe que
temos um triângulo retângulo em C, portando, aplicando o teorema de Pitágoras
temos o seguinte:</span></span></div>
<span style="font-size: small;">
</span><br />
<div class="MsoNormal">
<span style="font-size: small;">
</span></div>
<span style="font-size: small;">
</span><br />
<div class="MTDisplayEquation">
<span style="font-size: small;"> </span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNo9icRlwvtukMmqDzmVvcjicHx5rzZSeP3F3IoFT8Oz42Lq1LM7HuIsV7rd0r1d9vk2BuFHOgEsuwRHdE0AvvEXbufcmeuvs7sNRorIsXSB0qtLuMb7rE7s1nVal2UZzSOmVlm2bOJM_d/s1600/g1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNo9icRlwvtukMmqDzmVvcjicHx5rzZSeP3F3IoFT8Oz42Lq1LM7HuIsV7rd0r1d9vk2BuFHOgEsuwRHdE0AvvEXbufcmeuvs7sNRorIsXSB0qtLuMb7rE7s1nVal2UZzSOmVlm2bOJM_d/s1600/g1.jpg" /></a></div>
<div class="MTDisplayEquation">
<span style="font-size: small;"> </span></div>
<span style="font-size: small;">
</span><br />
<div class="MsoNormal">
<span style="font-size: small;"> <span style="line-height: 115%;"></span></span></div>
<span style="font-size: small;">
</span><br />
<div class="MsoNormal">
<br /></div>
<span style="font-size: small;">
</span><br />
<div class="MsoNormal">
<span style="font-size: small;"><span style="line-height: 115%;">Portanto,
temos agora a relação matemática que nos permite calcular a distância entre
dois pontos A e B quaisquer do Plano Cartesiano. Vamos agora resolver uma
situação onde aplicamos a fórmula de distância entre dois pontos.</span></span></div>
<span style="font-size: small;">
</span><br />
<div class="MsoNormal">
<br /></div>
<span style="font-size: small;">
</span><br />
<div class="MsoNormal">
<br /></div>
<span style="font-size: small;">
</span><br />
<span style="font-size: small;">
</span><br />
<div class="MsoNormal">
<br /></div>
<span style="font-size: small;">
</span><br />
<div class="MsoNormal">
<span style="font-size: small;"><span style="line-height: 115%;">Ex: Determine
a distância entre os pontos </span></span><span style="font-size: small;"><span style="line-height: 115%;"><span style="font-size: small;"><span style="line-height: 115%;">A(<span style="font-size: small;">2</span>,<span style="font-size: small;">3</span>) e B</span><span style="line-height: 115%;"><span style="line-height: 115%;">(<span style="font-size: small;">-2</span>,<span style="font-size: small;">5</span>).</span></span></span></span></span></div>
<div class="MsoNormal">
<span style="font-size: small;"><span style="line-height: 115%;"><span style="font-size: small;"><span style="line-height: 115%;"><span style="line-height: 115%;"> </span></span></span> </span></span></div>
<span style="font-size: small;">
</span><br />
<div class="MsoNormal">
<span style="font-size: small;"><span style="line-height: 115%;">Solução:</span> </span></div>
<div class="MsoNormal">
<span style="font-size: small;"> <span style="line-height: 115%;"></span></span></div>
<span style="font-size: small;">
</span><br />
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-size: small;"><span style="line-height: 115%;">
</span><span style="line-height: 115%;"></span></span></div>
<span style="font-size: small;">
</span><br />
<div class="MsoNormal">
<span style="font-size: small;"><span style="line-height: 115%;"><br /></span></span></div>
<div class="separator" style="clear: both; text-align: center;">
<span style="font-size: small;"><span style="line-height: 115%;"> </span></span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmJGRtk8Bbi7-AH13Mjxq4dcHX1PcI79ZOnObHKmsnQIqXlVI2bwHthVi_uGT3IoqKEUwHRvwkjJbhj8ZOkVZQL3-MYO9aLCzyL5Z3Hug5KYkyoJtkl4oWgQWBynHFoxIcHzXel491rAbh/s1600/g2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmJGRtk8Bbi7-AH13Mjxq4dcHX1PcI79ZOnObHKmsnQIqXlVI2bwHthVi_uGT3IoqKEUwHRvwkjJbhj8ZOkVZQL3-MYO9aLCzyL5Z3Hug5KYkyoJtkl4oWgQWBynHFoxIcHzXel491rAbh/s320/g2.jpg" width="289" /></a></div>
