{"id":11740,"date":"2014-02-03T20:19:15","date_gmt":"2014-02-03T20:19:15","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=11740"},"modified":"2022-01-22T01:30:37","modified_gmt":"2022-01-22T01:30:37","slug":"determine-graficamente","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=11740","title":{"rendered":"Determine graficamente"},"content":{"rendered":"<p><ul id='GTTabs_ul_11740' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_11740' class='GTTabs_curr'><a  id=\"11740_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_11740' ><a  id=\"11740_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_11740'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Determine, graficamente, as abcissas (com aproxima\u00e7\u00e3o \u00e0s mil\u00e9simas) dos pontos de interse\u00e7\u00e3o dos gr\u00e1ficos das fun\u00e7\u00f5es seguintes: \\[\\begin{array}{*{20}{c}}<br \/>\n{f\\left( x \\right) = \\frac{{{x^3} + 4x &#8211; 2}}{{{x^2} &#8211; 3}}}&amp;{\\text{e}}&amp;{g\\left( x \\right) = \\frac{{ &#8211; 2x + 1}}{{2{x^3} + 3{x^2} &#8211; 7x + 1}}}<br \/>\n\\end{array}\\]<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_11740' onClick='GTTabs_show(1,11740)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_11740'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<table border=\"0\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"width: 300px;\" valign=\"top\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/Janela1.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"11741\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11741\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/Janela1.jpg\" data-orig-size=\"264,136\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Janela de visualiza\u00e7\u00e3o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/Janela1.jpg\" class=\"aligncenter size-full wp-image-11741\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/Janela1.jpg\" alt=\"Janela de visualiza\u00e7\u00e3o\" width=\"264\" height=\"136\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/Janela1.jpg 264w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/Janela1-150x77.jpg 150w\" sizes=\"auto, (max-width: 264px) 100vw, 264px\" \/><\/a><\/td>\n<td style=\"width: 300px;\" valign=\"top\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/Grafico1.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"11742\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11742\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/Grafico1.jpg\" data-orig-size=\"264,136\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Gr\u00e1ficos\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/Grafico1.jpg\" class=\"aligncenter size-full wp-image-11742\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/Grafico1.jpg\" alt=\"Gr\u00e1ficos\" width=\"264\" height=\"136\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/Grafico1.jpg 264w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/Grafico1-150x77.jpg 150w\" sizes=\"auto, (max-width: 264px) 100vw, 264px\" \/><\/a><\/td>\n<td style=\"width: 300px;\" valign=\"top\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/PontoA.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"11743\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11743\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/PontoA.jpg\" data-orig-size=\"264,136\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Ponto A\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/PontoA.jpg\" class=\"aligncenter size-full wp-image-11743\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/PontoA.jpg\" alt=\"Ponto A\" width=\"264\" height=\"136\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/PontoA.jpg 264w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/PontoA-150x77.jpg 150w\" sizes=\"auto, (max-width: 264px) 100vw, 264px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 300px;\" valign=\"top\">Independentemente da janela de visualiza\u00e7\u00e3o escolhida, n\u00e3o \u00e9 f\u00e1cil obter, com suficiente legibilidade,\u00a0uma representa\u00e7\u00e3o dos dois gr\u00e1ficos que inclua os seus pontos de interse\u00e7\u00e3o.<\/td>\n<td style=\"width: 300px;\" valign=\"top\">Verifica-se ainda um conjunto de artefactos (que n\u00e3o devem ser confundidos com parte dos gr\u00e1ficos), que s\u00e3o devidos \u00e0 liga\u00e7\u00e3o de pontos calculados \u00e0 esquerda e \u00e0 direita de ass\u00edntotas verticais. No entanto, \u00e9 poss\u00edvel determinar as coordenadas dos 4 pontos de interse\u00e7\u00e3o dos dois gr\u00e1ficos.<\/td>\n<td style=\"width: 300px;\" valign=\"top\">\u00a0O ponto A tem abcissa ${x_A} \\approx\u00a0 &#8211; 2,848$.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 300px;\" valign=\"top\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/PontoB.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"11744\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11744\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/PontoB.jpg\" data-orig-size=\"264,136\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Ponto B\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/PontoB.jpg\" class=\"aligncenter size-full wp-image-11744\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/PontoB.jpg\" alt=\"Ponto B\" width=\"264\" height=\"136\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/PontoB.jpg 264w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/PontoB-150x77.jpg 150w\" sizes=\"auto, (max-width: 264px) 100vw, 264px\" \/><\/a><\/td>\n<td style=\"width: 300px;\" valign=\"top\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/PontoC.