<?xml version="1.0" encoding="UTF-8"?>
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<Version major="2018" minor="0"/>
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        <Metadata-attribute name="T\303\255tulo" value="&lt;default&gt;"/>
        <Metadata-attribute name="Palabras claves" value="&lt;default&gt;"/>
        <Metadata-attribute name="Autor" value="&lt;default&gt;"/>
        <Metadata-attribute name="Asunto " value="&lt;default&gt;"/>
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<Input><Text-field style="Text" bold="true" size="28" layout="Normal" alignment="centred"><Font size="28" bold="true" encoding="UTF-8">Sistema de coordenadas polares: gr\303\241ficas y \303\241reas</Font></Text-field>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L2" drawlabel="true">
<Input><Text-field style="Text" layout="Normal" alignment="centred"><Font bold="true" encoding="UTF-8">Dr. Ranfer\303\255 Guti\303\251rrez</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
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<Input><Text-field style="Text" size="14" layout="Normal"><Font size="14" encoding="UTF-8">El sistema de coordenadas polares se construye dibujando una serie de c\303\255rcunferencias conc\303\251ntricas de radio conocido,a intervalos regulares, as\303\255 como rayos, tambi\303\251n a intervalos regulares, tal como se muestra abajo en la Figura 1. Este proceso es similar al que se sigue en un sistema de coordenadas rectangulares, donde se dibujan rectas verticales y horizontales a intervalos regulares en cada caso.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font size="14">           </Font><Font bold="true">Figura 1. </Font>En (a) se muestra el sistema de coordenadas polares, formado por una serie de circunferencias de radio <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn</Equation><Font encoding="UTF-8"> uniformementes separadas, as\303\255 como una                                                         serie de rayos \316\270 distribuidas tambi\303\251n de forma uniforme.  En (b) se muestran valores asignados a las distintas circunferencias y rayos para un                                                                                  sistema de coordenadas polares arbitrario.</Font></Text-field>
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<Input><Text-field style="Text" size="14" layout="Normal"><Font size="14" encoding="UTF-8">El eje a partir del cual se mide los \303\241ngulos se denomina eje polar. Como se muestra en la Figura 2, un punto </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUEYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUEYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjZRJ25vcm1hbEYn</Equation><Font size="14"> en coordenada polares se representa como un par de la forma </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="14" encoding="UTF-8"> donde \316\270</Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LlEiPkYnLyUlc2l6ZUdRIzE0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y3LyUpc3RyZXRjaHlHRjcvJSpzeW1tZXRyaWNHRjcvJShsYXJnZW9wR0Y3LyUubW92YWJsZWxpbWl0c0dGNy8lJ2FjY2VudEdGNy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkYtSSNtbkdGJDYlUSIwRidGL0YyLyUrZXhlY3V0YWJsZUdGN0Yy">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LlEiPkYnLyUlc2l6ZUdRIzE0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y3LyUpc3RyZXRjaHlHRjcvJSpzeW1tZXRyaWNHRjcvJShsYXJnZW9wR0Y3LyUubW92YWJsZWxpbWl0c0dGNy8lJ2FjY2VudEdGNy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkYtSSNtbkdGJDYlUSIwRidGL0YyLyUrZXhlY3V0YWJsZUdGN0Yy</Equation><Font size="14"> si se mide en sentido contrario al del movimiento de las manecillas del reloj, y </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEnJiM5NTI7RicvJSVzaXplR1EjMTRGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlEiPEYnRi9GNS8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYlUSIwRidGL0Y1LyUrZXhlY3V0YWJsZUdGNEY1">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEnJiM5NTI7RicvJSVzaXplR1EjMTRGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlEiPEYnRi9GNS8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYlUSIwRidGL0Y1LyUrZXhlY3V0YWJsZUdGNEY1</Equation><Font size="14"> en caso contrario.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font size="14">Es posible considerar puntos en coordenadas polares de la forma </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="14">, </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="14">, midiendo </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYnLUYjNiUtSSNtaUdGJDYmUSJyRicvJSVzaXplR1EjMTRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GO1Enbm9ybWFsRidGNEZALyUlb3BlbkdRInxnckYnLyUmY2xvc2VHRkRGPUZA">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYnLUYjNiUtSSNtaUdGJDYmUSJyRicvJSVzaXplR1EjMTRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GO1Enbm9ybWFsRidGNEZALyUlb3BlbkdRInxnckYnLyUmY2xvc2VHRkRGPUZA</Equation><Font size="14"> unidades a lo largo del rayo </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEnJiM5NTI7RicvJSVzaXplR1EjMTRGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlEiK0YnRi9GNS8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkwtRiw2JlEnJiM5NjA7RidGL0YyRjUvJStleGVjdXRhYmxlR0Y0RjU=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEnJiM5NTI7RicvJSVzaXplR1EjMTRGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlEiK0YnRi9GNS8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkwtRiw2JlEnJiM5NjA7RidGL0YyRjUvJStleGVjdXRhYmxlR0Y0RjU=</Equation><Font size="14" encoding="UTF-8">.  