<div class="MsoNormal">
<br /></div>
<span style="font-size: small;">
</span><br />
<div class="MTDisplayEquation">
<span style="font-size: small;">
</span><span style="font-size: small;"><span style="font-size: small;"><span style="line-height: 115%;">Portanto
teremos: </span></span></span></div>
<div class="MTDisplayEquation">
<br /></div>
<div class="MTDisplayEquation">
<br /></div>
<div class="MTDisplayEquation">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwJbzdCW4t4kdFe-bMgUb98ga0DC7p_T7XUTTXq8GGx8nIi-VWD5bZpzE_o9y0WhyphenhyphenSjrZQcZG0LO6HRLwlFApl1lMeZDCMLG2aqZjOMdDSQR4MRwqR2e88AHUU7KtNYiqgV3TqS9a4Yf_i/s1600/g3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwJbzdCW4t4kdFe-bMgUb98ga0DC7p_T7XUTTXq8GGx8nIi-VWD5bZpzE_o9y0WhyphenhyphenSjrZQcZG0LO6HRLwlFApl1lMeZDCMLG2aqZjOMdDSQR4MRwqR2e88AHUU7KtNYiqgV3TqS9a4Yf_i/s1600/g3.jpg" /></a></div>
<div class="MTDisplayEquation">
<span style="font-size: small;"><span style="font-size: small;"><span style="line-height: 115%;"> </span></span> </span></div>
<span style="font-size: small;">
</span><br />
<div class="MsoNormal">
<br /></div>
<span style="font-size: small;">
</span><br />
<div class="MsoNormal">
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<span style="font-size: small;"><span style="line-height: 115%;">Mostramos aqui então, de forma simples e na prática neste artigo,a relação
matemática que usaremos para calcular distância entre dois pontos. Ficamos por
aqui, e até nosso próximo artigo sobre Geometria analítica. Um forte abraço!!</span></span></div>
Anonymoushttp://www.blogger.com/profile/10465574769320496687noreply@blogger.com0tag:blogger.com,1999:blog-2107902626616081432.post-53671375932742307122013-03-24T06:59:00.001-07:002013-05-24T15:07:05.635-07:00..::Parceria do Blog do Prof. Deivison e o Blog: União dos Blogs de Matemática::..<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyGsxczrtIUbN9MrphnxKtn_fqPCmtuJlxTDahbV3Phs7JzrqdVZctFLYsyCqNYMJ1XgCLh7RztwceH_JmbxS5cUYrZTwoVXqeEUu4nXNkqIwwgMR_Ysg6LXk6Q_M1fk4uJbtVUkpATrOY/s1600/UBM_300X100_B.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyGsxczrtIUbN9MrphnxKtn_fqPCmtuJlxTDahbV3Phs7JzrqdVZctFLYsyCqNYMJ1XgCLh7RztwceH_JmbxS5cUYrZTwoVXqeEUu4nXNkqIwwgMR_Ysg6LXk6Q_M1fk4uJbtVUkpATrOY/s300/UBM_300X100_B.jpg" /></a></div>
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Prof. Esp. Deivison da Silva e Silva</div>
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e-mail:deivisonflp@hotmail.com</div>
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<span style="font-size: large;">Neste dia 22 de Março, firmamos uma parceria co<span style="background-color: black;"></span>m o Blog: União dos Blogs de Matemática e fomos <span class="googie_link">contemplados</span> com o selo da UBM.<br />Esperamos que essa parceria venha somar com o Blog do Professor <span class="googie_link">Deivison</span>, bem como aumentar o número de informações por nós <span class="googie_link">disponibilizada</span>, trazendo <span class="googie_link">benefícios</span> no processo de ensino e <span class="googie_link">aprendizagem</span> dessa área tão bela e interessante.</span><br />
<br />Anonymoushttp://www.blogger.com/profile/10465574769320496687noreply@blogger.com0tag:blogger.com,1999:blog-2107902626616081432.post-50620137199420306962013-03-21T06:11:00.000-07:002013-03-21T06:11:56.775-07:00ApresentaçãoEste é o Blog do Prof. Deivison da Silva e Silva, destinado a publicações de assuntos relacionados à Matemática Pura e Aplicada.<br />
Aqui, você encontrará informações relativas ao Ensino Fundamental, Médio e Superior,para melhor atender ao público.<br />
Você também pode fazer parte da nossa comunidade no <a href="http://www.facebook.com/groups/281211485325194/" rel="nofollow" target="_blank">Facebook</a>, onde você encontrará também uma vasta lista de informações matemáticas.<br />