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"11745\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11745\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/PontoC.jpg\" data-orig-size=\"264,136\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Ponto C\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/PontoC.jpg\" class=\"aligncenter size-full wp-image-11745\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/PontoC.jpg\" alt=\"Ponto C\" width=\"264\" height=\"136\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/PontoC.jpg 264w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/PontoC-150x77.jpg 150w\" sizes=\"auto, (max-width: 264px) 100vw, 264px\" \/><\/a><\/td>\n<td style=\"width: 300px;\" valign=\"top\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/PontoD.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"11746\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11746\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/PontoD.jpg\" data-orig-size=\"264,136\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Ponto D\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/PontoD.jpg\" class=\"aligncenter size-full wp-image-11746\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/PontoD.jpg\" alt=\"Ponto D\" width=\"264\" height=\"136\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/PontoD.jpg 264w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/PontoD-150x77.jpg 150w\" sizes=\"auto, (max-width: 264px) 100vw, 264px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 300px;\" valign=\"top\">\u00a0O ponto\u00a0B tem abcissa ${x_B} \\approx\u00a0 &#8211; 0,069$<\/td>\n<td style=\"width: 300px;\" valign=\"top\">\u00a0O ponto\u00a0C tem abcissa ${x_C} \\approx 0,485$.<\/td>\n<td style=\"width: 300px;\" valign=\"top\">\u00a0O ponto D tem abcissa ${x_D} \\approx 1,211$.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 300px;\" valign=\"top\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/Funcoes1.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"11747\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11747\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/Funcoes1.jpg\" data-orig-size=\"264,136\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Fun\u00e7\u00e3o diferen\u00e7a\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/Funcoes1.jpg\" class=\"aligncenter size-full wp-image-11747\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/Funcoes1.jpg\" alt=\"Fun\u00e7\u00e3o diferen\u00e7a\" width=\"264\" height=\"136\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/Funcoes1.jpg 264w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/Funcoes1-150x77.jpg 150w\" sizes=\"auto, (max-width: 264px) 100vw, 264px\" \/><\/a><\/td>\n<td style=\"width: 300px;\" valign=\"top\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/Funcoes1D.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"11748\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11748\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/Funcoes1D.jpg\" data-orig-size=\"264,136\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Gr\u00e1fico da fun\u00e7\u00e3o diferen\u00e7a\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/Funcoes1D.jpg\" class=\"aligncenter size-full wp-image-11748\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/Funcoes1D.jpg\" alt=\"Gr\u00e1fico da fun\u00e7\u00e3o diferen\u00e7a\" width=\"264\" height=\"136\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/Funcoes1D.jpg 264w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/Funcoes1D-150x77.jpg 150w\" sizes=\"auto, (max-width: 264px) 100vw, 264px\" \/><\/a><\/td>\n<td style=\"width: 300px;\" valign=\"top\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/ZeroA.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"11749\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11749\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/ZeroA.jpg\" data-orig-size=\"264,136\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Zero da fun\u00e7\u00e3o diferen\u00e7a\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/ZeroA.jpg\" class=\"aligncenter size-full wp-image-11749\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/ZeroA.jpg\" alt=\"Zero da fun\u00e7\u00e3o diferen\u00e7a\" width=\"264\" height=\"136\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/ZeroA.jpg 264w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/ZeroA-150x77.jpg 150w\" sizes=\"auto, (max-width: 264px) 100vw, 264px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 300px;\" colspan=\"3\" valign=\"top\">Ainda com a mesma janela de visualiza\u00e7\u00e3o e procurando uma melhor legibilidade da representa\u00e7\u00e3o gr\u00e1fica, pode considerar-se a determina\u00e7\u00e3o dos zeros da fun\u00e7\u00e3o diferen\u00e7a ${f &#8211; g}$, j\u00e1 que $f\\left( x \\right) = g\\left( x \\right) \\Leftrightarrow f\\left( x \\right) &#8211; g\\left( x \\right) = 0$.