Esto es muy importante tomar en cuenta al momento de construir los gr\303\241ficos de ecuaciones en coordenadas polares.   As\303\255, por ejemplo, el punto </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="14" encoding="UTF-8"> se dibuja como un punto que est\303\241 a </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW5HRiQ2JVEiM0YnLyUlc2l6ZUdRIzE0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRidGMg==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW5HRiQ2JVEiM0YnLyUlc2l6ZUdRIzE0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRidGMg==</Equation><Font size="14" encoding="UTF-8"> unidades sobre un rayo que se encuentra a un \303\241ngulo </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkmbWZyYWNHRiQ2KC1GIzYmLUkjbW5HRiQ2JVEiM0YnLyUlc2l6ZUdRIzE0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlEifkYnRjRGNy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQC8lKXN0cmV0Y2h5R0ZALyUqc3ltbWV0cmljR0ZALyUobGFyZ2VvcEdGQC8lLm1vdmFibGVsaW1pdHNHRkAvJSdhY2NlbnRHRkAvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZPLUkjbWlHRiQ2JlElJnBpO0YnRjQvJSdpdGFsaWNHRkBGN0Y3LUYjNiQtRjE2JVEiNEYnRjRGN0Y3LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zcby8lKWJldmVsbGVkR0ZALUY7Ni5RIitGJ0Y0RjdGPkZBRkNGRUZHRklGSy9GTlEsMC4yMjIyMjIyZW1GJy9GUUZlby1GUzYmUScmIzk2MDtGJ0Y0RlZGNy1GOzYuUSI9RidGNEY3Rj5GQUZDRkVGR0ZJRksvRk5RLDAuMjc3Nzc3OGVtRicvRlFGXnAtRiw2KC1GIzYmLUYxNiVRIjdGJ0Y0RjdGOkZnb0Y3LUYjNiZGWkY0L0ZXUSV0cnVlRicvRjhRJ2l0YWxpY0YnRmduRmpuRl1vRl9vRjc=">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</Equation><Font size="14">, tal como se ilustra en la siguiente figura:</Font></Text-field>
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<Input><Text-field style="Text" size="14" layout="Normal"><Font size="14" encoding="UTF-8">En su curso de Prec\303\241lculo usted aprendi\303\263 que un posible procedimiento para construir la gr\303\241fica de una funci\303\263n </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="14"> es utilizar una tabla, como se ilustra abajo en la Figura 4, para el caso de </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="14">.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font size="14">                                                        </Font><Font bold="true">Figura 4.</Font><Font encoding="UTF-8"> Construcci\303\263n de la gr\303\241fica de </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> a partir de una tabla.</Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font size="14" encoding="UTF-8">Por lo general, se acostumbran utilizar valores &quot;f\303\241ciles&quot; de </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EieEYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EieEYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGNS9GOVEnbm9ybWFsRic=</Equation><Font size="14"> para valuar en </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiZkYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2JS1GLDYnUSJ4RidGL0YyRjVGOEY1L0Y5USdub3JtYWxGJ0YvRjVGQ0Y1RkM=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiZkYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2JS1GLDYnUSJ4RidGL0YyRjVGOEY1L0Y5USdub3JtYWxGJ0YvRjVGQ0Y1RkM=</Equation><Font size="14">, tales como los valores enteros mostrados en la Figura 2.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font size="14" encoding="UTF-8">En el caso de coordenadas polares, la construcci\303\263n de la gr\303\241fica de </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="14" encoding="UTF-8"> auxili\303\241ndose de una tabla, como en el caso de coordenadas cartesianas, no es el m\303\241s adecuado ya que al aplicar la misma idea de utilizar valores &quot;f\303\241ciles&quot; de \316\270 puede dar lugar a que se pierdan detalles de la gr\303\241fica de </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="14">.   </Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font size="14" encoding="UTF-8">Por ejemplo, construya una tabla similar a la tabla mostrada en la Figura 4, con valores que usted considere adecuados, y construya en un sistema de coordenadas polares la gr\303\241fica de </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="14" encoding="UTF-8">. Compare luego su gr\303\241fica con la soluci\303\263n que se indica a continuaci\303\263n: </Font>                                                                     </Text-field>
