tag:blogger.com,1999:blog-91753402338755834272024-03-08T09:41:19.124-08:00Inecuacioneslas inecuaciones como x < 3, asi te sirven bastante a la hora de ser un empresario con conocimientos de los procesos que sueles emprender en el presente blog se mostrara lo basico que se debe conosser sobre inecuaciones con valor absoluto, sus propiedades, inecuaciones cuadraticas y con coeficientes.Inecuacioneshttp://www.blogger.com/profile/06229709310883954815noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-9175340233875583427.post-67079367393975016982011-08-24T15:46:00.000-07:002011-08-24T15:46:44.079-07:00Inecuaciones con Coeficiente<!--[if gte mso 9]><xml> <o:OfficeDocumentSettings> <o:AllowPNG/> </o:OfficeDocumentSettings> </xml><![endif]--><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:TrackMoves/> <w:TrackFormatting/> <w:HyphenationZone>21</w:HyphenationZone> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:DoNotPromoteQF/> <w:LidThemeOther>ES</w:LidThemeOther> <w:LidThemeAsian>X-NONE</w:LidThemeAsian> <w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> <w:SplitPgBreakAndParaMark/> <w:EnableOpenTypeKerning/> <w:DontFlipMirrorIndents/> <w:OverrideTableStyleHps/> </w:Compatibility> <m:mathPr> <m:mathFont m:val="Cambria Math"/> <m:brkBin m:val="before"/> <m:brkBinSub m:val="--"/> <m:smallFrac m:val="off"/> <m:dispDef/> <m:lMargin m:val="0"/> <m:rMargin m:val="0"/> <m:defJc m:val="centerGroup"/> <m:wrapIndent m:val="1440"/> <m:intLim m:val="subSup"/> <m:naryLim m:val="undOvr"/> </m:mathPr></w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true"
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<div align="center" style="text-align: center;"><b><span style="font-size: 16pt;">Ecuaciones con coeficiente fraccionario</span></b></div><div align="center" style="text-align: center;"><br />
</div><span>Fraccionarios porque las variables aparecen multiplicadas por fracciones. Esta ecuación se resuelve de la siguiente manera:</span><br />
<span>Se multiplican ambos miembros por 12, que es el mínimo común múltiplo de los denominadores de la ecuación: 12(3/4x +4) = 12(5/6x +20/6)</span><br />
<span>Se eliminan los paréntesis efectuando </span><br />
Los productos<span> 36/4x +48 = 60/6x +240/6</span><br />
<span>Las fracciones resultantes siempre</span><br />
<span>Pueden convertirse en enteros 9x +48 = 10x +40</span><br />
<span>Se resuelve la ecuación de la forma usual 9x-10 + 48 = 10x-10x +40</span><br />
<span>-x +48-48 = 40-48</span><br />
<span>-x = -8</span><br />
<span>x = 8</span><br />
<span>Por lo tanto x es igual a 8.</span><br />
<span>Una ecuación con coeficientes fraccionarios se resuelve multiplicando ambos miembros de esta por el mínimo común múltiplo de los denominadores.</span><br />
<span>Otra forma de resolver ecuaciones con coeficiente fraccionario es operar directamente con las fracciones algebraicas. Por ejemplo: </span><br />
<span>Resolver la ecuación 5/4x +7/3x = 1/2</span><br />
<span>Se efectúa la suma 5/4x +7/3x (15x +28x) = ½</span><br />
<span>12</span><br />
<span>43x/12 = 1/2</span><br />
<span>Se multiplican ambos miembros de la ecuación por 12: </span><br />
<span>(12) 43x/12 = 1/2 (12)</span><br />
<span>43x = 6</span><br />
<span>Se dividen ambos miembros de la ecuación entre 43:</span><br />
<span>43x/43 = 6/43</span><br />
<span>x = 6/43</span><br />
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</div><a href="http://www.disfrutalasmatematicas.com/">www.disfrutalasmatematicas.com</a>Inecuacioneshttp://www.blogger.com/profile/06229709310883954815noreply@blogger.com0tag:blogger.com,1999:blog-9175340233875583427.post-61797574797864011472011-08-24T15:23:00.000-07:002011-08-24T15:23:24.966-07:00Inecuaciones cuadráticas<!--[if gte mso 9]><xml> <o:OfficeDocumentSettings> <o:AllowPNG/> </o:OfficeDocumentSettings> </xml><![endif]--><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:TrackMoves/> <w:TrackFormatting/> <w:HyphenationZone>21</w:HyphenationZone> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:DoNotPromoteQF/> <w:LidThemeOther>ES</w:LidThemeOther> <w:LidThemeAsian>X-NONE</w:LidThemeAsian> <w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> <w:SplitPgBreakAndParaMark/> <w:EnableOpenTypeKerning/> <w:DontFlipMirrorIndents/> <w:OverrideTableStyleHps/> </w:Compatibility> <m:mathPr> <m:mathFont m:val="Cambria Math"/> <m:brkBin m:val="before"/> <m:brkBinSub m:val="--"/> <m:smallFrac m:val="off"/> <m:dispDef/> <m:lMargin m:val="0"/> <m:rMargin m:val="0"/> <m:defJc m:val="centerGroup"/> <m:wrapIndent m:val="1440"/> <m:intLim m:val="subSup"/> <m:naryLim m:val="undOvr"/> </m:mathPr></w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true"
