{"id":8507,"date":"2012-04-18T18:48:14","date_gmt":"2012-04-18T17:48:14","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=8507"},"modified":"2022-01-29T23:57:44","modified_gmt":"2022-01-29T23:57:44","slug":"determine","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=8507","title":{"rendered":"Determine"},"content":{"rendered":"<p><ul id='GTTabs_ul_8507' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_8507' class='GTTabs_curr'><a  id=\"8507_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_8507' ><a  id=\"8507_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_8507'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<ol>\n<li>Determine $${\\mathop {\\lim }\\limits_{x \\to 0} \\frac{{1 &#8211; \\cos x}}{{{x^2}}}}$$ multiplicando os termos da fra\u00e7\u00e3o por $1 + \\cos x$.<\/li>\n<li>Com a sua calculadora gr\u00e1fica, represente a fun\u00e7\u00e3o $$x \\to \\frac{{1 &#8211; \\cos x}}{{{x^2}}}$$ e, recorrendo a um ZOOM perto de zero, verifique o valor obtido na al\u00ednea anterior.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_8507' onClick='GTTabs_show(1,8507)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_8507'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{\\mathop {\\lim }\\limits_{x \\to 0} \\frac{{1 &#8211; \\cos x}}{{{x^2}}}}&amp; = &amp;{\\mathop {\\lim }\\limits_{x \\to 0} \\frac{{\\left( {1 &#8211; \\cos x} \\right)\\left( {1 + \\cos x} \\right)}}{{{x^2}\\left( {1 + \\cos x} \\right)}}} \\\\<br \/>\n{}&amp; = &amp;{\\mathop {\\lim }\\limits_{x \\to 0} \\frac{{1 &#8211; {{\\cos }^2}x}}{{{x^2}\\left( {1 + \\cos x} \\right)}}} \\\\<br \/>\n{}&amp; = &amp;{\\mathop {\\lim }\\limits_{x \\to 0} \\frac{{{{\\operatorname{sen} }^2}x}}{{{x^2}\\left( {1 + \\cos x} \\right)}}} \\\\<br \/>\n{}&amp; = &amp;{\\mathop {\\lim }\\limits_{x \\to 0} \\frac{{{{\\operatorname{sen} }^2}x}}{{{x^2}}} \\times \\underbrace {\\mathop {\\lim }\\limits_{x \\to 0} \\frac{1}{{1 + \\cos x}}}_{\\frac{1}{2}}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{1}{2} \\times {{\\left( {\\underbrace {\\mathop {\\lim }\\limits_{x \\to 0} \\frac{{\\operatorname{sen} x}}{x}}_1} \\right)}^2}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{1}{2}}<br \/>\n\\end{array}$$<br \/>\n\u00ad<\/li>\n<li><span style=\"font-family: 'Segoe UI', Frutiger, 'Frutiger Linotype', 'Dejavu Sans', 'Helvetica Neue', Arial, sans-serif; font-size: revert; color: initial;\">\u00a0<\/span><\/li>\n<\/ol>\n<p><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"8513\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=8513\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag46-17.png\" data-orig-size=\"485,79\" 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\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag46-17.png\" class=\"aligncenter wp-image-8513 size-full\" title=\"Gr\u00e1fico\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag46-17.png\" alt=\"\" width=\"485\" height=\"79\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag46-17.png 485w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag46-17-300x48.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag46-17-150x24.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12pag46-17-400x65.png 400w\" sizes=\"auto, (max-width: 485px) 100vw, 485px\" \/><\/p>\n<p style=\"text-align: center;\"><script src=\"https:\/\/cdn.geogebra.org\/apps\/deployggb.js\"><\/script>\r\n<div id=\"ggbApplet\" style=\"margin: 0 auto;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet\",\r\n\"width\":679,\r\n\"height\":380,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 59 || 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 || 16 51 64 , 70 | 10 34 53 11 , 24  20 22 , 21 23 | 55 56 57 , 12 || 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 , 14 66 68 | 25 52 60 61 || 40 41 42 , 27 28 35 , 6\",\r\n\"showToolBarHelp\":false,\r\n\"showResetIcon\":true,\r\n\"enableLabelDrags\":false,\r\n\"enableShiftDragZoom\":false,\r\n\"enableRightClick\":false,\r\n\"errorDialogsActive\":false,\r\n\"useBrowserForJS\":false,\r\n\"preventFocus\":false,\r\n\"showFullscreenButton\":true,\r\n\"language\":\"pt\",\r\n\/\/ use this instead of ggbBase64 to load a material from GeoGebraTube\r\n\/\/ \"material_id\":12345,\r\n\"ggbBase64\":\"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\"};\r\n\/\/ is3D=is 3D applet using 3D view, AV=Algebra View, SV=Spreadsheet View, CV=CAS View, EV2=Graphics View 2, CP=Construction Protocol, PC=Probability Calculator, DA=Data Analysis, FI=Function Inspector, PV=Python, macro=Macro View\r\nvar views = {'is3D': 0,'AV': 0,'SV': 0,'CV': 0,'EV2': 0,'CP': 0,'PC': 0,'DA': 0,'FI': 0,'PV': 0,'macro': 0};\r\nvar applet = new GGBApplet(parameters, '5.0', views);\r\nwindow.onload = function() {applet.inject('ggbApplet')};\r\n<\/script><br \/>\n\u00ad<\/p>\n<p><strong>Nota<\/strong>: Como se sabe, ${D_f} = \\mathbb{R}\\backslash \\left\\{ 0 \\right\\}$.<br \/>\nO facto de o gr\u00e1fico n\u00e3o apresentar um &#8220;buraco&#8221; no ponto de coordenadas $\\left( {0,\\frac{1}{2}} \\right)$ significa que \u00e9 poss\u00edvel encontrar um prolongamento cont\u00ednuo\u00a0desta fun\u00e7\u00e3o. Note-se, contudo, que o ponto (que se pode arrastar) tende a desaparecer quando se aproxima suficientemente perto dessas coordenadas.<\/p>\n<table class=\" aligncenter\" style=\"width: 400px;\" border=\"0\" align=\"center\">\n<tbody>\n<tr>\n<td><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/graf1-12pag46-18.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"8519\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=8519\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/graf1-12pag46-18.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=\"Gr\u00e1fico\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/graf1-12pag46-18.png\" class=\"aligncenter wp-image-8519 size-full\" title=\"Gr\u00e1fico\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/graf1-12pag46-18.png\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/graf1-12pag46-18.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/graf1-12pag46-18-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/td>\n<td><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/tab1-12pag46-18.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"8520\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=8520\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/tab1-12pag46-18.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=\"Tabela\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/tab1-12pag46-18.png\" class=\"aligncenter wp-image-8520 size-full\" title=\"Tabela\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/tab1-12pag46-18.png\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/tab1-12pag46-18.png 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/tab1-12pag46-18-150x101.png 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_8507' onClick='GTTabs_show(0,8507)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Determine $${\\mathop {\\lim }\\limits_{x \\to 0} \\frac{{1 &#8211; \\cos x}}{{{x^2}}}}$$ multiplicando os termos da fra\u00e7\u00e3o por $1 + \\cos x$. Com a sua calculadora gr\u00e1fica, represente a fun\u00e7\u00e3o $$x \\to \\frac{{1&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":21096,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,295],"tags":[427,286],"series":[],"class_list":["post-8507","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-12--ano","category-aplicando","category-funcoes-seno-co-seno-e-tangente","tag-12-o-ano","tag-limites"],"views":2176,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/12V3Pag046-18_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8507","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=8507"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8507\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/21096"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8507"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8507"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8507"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=8507"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}