Bom, aproveite o Blog, comente os Posters, participe e desfrute do melhor que Matemática e suas aplicações tem a lhe oferecer.<br />
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<b>Prof. Esp. Deivison da Silva e Silva </b>Anonymoushttp://www.blogger.com/profile/10465574769320496687noreply@blogger.com2tag:blogger.com,1999:blog-2107902626616081432.post-25002942825988627972013-03-14T07:41:00.000-07:002013-05-24T15:06:48.724-07:00...::Definição de Função do 1º Grau e Zero de uma Função do 1º Grau::...<span style="font-size: large;"><b><span style="font-size: large;"><i> </i><span style="color: orange;"> </span></span><span style="color: orange;">FUNÇÃO DO 1º GRAU</span></b></span><br />
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Prof. Esp. Deivison da Silva e Silva</div>
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e-mail:deivisonflp@hotmail.com<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh87Y_xwxct0Re2huyu1k6aAlxDbtS_6djaUmAJqOff06jBCSnzbGydFUS1DTpJRHJ7JOzvZAURD7EPVPKOsS1TmNeNwAgnQUmT7ynNVBT0l0NPlGgnWHFexHtVppRuisZKMqK-ChPbruBb/s1600/img.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="164" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh87Y_xwxct0Re2huyu1k6aAlxDbtS_6djaUmAJqOff06jBCSnzbGydFUS1DTpJRHJ7JOzvZAURD7EPVPKOsS1TmNeNwAgnQUmT7ynNVBT0l0NPlGgnWHFexHtVppRuisZKMqK-ChPbruBb/s320/img.jpg" width="320" /></a></div>
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<span style="font-size: large;"><br /><br /><u><b>DEFINIÇÃO</b></u>: é toda função do tipo f(x) = ax + b, com "a" e "b" pertencentes aos reais e "a" diferente de zero.<br /> </span><br />
<span style="font-size: large;">Exemplos: a) t(x) = x +1 ==>> a = 1 <span style="font-size: large;"></span>b = 1.<br /><br /> b) h(x) = 2x-1 ==>> a = 2 b = -1.<br /><br /> c) t(x) = - x ==>> a = -1 b = 0.<br /><br /> <span style="font-size: large;"></span>d) g(x) = -3x - 2 ==>> a = -3 b = -2.</span><br />
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<span style="font-size: large;"><br /> <i><b>ZERO OU RAÍZ DE UMA FUNÇÃO DO 1º GRAU</b></i></span><br />
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<span style="font-size: large;"><br /><u><b>DEFINIÇÃO </b></u>: <i>dada fum função f(x) = ax + b , zero ou raíz da função<span style="font-size: large;"> </span>f(x) = ax + b é o valor de x que torna a função nula, ou seja é o valor de x para que se tenha f(x) = 0 . </i></span><br />
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<span style="font-size: large;"><br />Exemplos: a) f(x) = 2 x + 1 , x = -1/2 é a raíz, pois f(-1/2) = 0.<br /><br /> b) g(t) = t - 4 , t = 4 é a raíz, pois t(-4) = 0 . </span><br />
<span style="font-size: large;"><br /><br /> <b><i>COMO CALCULAR O ZERO DA FUNÇÃO DO 1º GRAU?</i></b><br /><br />Exemplo: a ) f(x) = 2x + 4 , tomamos a função " 2x + 4 " e igualamos a "zero" , ficando assim:<br /><br /><br /> 2x + 4 = 0 resolvendo<span style="font-size: large;"> a equação </span>teremos :<br /> <br /> <span style="font-size: large;"><b> </b></span> <b>x= -2</b>. Portanto, <i><b>x = -2</b></i> é a<i><b> ra<span style="font-size: large;">í</span>z</b></i> da função dada.</span><br />
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<span style="font-size: large;"> b) h(t) = t -3, tomamos a função " t - 3 " e igualamos<span style="font-size: large;"> </span>a "zero" , ficando assim:<br /><br /> t - 3 = 0 resolvendo a equação teremos :<br /> <br /> <span style="font-size: large;"> </span> <b>t = 3. </b>Portanto , <i><b>t = 3</b></i> é a <i><b>ra<span style="font-size: large;">í</span>z</b></i> da função dada.</span><br />
