{"id":7401,"date":"2012-03-02T22:17:43","date_gmt":"2012-03-02T22:17:43","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7401"},"modified":"2021-12-28T01:30:15","modified_gmt":"2021-12-28T01:30:15","slug":"limites-laterais-da-funcao-f","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7401","title":{"rendered":"Limites laterais da fun\u00e7\u00e3o $f$"},"content":{"rendered":"<p><ul id='GTTabs_ul_7401' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7401' class='GTTabs_curr'><a  id=\"7401_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7401' ><a  id=\"7401_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_7401'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Sabe-se que $f({u_n}) = 2$ e $f({v_n}) =\u00a0 &#8211; 2$ para todas as sucess\u00f5es $({u_n})$ e $({v_n})$ nas condi\u00e7\u00f5es seguintes:<\/p>\n<ul>\n<li>$\\begin{array}{*{20}{l}} \u00a0 {({u_n} \\in {D_f}}&amp; \\wedge &amp;{{u_n} &gt; 3,}&amp;{\\forall n \\in \\mathbb{N})}&amp; \\wedge &amp;{{u_n} \\to 3} \\end{array}$<\/li>\n<li>$\\begin{array}{*{20}{l}} \u00a0 {({v_n} \\in {D_f}}&amp; \\wedge &amp;{{v_n} &lt; 3,}&amp;{\\forall n \\in \\mathbb{N})}&amp; \\wedge &amp;{{v_n} \\to 3} \\end{array}$<\/li>\n<\/ul>\n<p>Conclua, caso seja poss\u00edvel, quanto \u00e0 exist\u00eancia e ao valor:<\/p>\n<ol>\n<li>dos limites laterais da fun\u00e7\u00e3o $f$ no ponto de abcissa 3;<\/li>\n<li>do limite da fun\u00e7\u00e3o $f$ no ponto de abcissa 3.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7401' onClick='GTTabs_show(1,7401)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7401'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Como para toda a sucess\u00e3o $({u_n})$, tal que $\\begin{array}{*{20}{l}} \u00a0 {({u_n} \\in {D_f}}&amp; \\wedge &amp;{{u_n} &gt; 3,}&amp;{\\forall n \\in \\mathbb{N})}&amp; \\wedge &amp;{{u_n} \\to 3} \\end{array}$, se tem $\\mathop {\\lim }\\limits_{} \\left( {f({u_n})} \\right) = 2$, ent\u00e3o \\[\\mathop {\\lim }\\limits_{x \\to {3^ + }} f\\left( x \\right) = 2\\]<br \/>\nComo para toda a sucess\u00e3o $({v_n})$, tal que $\\begin{array}{*{20}{l}} \u00a0 {({v_n} \\in {D_f}}&amp; \\wedge &amp;{{v_n} &lt; 3,}&amp;{\\forall n \\in \\mathbb{N})}&amp; \\wedge &amp;{{v_n} \\to 3} \\end{array}$, se tem $\\mathop {\\lim }\\limits_{} \\left( {f({v_n})} \\right) =\u00a0 &#8211; 2$, ent\u00e3o \\[\\mathop {\\lim }\\limits_{x \\to {3^ &#8211; }} f(x) = \u00a0&#8211; 2\\]<\/li>\n<li>N\u00e3o existe $$\\mathop {\\lim }\\limits_{x \\to 3} f(x)$$ pois $$\\mathop {\\lim }\\limits_{x \\to {3^ &#8211; }} f(x) \\ne \\mathop {\\lim }\\limits_{x \\to {3^ + }} f(x)$$<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7401' onClick='GTTabs_show(0,7401)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Sabe-se que $f({u_n}) = 2$ e $f({v_n}) =\u00a0 &#8211; 2$ para todas as sucess\u00f5es $({u_n})$ e $({v_n})$ nas condi\u00e7\u00f5es seguintes: $\\begin{array}{*{20}{l}} \u00a0 {({u_n} \\in {D_f}}&amp; \\wedge &amp;{{u_n} &gt; 3,}&amp;{\\forall n \\in&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19494,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,285],"tags":[427,286],"series":[],"class_list":["post-7401","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-12--ano","category-aplicando","category-teoria-de-limites","tag-12-o-ano","tag-limites"],"views":2613,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/03\/Grafico-12_2P204-Ex14.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7401","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=7401"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7401\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19494"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7401"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7401"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7401"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7401"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}