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<Input><Text-field style="Text" size="14" layout="Normal"><Font size="14" encoding="UTF-8">Una manera mas eficiente de construir la gr\303\241fica de </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="14" encoding="UTF-8"> es primero construir la gr\303\241fica en coordenas rectangulares y luego utilizar la informaci\303\263n ah\303\255 mostrada para construir la gr\303\241fica en coordenadas polares.  Como indica Stewart en su libro de Prec\303\241lculo (p\303\241gina 549, 6a. Edici\303\263n): &quot;<Font foreground="[255,0,0]" italic="true">Podemos considerar esta gr\303\241fica</Font><Font foreground="[255,0,0]"> -la gr\303\241fica de </Font></Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="14" foreground="[255,0,0]"> en coordenadas polares- <Font italic="true">como una tabla de valores que hace posible que leamos de un vistazo los valores de </Font></Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEickYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZm9yZWdyb3VuZEdRKlsyNTUsMCwwXUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGNUY4Rjo=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEickYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZm9yZWdyb3VuZEdRKlsyNTUsMCwwXUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGNUY4Rjo=</Equation><Font size="14" foreground="[255,0,0]"> <Font italic="true">que corresponden a valores crecientes de</Font><Font encoding="UTF-8"> \316\270.</Font></Font><Font size="14" encoding="UTF-8">&quot;  Utilice la barra deslizante mostrada abajo entre las dos gr\303\241ficas y observe c\303\263mo, a partir de la gr\303\241fica de la derecha -la gr\303\241fica de </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="14" encoding="UTF-8">en un sistema de coordenadas rectangulares- se construye la gr\303\241fica de la izquierda de </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="14" encoding="UTF-8"> en un sistema de coordenadas polares. Recuerde la convenci\303\263n para localizar puntos en coordenadas polares, en especial, lo relacionado con los casos en que los puntos son de la forma </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="14">, </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="14">.  </Font></Text-field>
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<Input><Text-field style="Text" size="14" layout="Normal"><Font size="14" encoding="UTF-8">El punto azul en la gr\303\241fica de la izquierda, abajo, indica la localizaci\303\263n de los puntos si </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEickYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEickYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjZRJ25vcm1hbEYn</Equation><Font size="14"> <Font opaque="true" background="[255,255,0]">fuera siempre mayor que cero</Font>.  Recuerde que cuando </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEickYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPEYnRi8vRjZRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZALyUpc3RyZXRjaHlHRkAvJSpzeW1tZXRyaWNHRkAvJShsYXJnZW9wR0ZALyUubW92YWJsZWxpbWl0c0dGQC8lJ2FjY2VudEdGQC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRk8tSSNtbkdGJDYlUSIwRidGL0Y8LyUrZXhlY3V0YWJsZUdGQEY8">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEickYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPEYnRi8vRjZRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZALyUpc3RyZXRjaHlHRkAvJSpzeW1tZXRyaWNHRkAvJShsYXJnZW9wR0ZALyUubW92YWJsZWxpbWl0c0dGQC8lJ2FjY2VudEdGQC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRk8tSSNtbkdGJDYlUSIwRidGL0Y8LyUrZXhlY3V0YWJsZUdGQEY8</Equation><Font size="14" encoding="UTF-8">, el punto debe dibujarse a un \303\241ngulo </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2J1EnJiM5NTI7RicvJSVzaXplR1EjMTRGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi9RIitGJ0YvRjVGOC8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRk8tRiw2J1ElJnBpO0YnRi9GMkY1RjgvJStleGVjdXRhYmxlR0Y0Rjg=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2J1EnJiM5NTI7RicvJSVzaXplR1EjMTRGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi9RIitGJ0YvRjVGOC8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRk8tRiw2J1ElJnBpO0YnRi9GMkY1RjgvJStleGVjdXRhYmxlR0Y0Rjg=</Equation><Font size="14">.</Font></Text-field>
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id="Slider0" lower-bound="0.0" upper-bound="6.28" control-position="0.11349398" major-tick-spacing="1.0" minor-ticks="0.5" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="false" show-ticks="true" snap-to-ticks="false" continuous-update="true" pixel-width="190" pixel-height="38" fontcolor="[0,0,0]" fillcolor="[255,255,255]"><MapleCode action="position-event-handler">use DocumentTools in 
with(plots);
with(plottools);
Do(a=%Slider0);
gp:=plots[polarplot](1+2*cos(theta),theta=0..a,thickness=2,coordinateview=[0..3,0..2*Pi]);
lr:=plottools[line]([-3*cos(a),-3*sin(a)],[3*cos(a),3*sin(a)],color=green);
pr:=plottools[point]([(1+2*cos(a))*signum(1+2*cos(a))*cos(a),(1+2*cos(a))*signum(1+2*cos(a))*sin(a)],color=blue,symbolsize=15,symbol=solidcircle);