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<span style="font-size: large;">Bom pessoal, não tem muito segredo não, basicamente é isso que temos sobre a <b><i>deifinição</i></b> e<b><i> raíz</i></b> de uma Função do 1 º Grau. </span><br />
<span style="font-size: large;"> Um forte abraço e até o próximo post!!!! </span><br />
<span style="font-size: large;"> <span style="font-size: large;"> </span></span><br />
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<li><span style="font-size: large;"><span style="font-size: large;"><span style="font-size: large;">Canal no</span> YOUTUBE: <a href="https://www.youtube.com/profdeivison">https://www.youtube.com/profdeivison</a></span></span></li>
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<span style="font-size: large;"><span style="font-size: large;"> acessem<span style="font-size: large;">, escrevam-se</span> para receber as vídeo aulas.</span></span><br />
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<span style="font-size: large;"><i><b> Lembre-se, "Matemática aprende-se fazendo!!!"</b></i></span>Anonymoushttp://www.blogger.com/profile/10465574769320496687noreply@blogger.com0tag:blogger.com,1999:blog-2107902626616081432.post-69672126391936933022013-02-03T14:42:00.000-08:002013-02-03T14:42:23.627-08:00...::De volta ao Blog::..Bom pessoal, estava ausente do Blog esses meses por motivos superiores (deixei vocês curiosos heim? rsrsr). De volta nesse novo Ano de 2013 para dar o máximo para que ele seja melhor do que o ano de 2012. Aproveito o momento (meio que atrasadíssimo) para desejar um 2013 cheio de felicidades, conquistas, muita paz, saúde a todos. <br />É isso ai, em breve novas postagens para a galera que acompanha o blog, com muitas novidades, algumas vídeo aulas etc...não esquecendo participe de nosso <a href="http://www.facebook.com/groups/281211485325194/" target="_blank">Grupo no Facebook</a> um forte abraço!! <br /><br />...:::Prof. Deivison da Silva e Silva:::... :-)<br /><br />Anonymoushttp://www.blogger.com/profile/10465574769320496687noreply@blogger.com0tag:blogger.com,1999:blog-2107902626616081432.post-2391178585270313582012-10-23T16:42:00.003-07:002012-10-23T16:42:46.164-07:00...::Factrais::...<br />
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São figuras geométricas muito loucas, produzidas por meio de equações matemáticas que podem ser interpretadas como formas e cores por programas de computador. Sua principal característica é a autossimilaridade. "Eles contêm, dentro de si, cópias menores deles mesmos. Essas cópias, por sua vez, contêm cópias ainda menores e assim sucessivamente", explica Eduardo Colli, professor do Instituto de Matemática e Estatística da Universidade de São Paulo (IME-USP). Os fractais estão ligados a áreas da física e da matemática chamadas Sistemas Dinâmicos e Teoria do Caos, porque suas equações são usadas para descrever fenômenos que, apesar de parecerem aleatórios, obedecem a certas regras - como o fluxo dos rios. Eles não são explicados pela geometria euclidiana (aquela que você aprende na escola), pois possuem dimensão fracionária. "Essa fração está relacionada com a quantidade e a escala de ampliação das cópias da figura contidas dentro dela mesma", diz Colli. Outra característica é que possuem complexidade infinita: um zoom em um detalhe da imagem revela novos detalhes.</div>
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Fonte: <a href="http://cienciafacil10.blogspot.com.br/" style="background-color: transparent;">http://cienciafacil10.blogspot.com.br</a></div>
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Modelo 1: </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaTY1_pPDASG1AmeHyDKGKYkW_6W3t-o4p6vHBuRYIBjxE2BkFqmF1VUgAmqlmctrzQirishKaHC1N4UCAYnrgl3YGXwOI09KMieRGczAoXmxg5c-7UdoDc-p033xwgDByNtpXgEfVVD5e/s1600/formas-fractais-final-2.0_Page_1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="226" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaTY1_pPDASG1AmeHyDKGKYkW_6W3t-o4p6vHBuRYIBjxE2BkFqmF1VUgAmqlmctrzQirishKaHC1N4UCAYnrgl3YGXwOI09KMieRGczAoXmxg5c-7UdoDc-p033xwgDByNtpXgEfVVD5e/s320/formas-fractais-final-2.0_Page_1.jpg" width="320" /></a></div>
