{"id":11800,"date":"2014-02-20T23:09:53","date_gmt":"2014-02-20T23:09:53","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=11800"},"modified":"2022-01-22T02:23:25","modified_gmt":"2022-01-22T02:23:25","slug":"a-continuidade-da-funcao","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=11800","title":{"rendered":"A continuidade da fun\u00e7\u00e3o"},"content":{"rendered":"<p><ul id='GTTabs_ul_11800' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_11800' class='GTTabs_curr'><a  id=\"11800_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_11800' ><a  id=\"11800_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_11800'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Com a ajuda da calculadora gr\u00e1fica, estude a continuidade das seguintes fun\u00e7\u00f5es\u00a0de acordo com os valores que o par\u00e2metro real $m$ toma.<\/p>\n<p>\\[\\begin{array}{*{20}{c}}<br \/>\n{h\\left( x \\right) = \\left\\{ {\\begin{array}{*{20}{l}}<br \/>\n{\\frac{m}{x}}&amp; \\Leftarrow &amp;{0 &lt; x \\leqslant 2} \\\\<br \/>\n{ &#8211; {x^2} + 10x + 3}&amp; \\Leftarrow &amp;{x &gt; 2}<br \/>\n\\end{array}} \\right.}&amp;{}&amp;{\\text{e}}&amp;{}&amp;{p\\left( x \\right) = \\left\\{ {\\begin{array}{*{20}{l}}<br \/>\n{\\frac{3}{x}}&amp; \\Leftarrow &amp;{0 &lt; x \\leqslant 1} \\\\<br \/>\n{1 + mx}&amp; \\Leftarrow &amp;{x &gt; 1}<br \/>\n\\end{array}} \\right.}<br \/>\n\\end{array}\\]<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_11800' onClick='GTTabs_show(1,11800)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_11800'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<\/p>\n<blockquote>\n<p>\\[{h\\left( x \\right) = \\left\\{ {\\begin{array}{*{20}{l}}<br \/>\n{\\frac{m}{x}}&amp; \\Leftarrow &amp;{0 &lt; x \\leqslant 2} \\\\<br \/>\n{ &#8211; {x^2} + 10x + 3}&amp; \\Leftarrow &amp;{x &gt; 2}<br \/>\n\\end{array}} \\right.}\\]<\/p>\n<\/blockquote>\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\":910,\r\n\"height\":500,\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\/\/ 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\\[\\begin{array}{*{20}{c}} {h\\left( x \\right) = \\left\\{ {\\begin{array}{*{20}{l}} {\\frac{m}{x}}&amp; 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