Do(%Plot0=plots[display]({gp,lr,pr}));
lv:=plottools[line]([a,0],[a,1+2*cos(a)],color=green);
lh:=plottools[line]([a,1+2*cos(a)],[0,1+2*cos(a)],linestyle=dash);
gp:=plot(1+2*cos(x),x=0..2*Pi, tickmarks=[spacing(Pi/3),default]);
prc:=plottools[point]([a,1+2*cos(a)],color=blue,symbol=solidcircle,symbolsize=15);
Do(%Plot1=plots[display]({gp,lv,lh,prc},labels=[theta,r],font=[Times,roman,14],title=&quot;r(theta) vrs theta&quot;));

end use; 
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<Input><Text-field style="Text" size="14" layout="Normal"><Font size="14" encoding="UTF-8">Abajo se muestra una figura, tomada del libro de Prec\303\241lculo (6a. Edici\303\263n) de Stewart, la cual puede ayudarle a complementar su comprensi\303\263n acerca de la construcci\303\263n de la gr\303\241fica de </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="14" encoding="UTF-8">   La curva roja en la figura de abajo, a la izquierda, sirve para construir la curva roja de abajo, a la derecha.  Lo mismo es v\303\241lido para la curva azul.</Font></Text-field>
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id="Slider1" lower-bound="0.0" upper-bound="6.28" control-position="4.63055422" major-tick-spacing="1.0" minor-ticks="0.5" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="false" show-ticks="true" snap-to-ticks="false" continuous-update="true" pixel-width="190" pixel-height="38" fontcolor="[0,0,0]" fillcolor="[255,255,255]"><MapleCode action="position-event-handler">use DocumentTools in 
with(plots);
with(plottools);
Do(a=%Slider1);
gp:=plots[polarplot](2-2*cos(theta),theta=0..a,thickness=2,coordinateview=[0..4,0..2*Pi]);
lr:=plottools[line]([-4*cos(a),-4*sin(a)],[4*cos(a),4*sin(a)],color=green);
pr:=plottools[point]([(2-2*cos(a))*signum(2-2*cos(a))*cos(a),(2-2*cos(a))*signum(2-2*cos(a))*sin(a)],color=blue,symbolsize=15,symbol=solidcircle);
Do(%Plot2=plots[display]({gp,lr,pr}));
lv:=plottools[line]([a,0],[a,(2-2*cos(a))],color=green);
lh:=plottools[line]([a,(2-2*cos(a))],[0,(2-2*cos(a))],linestyle=dash);
gp:=plot(2-2*cos(x),x=0..2*Pi);
prc:=plottools[point]([a,(2-2*cos(a))],color=blue,symbol=solidcircle,symbolsize=15);
Do(%Plot3=plots[display]({gp,lv,lh,prc},labels=[theta,r],font=[Times,roman,14],title=&quot;r(theta) vrs theta&quot;));

end use; 
</MapleCode></EC-Slider><EC-Plot id="Plot3" visible="true" pixel-width="400" pixel-height="400" continuous="false" delay="100" fillcolor="[255,255,255]" clickx="0.0" clicky="0.0" hoverx="0.0" hovery="0.0" startx="2.3082314940643314" starty="1.4575671145343274" endx="0.0" endy="0.0" clickdefault="false" labelreference="L7208" drawcaption="false" captionposition="1" captionalignment="0" show-border="true"><Plot height="400.0" type="two-dimensional" width="400.0" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" 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id="Slider2" lower-bound="0.0" upper-bound="6.28" control-position="6.28" major-tick-spacing="1.0" minor-ticks="0.5" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="false" show-ticks="true" snap-to-ticks="false" continuous-update="true" pixel-width="190" pixel-height="38" fontcolor="[0,0,0]" fillcolor="[255,255,255]"><MapleCode action="position-event-handler">use DocumentTools in 
with(plots);
with(plottools);
Do(a=%Slider2);
gp:=plots[polarplot](1+sin(theta),theta=0..a,thickness=2,coordinateview=[0..2,0..2*Pi]);
lr:=plottools[line]([-2*cos(a),-2*sin(a)],[2*cos(a),2*sin(a)],color=green);
pr:=plottools[point]([(1+sin(a))*signum(1+sin(a))*cos(a),(1+sin(a))*signum(1+sin(a))*sin(a)],color=blue,symbolsize=15,symbol=solidcircle);
Do(%Plot4=plots[display]({gp,lr,pr}));
lv:=plottools[line]([a,0],[a,(1+sin(a))],color=green);
lh:=plottools[line]([a,(1+sin(a))],[0,(1+sin(a))],linestyle=dash);
gp:=plot(1+sin(x),x=0..2*Pi);
prc:=plottools[point]([a,1+sin(a)],color=blue,symbol=solidcircle,symbolsize=15);
Do(%Plot5=plots[display]({gp,lv,lh,prc},labels=[theta,r],font=[Times,roman,14],title=&quot;r(theta) vrs theta&quot;));

end use; 
</MapleCode></EC-Slider><EC-Plot id="Plot5" visible="true" pixel-width="400" pixel-height="400" continuous="false" delay="100" fillcolor="[255,255,255]" clickx="0.0" clicky="0.0" hoverx="0.0" hovery="0.0" startx="2.3082314940643314" starty="1.4575671145343274" endx="0.0" endy="0.0" clickdefault="false" labelreference="L8740" drawcaption="false" captionposition="1" captionalignment="0" show-border="true"><Plot height="400.0" type="two-dimensional" width="400.0" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" 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id="Slider3" lower-bound="0.0" upper-bound="6.28" control-position="5.652" major-tick-spacing="1.0" minor-ticks="0.5" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="false" show-ticks="true" snap-to-ticks="false" continuous-update="true" pixel-width="190" pixel-height="38" fontcolor="[0,0,0]" fillcolor="[255,255,255]"><MapleCode action="position-event-handler">use DocumentTools in 