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Modelo 2:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjt9_fKU8XgL4c2X3D5tD6e0naNxPb5PLs3-xtwUCY3PB3GulUKPqZJj2e7nQk5AJ_LjBtpgRRv0EdOjDvKTa0iU8VipC7PzuPCU77sesGmRoIgGkHSZovhUdqV122586ytceEgxhXY4sp8/s1600/fractais.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="232" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjt9_fKU8XgL4c2X3D5tD6e0naNxPb5PLs3-xtwUCY3PB3GulUKPqZJj2e7nQk5AJ_LjBtpgRRv0EdOjDvKTa0iU8VipC7PzuPCU77sesGmRoIgGkHSZovhUdqV122586ytceEgxhXY4sp8/s320/fractais.jpg" width="320" /></a></div>
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Modelo3:</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXC5Enn8H-E7kgXE4kh4tCHmDocreefUeDQVMXcCJBd9kEIs-e68Pw6eqt9yyDIRM5fwQrgWkHUa7tKFMeu9HECmqjx1GihKIKpQVWKK_S1ejg300cG3HO3Y-6uXmqg8zsodYPddRzoMWw/s1600/fractal7261fp.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="228" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXC5Enn8H-E7kgXE4kh4tCHmDocreefUeDQVMXcCJBd9kEIs-e68Pw6eqt9yyDIRM5fwQrgWkHUa7tKFMeu9HECmqjx1GihKIKpQVWKK_S1ejg300cG3HO3Y-6uXmqg8zsodYPddRzoMWw/s320/fractal7261fp.gif" width="320" /></a></div>
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Anonymoushttp://www.blogger.com/profile/10465574769320496687noreply@blogger.com0tag:blogger.com,1999:blog-2107902626616081432.post-969080792754731122012-10-03T07:31:00.000-07:002015-06-22T19:03:03.497-07:00...::Definição de Limite de uma Função:::...<div class="separator" style="clear: both; text-align: center;">
Bom dia pessoal, olha só assistam essa vídeo aula para esclarecer a <b>definição de limite de uma função</b> com o Prof. Marcos Freitas. </div>
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Espero que esse vídeo venha ajudar a entender essa linda definição. <iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/8c0fA9N2ZRA?feature=player_embedded' frameborder='0'></iframe></div>
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<br />Anonymoushttp://www.blogger.com/profile/10465574769320496687noreply@blogger.com0tag:blogger.com,1999:blog-2107902626616081432.post-74988727306167838882012-09-20T05:54:00.002-07:002012-09-20T05:54:47.159-07:00Excelentes Cursos Matricule-se e faça logo o seu.<span style="background-color: white; color: #333333; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px;">Olha só pessoal uma excelente oportunidade para você melhorar seu Curriculum!!! Cursos em várias áreas do conhecimento. Escolha o seu, matricule-se agora mesmo e aproveite essa oportunidade!!</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfAstAjkipmTk90jK60Ikcz5d1I96AJauiHLwJVu0To1dbcZZI_AjaP4H0uv3jXcoiaIt0T2L4gNmRiz-6d0OfBPFdTyv2yOmfF05ddsszrekxL0JgAXSrXxcPevijQqn1fQBEypl-qRJt/s1600/safe_image.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfAstAjkipmTk90jK60Ikcz5d1I96AJauiHLwJVu0To1dbcZZI_AjaP4H0uv3jXcoiaIt0T2L4gNmRiz-6d0OfBPFdTyv2yOmfF05ddsszrekxL0JgAXSrXxcPevijQqn1fQBEypl-qRJt/s1600/safe_image.jpg" /></a></div>
<br style="background-color: white; color: #333333; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px;" /><a href="http://www.cursos24horas.com.br/?id=deivison" rel="nofollow nofollow" style="background-color: white; color: #3b5998; cursor: pointer; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px; text-decoration: none;" target="_blank">http://www.cursos24horas.com.br/?id=deivison</a> <br style="background-color: white; color: #333333; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px;" />Anonymoushttp://www.blogger.com/profile/10465574769320496687noreply@blogger.com0tag:blogger.com,1999:blog-2107902626616081432.post-88105018591719884182012-09-18T07:42:00.000-07:002012-09-18T07:42:37.647-07:00Aprendendo Cálculo com Maple em Português<br />