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mso-para-margin-left:0cm;
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mso-ascii-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
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mso-bidi-theme-font:minor-bidi;
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</style> <![endif]--> <div class="MsoNormal">Sean a, b, c constantes reales tales que<span> </span>A es diferente de cero. Sea x una variable real. Llamaremos inecuación cuadrática a toda inecuación en la cual uno de sus miembros es una expresión cuadrada <span> </span>y el otro miembro es cero.</div><div class="MsoNormal" style="line-height: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Son inecuaciones cuadráticas: </span></div><a href="http://www.cidse.itcr.ac.cr/">http://www.cidse.itcr.ac.cr</a>Inecuacioneshttp://www.blogger.com/profile/06229709310883954815noreply@blogger.com0tag:blogger.com,1999:blog-9175340233875583427.post-67116532373745673812011-08-24T15:00:00.000-07:002011-08-24T15:00:22.854-07:00Propiedades de la Funcion Valor Absoluto<h3><span class="mw-headline" id="Propiedades_fundamentales"></span><b><span style="font-family: "Times New Roman","serif"; font-size: 13.5pt;">Propiedades del valor absoluto</span></b></h3><!--[if gte mso 9]><xml> <o:OfficeDocumentSettings> <o:AllowPNG/> </o:OfficeDocumentSettings> </xml><![endif]--><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:TrackMoves/> <w:TrackFormatting/> <w:HyphenationZone>21</w:HyphenationZone> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:DoNotPromoteQF/> <w:LidThemeOther>ES</w:LidThemeOther> <w:LidThemeAsian>X-NONE</w:LidThemeAsian> <w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> <w:SplitPgBreakAndParaMark/> <w:EnableOpenTypeKerning/> <w:DontFlipMirrorIndents/> <w:OverrideTableStyleHps/> </w:Compatibility> <m:mathPr> <m:mathFont m:val="Cambria Math"/> <m:brkBin m:val="before"/> <m:brkBinSub m:val="--"/> <m:smallFrac m:val="off"/> <m:dispDef/> <m:lMargin m:val="0"/> <m:rMargin m:val="0"/> <m:defJc m:val="centerGroup"/> <m:wrapIndent m:val="1440"/> <m:intLim m:val="subSup"/> <m:naryLim m:val="undOvr"/> </m:mathPr></w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true"
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</style> <![endif]--> <div class="MsoNormal" style="line-height: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1 Los <b>números opuestos</b> tienen <b>igual valor absoluto</b>.</span></div><div class="MsoNormal" style="line-height: normal;"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">|a| = |−a|</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"></span></div><div class="MsoNormal" style="line-height: normal;"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">|5| = |−5| = 5 </span></b><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"></span></div><div class="MsoNormal" style="line-height: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">2El <b>valor absoluto de un producto</b> es igual al <b>producto de los valores absolutos</b> de los factores.</span></div><div class="MsoNormal" style="line-height: normal;"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">|a · b| = |a|</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> ·<b>|b|</b> </span></div><div class="MsoNormal" style="line-height: normal;"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">|5 · (−2)| = |5| · |(−2)|</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> <b>|− 10| = |5| · |2|</b> 10 = 10 </span></div><div class="MsoNormal" style="line-height: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">3El <b>valor absoluto de una suma es menor o igual que la suma de los valores absolutos de los sumandos</b>.</span></div><div class="MsoNormal" style="line-height: normal;"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">|a + b| ≤ |a|</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> + <b>|b|</b> </span></div><div class="MsoNormal" style="line-height: normal;"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">|5 + (−2)| ≤ |5| + |(−2)|</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> <b>|3| = |5| + |2|</b> 3 ≤ 7 </span></div><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt;"><br />