with(plots);
with(plottools);
Do(a=%Slider3);
gp:=plots[polarplot](1+2*sin(theta),theta=0..a,thickness=2,coordinateview=[0..3,0..2*Pi]);
lr:=plottools[line]([-3*cos(a),-3*sin(a)],[3*cos(a),3*sin(a)],color=green);
pr:=plottools[point]([(1+2*sin(a))*signum(1+2*sin(a))*cos(a),(1+2*sin(a))*signum(1+2*sin(a))*sin(a)],color=blue,symbolsize=15,symbol=solidcircle);
Do(%Plot6=plots[display]({gp,lr,pr}));
lv:=plottools[line]([a,0],[a,1+2*sin(a)],color=green);
lh:=plottools[line]([a,1+2*sin(a)],[0,1+2*sin(a)],linestyle=dash);
gp:=plot(1+2*sin(x),x=0..2*Pi);
prc:=plottools[point]([a,1+2*sin(a)],color=blue,symbol=solidcircle,symbolsize=15);
Do(%Plot7=plots[display]({gp,lv,lh,prc},labels=[theta,r],font=[Times,roman,14],title=&quot;r(theta) vrs theta&quot;));

end use; 
</MapleCode></EC-Slider><EC-Plot id="Plot7" visible="true" pixel-width="400" pixel-height="400" continuous="false" delay="100" fillcolor="[255,255,255]" clickx="0.0" clicky="0.0" hoverx="0.0" hovery="0.0" startx="2.3082314940643314" starty="1.4575671145343274" endx="0.0" endy="0.0" clickdefault="false" labelreference="L11160" drawcaption="false" captionposition="1" captionalignment="0" show-border="true"><Plot height="400.0" type="two-dimensional" width="400.0" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" 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</Section>
<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 2" layout="Heading 2"><Equation executable="false" style="Heading 2" input-equation="" display="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">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</Equation></Text-field></Title><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L11161" drawlabel="true" applyint="true" applyrational="true">
<Input><Text-field style="Text" layout="Normal"><EC-Plot id="Plot8" visible="true" pixel-width="400" pixel-height="400" continuous="false" delay="100" fillcolor="[255,255,255]" clickx="0.0" clicky="0.0" hoverx="0.0" hovery="0.0" startx="1.8842298578079335" starty="0.04918253273427707" endx="0.0" endy="0.0" clickdefault="false" labelreference="L11180" drawcaption="false" captionposition="1" captionalignment="0" show-border="true"><Plot height="400.0" type="two-dimensional" width="400.0" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="7" 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id="Slider4" lower-bound="0.0" upper-bound="3.14159" control-position="2.827431" major-tick-spacing="1.0" minor-ticks="0.5" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="false" show-ticks="true" snap-to-ticks="false" continuous-update="true" pixel-width="190" pixel-height="38" fontcolor="[0,0,0]" fillcolor="[255,255,255]"><MapleCode action="position-event-handler">use DocumentTools in 
with(plots);
with(plottools);
Do(a=%Slider4);
gp:=plots[polarplot](2*sin(theta),theta=0..a,thickness=2,coordinateview=[0..2,0..2*Pi]);
lr:=plottools[line]([-2*cos(a),-2*sin(a)],[2*cos(a),2*sin(a)],color=green);
pr:=plottools[point]([(2*sin(a))*signum(2*sin(a))*cos(a),(2*sin(a))*signum(2*sin(a))*sin(a)],color=blue,symbolsize=15,symbol=solidcircle);
Do(%Plot8=plots[display]({gp,lr,pr}));
lv:=plottools[line]([a,0],[a,2*sin(a)],color=green);
lh:=plottools[line]([a,2*sin(a)],[0,2*sin(a)],linestyle=dash);
gp:=plot(2*sin(x),x=0..Pi);
prc:=plottools[point]([a,2*sin(a)],color=blue,symbol=solidcircle,symbolsize=15);
Do(%Plot9=plots[display]({gp,lv,lh,prc},labels=[theta,r],font=[Times,roman,14],title=&quot;r(theta) vrs theta&quot;));

end use; 
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</Section>
<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 2" layout="Heading 2"><Equation executable="false" style="Heading 2" input-equation="" display="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">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</Equation></Text-field></Title><Presentation-Block>
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<Input><Text-field style="Text" layout="Normal"><EC-Plot id="Plot10" visible="true" pixel-width="400" pixel-height="400" continuous="false" delay="100" fillcolor="[255,255,255]" clickx="0.0" clicky="0.0" hoverx="0.0" hovery="0.0" startx="1.8842298578079335" starty="0.04918253273427707" endx="0.0" endy="0.0" clickdefault="false" labelreference="L12699" drawcaption="false" captionposition="1" captionalignment="0" show-border="true"><Plot height="400.0" type="two-dimensional" width="400.0" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="7" 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id="Slider5" lower-bound="0.0" upper-bound="3.14159" control-position="1.51401928" major-tick-spacing="1.0" minor-ticks="0.5" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="false" show-ticks="true" snap-to-ticks="false" continuous-update="true" pixel-width="190" pixel-height="38" fontcolor="[0,0,0]" fillcolor="[255,255,255]"><MapleCode action="position-event-handler">use DocumentTools in 
with(plots);
