{"id":12800,"date":"2017-10-29T01:57:36","date_gmt":"2017-10-29T01:57:36","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=12800"},"modified":"2022-01-08T17:50:33","modified_gmt":"2022-01-08T17:50:33","slug":"qual-e-o-erro-maximo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=12800","title":{"rendered":"Qual \u00e9 o erro m\u00e1ximo?"},"content":{"rendered":"<p><ul id='GTTabs_ul_12800' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_12800' class='GTTabs_curr'><a  id=\"12800_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_12800' ><a  id=\"12800_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_12800'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Considera que\u00a0\\(3\\) \u00e9 uma aproxima\u00e7\u00e3o de um n\u00famero real\u00a0\\(x\\) com um erro inferior a\u00a0\\(0,2\\) e que\u00a0\\( &#8211; 4\\) \u00e9 uma aproxima\u00e7\u00e3o de um n\u00famero\u00a0\\(y\\) com um erro inferior a \\({0,1}\\).<\/p>\n<p>Qual \u00e9 o erro m\u00e1ximo que se comete ao aproximar\u00a0\\(x + y\\) por\u00a0\\(3 + \\left( { &#8211; 4} \\right) = &#8211; 1\\)?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_12800' onClick='GTTabs_show(1,12800)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_12800'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Como:<\/p>\n<ul style=\"list-style-type: disc;\">\n<li>\\(3\\) \u00e9 uma aproxima\u00e7\u00e3o de um n\u00famero real\u00a0\\(x\\) com um erro inferior a\u00a0\\(0,2\\)<\/li>\n<li>\\( &#8211; 4\\) \u00e9 uma aproxima\u00e7\u00e3o de um n\u00famero\u00a0\\(y\\) com um erro inferior a \\({0,1}\\)<\/li>\n<\/ul>\n<p>ser\u00e1:<\/p>\n<p>\\[\\begin{array}{*{20}{c}}{3 &#8211; 0,2 &lt; x &lt; 3 + 0,2}&amp; \\Leftrightarrow &amp;{2,8 &lt; x &lt; 3,2}\\end{array}\\]<\/p>\n<p>\\[\\begin{array}{*{20}{c}}{ &#8211; 4 &#8211; 0,1 &lt; y &lt; &#8211; 4 + 0,1}&amp; \\Leftrightarrow &amp;{ &#8211; 4,1 &lt; y &lt; &#8211; 3,9}\\end{array}\\]<\/p>\n<p>Assim, tem-se:<\/p>\n<p>\\[\\begin{array}{*{20}{c}}{2,8 &lt; x &lt; 3,2}\\\\{ &#8211; 4,1 &lt; y &lt; &#8211; 3,9}\\\\\\hline{ &#8211; 1,3 &lt; x + y &lt; &#8211; 0,7}\\end{array}\\]<\/p>\n<p>Como\u00a0\\(\\left| { &#8211; 1,3 &#8211; \\left( { &#8211; 1} \\right)} \\right| = \\left| { &#8211; 0,7 &#8211; \\left( { &#8211; 1} \\right)} \\right| = 0,3\\), ent\u00e3o o\u00a0erro m\u00e1ximo que se comete ao aproximar\u00a0\\(x + y\\) por\u00a0\\(3 + \\left( { &#8211; 4} \\right) = &#8211; 1\\) \u00e9 inferior a\u00a0\\(0,3 = 0,2 + 0,1\\).<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_12800' onClick='GTTabs_show(0,12800)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera que\u00a0\\(3\\) \u00e9 uma aproxima\u00e7\u00e3o de um n\u00famero real\u00a0\\(x\\) com um erro inferior a\u00a0\\(0,2\\) e que\u00a0\\( &#8211; 4\\) \u00e9 uma aproxima\u00e7\u00e3o de um n\u00famero\u00a0\\(y\\) com um erro inferior a \\({0,1}\\). Qual&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":12805,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,258],"tags":[443,444,442],"series":[],"class_list":["post-12800","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-os-numeros-reais","tag-enquadramento","tag-erro","tag-valor-aproximado"],"views":2494,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/10\/Enquadramento2.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12800","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=12800"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/12800\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/12805"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12800"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12800"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12800"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=12800"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}