</div><div class="MsoNormal" style="line-height: normal;"><b><span style="font-family: "Times New Roman","serif"; font-size: 18pt;">Función valor absoluto</span></b></div><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt;"><br />
</div><div class="MsoNormal" style="line-height: normal;"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Las funciones en valor absoluto se transforman en funciones a trozos</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">, siguiendo los siguientes pasos:</span></div><div class="MsoNormal" style="line-height: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">1. <b>Se iguala a cero</b> la función, sin el valor absoluto, y <b>se calculan sus raíces</b>.</span></div><div class="MsoNormal" style="line-height: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">2. Se forman <b>intervalos con las raíces y se evalúa el signo</b> de cada intervalo.</span></div><div class="MsoNormal" style="line-height: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">3. Definimos la función a trozos, teniendo en cuenta que en l<b>os intervalos donde la x es negativa se cambia el signo de la función</b>. </span></div><div class="MsoNormal" style="line-height: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">4 Representamos la función resultante.</span></div><div class="MsoNormal" style="line-height: normal;"><br />
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</div>Inecuacioneshttp://www.blogger.com/profile/06229709310883954815noreply@blogger.com0tag:blogger.com,1999:blog-9175340233875583427.post-37051589825207682432011-08-24T14:19:00.000-07:002011-08-24T14:19:50.304-07:00Inecuaciones Con Valor Absoluto<a href="http://www.blogger.com/post-edit.g?blogID=9175340233875583427&postID=3705158982520768243" name="SECTION00130000000000000000"><b>Inecuaciones que involucran valor absoluto</b></a><br />
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Resolveremos inecuaciones que involucran valor absoluto de expresiones de la forma <img align="middle" alt="$ax+b$" border="0" height="24" src="http://www.cidse.itcr.ac.cr/cursos-linea/MATEGENERAL/t4-valorabsoluto/valor-absoluto-julioetall/img1.gif" width="39" />, donde <img align="bottom" alt="$a$" border="0" height="11" src="http://www.cidse.itcr.ac.cr/cursos-linea/MATEGENERAL/t4-valorabsoluto/valor-absoluto-julioetall/img2.gif" width="10" /> y <img align="bottom" alt="$b$" border="0" height="13" src="http://www.cidse.itcr.ac.cr/cursos-linea/MATEGENERAL/t4-valorabsoluto/valor-absoluto-julioetall/img3.gif" width="9" /> son constantes con <img align="middle" alt="$a\neq0$" border="0" height="24" src="http://www.cidse.itcr.ac.cr/cursos-linea/MATEGENERAL/t4-valorabsoluto/valor-absoluto-julioetall/img4.gif" width="34" /> y <img align="bottom" alt="$x$" border="0" height="11" src="http://www.cidse.itcr.ac.cr/cursos-linea/MATEGENERAL/t4-valorabsoluto/valor-absoluto-julioetall/img5.gif" width="11" /> es una variable real. Para esto utilizaremos la definición de valor absoluto, y en los casos en donde sea posible usar alguna de las propiedades estudiadas las aplicaremos, con el fin de facilitar el procedimiento de resolución.<br />
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<div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt;"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">La noción de <i>valor absoluto </i></span></b><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">surge de una manera natural en problemas de distancia. En</span></div><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">una recta coordenada, sean A y B puntos con coordenadas a y b. Debido a que la distancia es siempre no negativa, la distancia <i>d </i>entre A y B es <i>d </i></span><span style="font-family: Symbol; font-size: 12pt;">= </span><i><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">b </span></i><span style="font-family: Symbol; font-size: 12pt;">- </span><i><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">a </span></i><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">cuando B está a la derecha de A y <i>d </i></span><span style="font-family: Symbol; font-size: 12pt;">= </span><i><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">a </span></i><span style="font-family: Symbol; font-size: 12pt;">- </span><i><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">b </span></i><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">cuando B está a la izquierda de A.</span></div>Inecuacioneshttp://www.blogger.com/profile/06229709310883954815noreply@blogger.com0