with(plottools);
Do(a=%Slider5);
gp:=plots[polarplot](2*cos(theta),theta=0..a,thickness=2,coordinateview=[0..2,0..2*Pi]);
lr:=plottools[line]([-2*cos(a),-2*sin(a)],[2*cos(a),2*sin(a)],color=green);
pr:=plottools[point]([(2*cos(a))*signum(2*cos(a))*cos(a),(2*cos(a))*signum(2*cos(a))*sin(a)],color=blue,symbolsize=15,symbol=solidcircle);
Do(%Plot10=plots[display]({gp,lr,pr}));
lv:=plottools[line]([a,0],[a,2*cos(a)],color=green);
lh:=plottools[line]([a,2*cos(a)],[0,2*cos(a)],linestyle=dash);
gp:=plot(2*cos(x),x=0..Pi);
prc:=plottools[point]([a,2*cos(a)],color=blue,symbol=solidcircle,symbolsize=15);
Do(%Plot11=plots[display]({gp,lv,lh,prc},labels=[theta,r],font=[Times,roman,14],title=&quot;r(theta) vrs theta&quot;));

end use; 
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id="Slider6" lower-bound="0.0" upper-bound="6.29" control-position="6.29" major-tick-spacing="1.0" minor-ticks="0.5" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="false" show-ticks="true" snap-to-ticks="false" continuous-update="true" pixel-width="190" pixel-height="38" fontcolor="[0,0,0]" fillcolor="[255,255,255]"><MapleCode action="position-event-handler">use DocumentTools in 
with(plots);
with(plottools);
Do(a=%Slider6);
gp:=plots[polarplot](2*cos(2*theta),theta=0..a,thickness=2,coordinateview=[0..2,0..2*Pi]);
lr:=plottools[line]([-2*cos(a),-2*sin(a)],[2*cos(a),2*sin(a)],color=green);
pr:=plottools[point]([(2*cos(2*a))*signum(2*cos(2*a))*cos(a),(2*cos(2*a))*signum(2*cos(2*a))*sin(a)],color=blue,symbolsize=15,symbol=solidcircle);
Do(%Plot12=plots[display]({gp,lr,pr}));
lv:=plottools[line]([a,0],[a,2*cos(2*a)],color=green);
lh:=plottools[line]([a,2*cos(2*a)],[0,2*cos(2*a)],linestyle=dash);
gp:=plot(2*cos(2*x),x=0..2*Pi);
prc:=plottools[point]([a,2*cos(2*a)],color=blue,symbol=solidcircle,symbolsize=15);
Do(%Plot13=plots[display]({gp,lv,lh,prc},labels=[theta,r],font=[Times,roman,14],title=&quot;r(theta) vrs theta&quot;));

end use; 
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</Group></Presentation-Block>
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<Input><Text-field style="Text" size="14" layout="Normal"><Font size="14">La pendiente </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEibUYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEibUYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjZRJ25vcm1hbEYn</Equation><Font size="14" encoding="UTF-8"> de la recta tangente en un punto de la gr\303\241fica de </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlEickYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRi8vRjZRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZALyUpc3RyZXRjaHlHRkAvJSpzeW1tZXRyaWNHRkAvJShsYXJnZW9wR0ZALyUubW92YWJsZWxpbWl0c0dGQC8lJ2FjY2VudEdGQC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRk9GKy1JKG1mZW5jZWRHRiQ2JS1GIzYlLUYsNiZRJyYjOTUyO0YnRi8vRjNGQEY8LyUrZXhlY3V0YWJsZUdGQEY8Ri9GPEZlbkY8">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlEickYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRi8vRjZRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZALyUpc3RyZXRjaHlHRkAvJSpzeW1tZXRyaWNHRkAvJShsYXJnZW9wR0ZALyUubW92YWJsZWxpbWl0c0dGQC8lJ2FjY2VudEdGQC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRk9GKy1JKG1mZW5jZWRHRiQ2JS1GIzYlLUYsNiZRJyYjOTUyO0YnRi8vRjNGQEY8LyUrZXhlY3V0YWJsZUdGQEY8Ri9GPEZlbkY8</Equation><Font size="14"> se obtiene a partir de </Font></Text-field>
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<Input><Text-field style="Text" size="14" layout="Normal"><Font size="14" encoding="UTF-8">Determine la ecuaci\303\263n rectangular de la recta tangente en los puntos indicados en la figura.  La gr\303\241fica corresponde a la ecuaci\303\263n </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="14">.</Font></Text-field>
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id="Slider7" lower-bound="0.0" upper-bound="3.14159" control-position="3.14159" major-tick-spacing="1.0" minor-ticks="0.5" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="false" show-ticks="true" snap-to-ticks="false" continuous-update="true" pixel-width="190" pixel-height="38" fontcolor="[0,0,0]" fillcolor="[255,255,255]"><MapleCode action="position-event-handler">use DocumentTools in 
with(plots);
with(plottools);
Do(a=%Slider7);
gp:=plots[polarplot](4*cos(3*theta),theta=0..a,thickness=2,coordinateview=[0..4,0..2*Pi]);
lr:=plottools[line]([-4*cos(a),-4*sin(a)],[4*cos(a),4*sin(a)],color=green);
pr:=plottools[point]([(4*cos(3*a))*signum(4*cos(3*a))*cos(a),(4*cos(3*a))*signum(4*cos(3*a))*sin(a)],color=blue,symbolsize=15,symbol=solidcircle);
Do(%Plot14=plots[display]({gp,lr,pr}));
lv:=plottools[line]([a,0],[a,(4*cos(3*a))],color=green);
lh:=plottools[line]([a,(4*cos(3*a))],[0,(4*cos(3*a))],linestyle=dash);
gp:=plot(4*cos(3*x),x=0..Pi,tickmarks = [spacing(Pi/3), default]);
prc:=plottools[point]([a,(4*cos(3*a))],color=blue,symbol=solidcircle,symbolsize=15);
Do(%Plot15=plots[display]({gp,lv,lh,prc},labels=[theta,r],font=[Times,roman,14],title=&quot;r(theta) vrs theta&quot;));