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 300px;\" valign=\"top\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/texas1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"11750\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11750\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/texas1.png\" data-orig-size=\"198,134\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Fun\u00e7\u00f5es\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/texas1.png\" class=\"aligncenter size-full wp-image-11750\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/texas1.png\" alt=\"Fun\u00e7\u00f5es\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/texas1.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/texas1-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/td>\n<td style=\"width: 300px;\" valign=\"top\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/texas2.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"11751\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11751\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/texas2.png\" data-orig-size=\"198,134\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Ponto de interse\u00e7\u00e3o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/texas2.png\" class=\"aligncenter size-full wp-image-11751\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/texas2.png\" alt=\"Ponto de interse\u00e7\u00e3o\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/texas2.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/texas2-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/td>\n<td style=\"width: 300px;\" valign=\"top\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/texas3.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"11752\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11752\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/texas3.png\" data-orig-size=\"198,134\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Zero da fun\u00e7\u00e3o diferen\u00e7a\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/texas3.png\" class=\"aligncenter size-full wp-image-11752\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/texas3.png\" alt=\"Zero da fun\u00e7\u00e3o diferen\u00e7a\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/texas3.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/texas3-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 300px;\" colspan=\"3\" valign=\"top\">Ilustra-se agora a utiliza\u00e7\u00e3o de\u00a0outro modelo de calculadora, na mesma janela de visualiza\u00e7\u00e3o.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"attachment_11753\" style=\"width: 832px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2pag-49-12.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-11753\" data-attachment-id=\"11753\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11753\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2pag-49-12.png\" data-orig-size=\"1028,525\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Gr\u00e1ficos\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;Determina\u00e7\u00e3o das coordenadas dos pontos de interse\u00e7\u00e3o dos gr\u00e1fios das fun\u00e7\u00f5es $f$ e $g$&lt;\/p&gt;\n\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2pag-49-12-1024x522.png\" class=\" wp-image-11753 \" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2pag-49-12.png\" alt=\"Determina\u00e7\u00e3o das coordenadas dos pontos de interse\u00e7\u00e3o dos gr\u00e1fios das fun\u00e7\u00f5es $f$ e $g$\" width=\"822\" height=\"420\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2pag-49-12.png 1028w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2pag-49-12-300x153.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2pag-49-12-1024x522.png 1024w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2pag-49-12-150x76.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11-2pag-49-12-400x204.png 400w\" sizes=\"auto, (max-width: 822px) 100vw, 822px\" \/><\/a><p id=\"caption-attachment-11753\" class=\"wp-caption-text\">Determina\u00e7\u00e3o das coordenadas dos pontos de interse\u00e7\u00e3o dos gr\u00e1fios das fun\u00e7\u00f5es $f$ e $g$<\/p><\/div>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_11740' onClick='GTTabs_show(0,11740)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Determine, graficamente, as abcissas (com aproxima\u00e7\u00e3o \u00e0s mil\u00e9simas) dos pontos de interse\u00e7\u00e3o dos gr\u00e1ficos das fun\u00e7\u00f5es seguintes: \\[\\begin{array}{*{20}{c}} {f\\left( x \\right) = \\frac{{{x^3} + 4x &#8211; 2}}{{{x^2} &#8211; 3}}}&amp;{\\text{e}}&amp;{g\\left( x \\right)&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20869,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,125],"tags":[422,160,126],"series":[],"class_list":["post-11740","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-funcoes-racionais","tag-11-o-ano","tag-equacao","tag-funcao-racional"],"views":1586,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11V2Pag49-12_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11740","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=11740"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11740\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20869"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11740"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11740"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11740"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=11740"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}