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Assista: <a href="http://www.maplesoft.com/demo/streaming/AprendendoCalculocomMapleemPortugues.aspx" target="_blank">Clique aqui!</a></div>
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Description</div>
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Presenter: Renato Doria and Professor Washington Inacio de Souza Soares<br /><br />Nessa apresentação, todos os tópicos de cálculo de uma <a href="http://www.maplesoft.com/demo/streaming/AprendendoCalculocomMapleemPortugues.aspx#" id="_GPLITA_0" in_rurl="http://i.trkjmp.com/click?v=QlI6MjA2NDk6MzMyOnZhcmnDoXZlbDozZDAzZmM5MTBhN2U3Mzc4ZGRlODQ5MDcyZjIwN2E5OTp6LTEyNjUtNjgyMzQ6d3d3Lm1hcGxlc29mdC5jb206NDE2NTp0ZXh0X29ubHk" title="Click to Continue > by Text-Enhance">variável</a> serão explorados de forma interativa utilizando a poderosa ferramenta de cálculo do Maple.<br /><br />Indo da definição de Limite, passando por Derivadas e abordando o cálculo de Integrais de forma passo a passo e abordando aplicações como Máximos e Mínimos, após esta apresentação, o aprendizado de Cálculo se tornará muito mais simples, possibilitando ao aluno compreender esses <a href="http://www.maplesoft.com/demo/streaming/AprendendoCalculocomMapleemPortugues.aspx#" id="_GPLITA_1" in_rurl="http://i.trkjmp.com/click?v=QlI6MjA2NDk6MzMyOnTDs3BpY29zOmJkMTViNTY1MmJiOTdiMDY1NmRlZDIxZDc0NWRmOTk3OnotMTI2NS02ODIzNDp3d3cubWFwbGVzb2Z0LmNvbTo0MTY1OnRleHRfb25seQ" title="Click to Continue > by Text-Enhance">tópicos</a> de forma muito mais clara.<br /><a href="http://www.maplesoft.com/demo/streaming/AprendendoCalculocomMapleemPortugues.aspx#" id="_GPLITA_2" in_rurl="http://i.trkjmp.com/click?v=QlI6MjA2NDk6MzMyOmFsw6ltOjIzODJkNWQ0OWY2ZDFlYzc5OTU1MzE3ZThkYzNlM2Q1OnotMTI2NS02ODIzNDp3d3cubWFwbGVzb2Z0LmNvbTo0MTY1OnRleHRfb25seQ" title="Click to Continue > by Text-Enhance">Além</a> disso, utilizaremos os recursos do Maple para calcular Limites, Derivadas e Integrais de forma passo a passo, onde o aluno verá todas as etapas necessárias no cálculo, com a explicação detalhada dos métodos utiliizados em cada etapa.</div>
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Fonte: <a href="http://www.maplesoft.com/">http://www.maplesoft.com</a></div>
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Anonymoushttp://www.blogger.com/profile/10465574769320496687noreply@blogger.com0tag:blogger.com,1999:blog-2107902626616081432.post-17596065699860940032012-09-18T06:22:00.005-07:002012-09-18T06:29:38.735-07:00Estudando Física com EXCEL<span style="background-color: white; color: #333333; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 17px;">Um belo Tutorial utilizando o Microsoft Excel no Ensino da Física. Você pode Plotar Gráficos de movimentos para entender melhor o estudo do fenômeno!! Vale apena conferir!!<br />Veja: </span><span style="background-color: white; color: #333333; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 17px;"> </span><a href="http://www.slideshare.net/ValmirHeckler/instrues-bsicas-para-uso-do-excel-no-ensino-de-fsica" rel="nofollow nofollow" style="background-color: white; color: #3b5998; cursor: pointer; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 17px; text-decoration: none;" target="_blank">http://www.slideshare.net/<wbr></wbr><span class="word_break" style="display: inline-block;"></span>ValmirHeckler/<wbr></wbr><span class="word_break" style="display: inline-block;"></span>instrues-bsicas-para-uso-do-exc<wbr></wbr><span class="word_break" style="display: inline-block;"></span>el-no-ensino-de-fsica</a><br />
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