end use; 
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<Input><Text-field style="Text" size="14" layout="Normal"><Font size="14" encoding="UTF-8">Los puntos mostrados en la Figura 10.6.11 corresponden a la soluci\303\263n de las ecuaciones trigonom\303\251tricas </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="12"> y </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="12">.  </Font><Font size="14">Las soluciones generales a cada una de estas ecuaciones son, respectivamente:</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="14"> </Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font size="14">Las rectas mostradas en la Figura 10.6.11 corresponden a </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1JI21pR0YkNiZRJyYjOTYwO0YnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYmLUkjbW5HRiQ2JVEiM0YnRjJGOEYyL0Y2USV0cnVlRicvRjlRJ2l0YWxpY0YnLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZKLyUpYmV2ZWxsZWRHRjcvJStleGVjdXRhYmxlR0Y3Rjg=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1JI21pR0YkNiZRJyYjOTYwO0YnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYmLUkjbW5HRiQ2JVEiM0YnRjJGOEYyL0Y2USV0cnVlRicvRjlRJ2l0YWxpY0YnLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZKLyUpYmV2ZWxsZWRHRjcvJStleGVjdXRhYmxlR0Y3Rjg=</Equation><Font size="14"> y </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="14">.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font size="14">Las coordenadas </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjZRJ25vcm1hbEYn</Equation><Font size="14"> e </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieUYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieUYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjZRJ25vcm1hbEYn</Equation><Font size="14" encoding="UTF-8"> para cada uno de los \303\241ngulos son:</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="14"> </Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font size="14">Las ecuaciones de las rectas pedidas son:</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal" initial="-1" bulletsuffix="." bullet="numeric"><Font size="14">Para </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="14">.</Font></Text-field>
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id="Slider10" lower-bound="0.0" upper-bound="6.28" control-position="2.09333333" major-tick-spacing="1.0" minor-ticks="0.5" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="false" show-ticks="true" snap-to-ticks="false" continuous-update="true" pixel-width="190" pixel-height="38" fontcolor="[0,0,0]" fillcolor="[255,255,255]"><MapleCode action="position-event-handler">use DocumentTools in 
with(plots);
with(plottools);
Do(a=%Slider10);
gp:=plots[polarplot](1+2*cos(theta),theta=0..a,thickness=2,coordinateview=[0..3,0..2*Pi]);
lr:=plottools[line]([-3*cos(a),-3*sin(a)],[3*cos(a),3*sin(a)],color=green);
pr:=plottools[point]([(1+2*cos(a))*signum(1+2*cos(a))*cos(a),(1+2*cos(a))*signum(1+2*cos(a))*sin(a)],color=blue,symbolsize=15,symbol=solidcircle);
Do(%Plot20=plots[display]({gp,lr,pr}));
lv:=plottools[line]([a,0],[a,1+2*cos(a)],color=green);
lh:=plottools[line]([a,1+2*cos(a)],[0,1+2*cos(a)],linestyle=dash);
gp:=plot(1+2*cos(x),x=0..2*Pi,tickmarks=[spacing(Pi/3),default]);
prc:=plottools[point]([a,1+2*cos(a)],color=blue,symbol=solidcircle,symbolsize=15);
Do(%Plot21=plots[display]({gp,lv,lh,prc},labels=[theta,r],font=[Times,roman,14],title=&quot;r(theta) vrs theta&quot;));

end use; 
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<Input><Text-field style="Text" layout="Normal"><Font size="14" encoding="UTF-8">La figura muestra la gr\303\241fica de </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="14" encoding="UTF-8">.  Determine el \303\241rea de la regi\303\263n sombreada.</Font></Text-field>
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<Input><Text-field style="Text" size="14" layout="Normal"><Font size="14" encoding="UTF-8">La figura muestra la gr\303\241fica de </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="14" encoding="UTF-8">.  Determine el \303\241rea de la regi\303\263n sombreada.</Font></Text-field>
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id="Slider9" lower-bound="0.0" upper-bound="6.28" control-position="5.22072289" major-tick-spacing="1.0" minor-ticks="0.5" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="false" show-ticks="true" snap-to-ticks="false" continuous-update="true" pixel-width="190" pixel-height="38" fontcolor="[0,0,0]" fillcolor="[255,255,255]"><MapleCode action="position-event-handler">use DocumentTools in 
with(plots);
with(plottools);
Do(a=%Slider9);
gp:=plots[polarplot](sqrt(theta),theta=0..a,thickness=2,coordinateview=[0..3,0..2*Pi]);
lr:=plottools[line]([-3*cos(a),-3*sin(a)],[3*cos(a),3*sin(a)],color=green);
pr:=plottools[point]([(sqrt(a))*signum(sqrt(a))*cos(a),(sqrt(a))*signum(sqrt(a))*sin(a)],color=blue,symbolsize=15,symbol=solidcircle);
Do(%Plot18=plots[display]({gp,lr,pr}));
lv:=plottools[line]([a,0],[a,sqrt(a)],color=green);
lh:=plottools[line]([a,sqrt(a)],[0,sqrt(a)],linestyle=dash);
gp:=plot(sqrt(x),x=0..2*Pi,tickmarks=[spacing(Pi/3),default]);
prc:=plottools[point]([a,sqrt(a)],color=blue,symbol=solidcircle,symbolsize=15);
Do(%Plot19=plots[display]({gp,lv,lh,prc},labels=[theta,r],font=[Times,roman,14],title=&quot;r(theta) vrs theta&quot;));

end use; 
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<Input><Text-field style="Text" size="14" layout="Normal"><Font size="14" encoding="UTF-8">El \303\241rea </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQUYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQUYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjZRJ25vcm1hbEYn</Equation><Font size="14"> pedida es</Font></Text-field>
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<Input><Text-field style="Text" size="14" layout="Normal"><Font size="14" encoding="UTF-8">Obtenga el \303\241rea de la regi\303\263n mostrada en la figura, la cual se encuentra dentro de la circunferencia </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEickYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRi8vRjZRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZALyUpc3RyZXRjaHlHRkAvJSpzeW1tZXRyaWNHRkAvJShsYXJnZW9wR0ZALyUubW92YWJsZWxpbWl0c0dGQC8lJ2FjY2VudEdGQC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRk8tSSNtbkdGJDYlUSIxRidGL0Y8LyUrZXhlY3V0YWJsZUdGQEY8">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEickYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRi8vRjZRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZALyUpc3RyZXRjaHlHRkAvJSpzeW1tZXRyaWNHRkAvJShsYXJnZW9wR0ZALyUubW92YWJsZWxpbWl0c0dGQC8lJ2FjY2VudEdGQC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRk8tSSNtbkdGJDYlUSIxRidGL0Y8LyUrZXhlY3V0YWJsZUdGQEY8</Equation><Font size="14"> y fuera del cardiode </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font size="14" encoding="UTF-8">Obtenga el \303\241rea de la regi\303\263n que se encuentra dentro de la circunferencia </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEickYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRi8vRjZRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZALyUpc3RyZXRjaHlHRkAvJSpzeW1tZXRyaWNHRkAvJShsYXJnZW9wR0ZALyUubW92YWJsZWxpbWl0c0dGQC8lJ2FjY2VudEdGQC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRk8tSSNtbkdGJDYlUSIxRidGL0Y8LyUrZXhlY3V0YWJsZUdGQEY8">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEickYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRi8vRjZRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZALyUpc3RyZXRjaHlHRkAvJSpzeW1tZXRyaWNHRkAvJShsYXJnZW9wR0ZALyUubW92YWJsZWxpbWl0c0dGQC8lJ2FjY2VudEdGQC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRk8tSSNtbkdGJDYlUSIxRidGL0Y8LyUrZXhlY3V0YWJsZUdGQEY8</Equation><Font size="14"> y fuera del cardioide </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="14" encoding="UTF-8">. En la figura se muestra la regi\303\263n pedida.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font size="14">donde </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="14"> y </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2JlEiZ0YnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEnJiM5NTI7RidGLy9GM1EmZmFsc2VGJy9GNlEnbm9ybWFsRicvJStleGVjdXRhYmxlR0ZBRkJGL0ZCLUkjbW9HRiQ2LlEiPUYnRi9GQi8lJmZlbmNlR0ZBLyUqc2VwYXJhdG9yR0ZBLyUpc3RyZXRjaHlHRkEvJSpzeW1tZXRyaWNHRkEvJShsYXJnZW9wR0ZBLyUubW92YWJsZWxpbWl0c0dGQS8lJ2FjY2VudEdGQS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlotSSNtbkdGJDYlUSIxRidGL0ZCLUZHNi5RKCZtaW51cztGJ0YvRkJGSkZMRk5GUEZSRlRGVi9GWVEsMC4yMjIyMjIyZW1GJy9GZm5GX28tRiw2JlEkY29zRidGL0ZARkJGOEZERkI=">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</Equation><Font size="14" encoding="UTF-8">.  Por simetr\303\255a, se puede calcular el \303\241rea de la regi\303\263n comprendida entre los l\303\255mites </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEnJiM5NDU7RicvJSVzaXplR1EjMTRGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlEiPUYnRi9GNS8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYlUSIwRidGL0Y1LyUrZXhlY3V0YWJsZUdGNEY1">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEnJiM5NDU7RicvJSVzaXplR1EjMTRGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlEiPUYnRi9GNS8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYlUSIwRidGL0Y1LyUrZXhlY3V0YWJsZUdGNEY1</Equation><Font size="14"> y </Font><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation><Font size="14" encoding="UTF-8">, y luego multiplicar por 2 para obtener el \303\241rea </Font><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQUYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQUYnLyUlc2l6ZUdRIzE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjZRJ25vcm1hbEYn</Equation><Font size="14" encoding="UTF-8"> de la regi\303\263n sombreada:</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="true" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
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