{"id":119,"date":"2010-11-07T01:32:20","date_gmt":"2010-11-07T01:32:20","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/jloy\/?p=119"},"modified":"2010-11-07T01:48:59","modified_gmt":"2010-11-07T01:48:59","slug":"the-rigorous-study-of-limits","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/jloy\/2010\/11\/07\/the-rigorous-study-of-limits\/","title":{"rendered":"The rigorous study of limits."},"content":{"rendered":"<pre><strong>Prove that<\/strong><\/pre>\n<pre><strong>lim\u00a0(3x - 7) = 5.<\/strong><\/pre>\n<pre><strong>x\u21924<\/strong><\/pre>\n<pre><span style=\"font-weight: normal;line-height: normal;font-size: small\"><span style=\"font-size: xx-small\"><span style=\"color: #000000\"><strong>0\u00a0<\/strong><\/span><\/span><span style=\"font-family: Verdana, Arial, Helvetica;color: #ff6600;font-size: xx-small\"><span style=\"color: #000000\"><strong>&lt;<\/strong><\/span><\/span><span style=\"font-weight: bold;font-size: xx-small\"><span style=\"color: #000000\"><strong>\u00a0<\/strong><\/span><\/span><\/span><span style=\"font-weight: bold\"><span style=\"color: #000000\"><strong>x - 4\u00a0<\/strong><\/span><\/span><span style=\"font-family: 'Times New Roman';line-height: normal;font-size: small\"><span style=\"font-size: xx-small\"><span style=\"color: #000000\"><strong>&lt;\u00a0<\/strong><\/span><\/span><\/span><span style=\"font-family: sans-serif\"><span style=\"color: #000000\"><strong>\u03b4 \u00a0<\/strong><\/span><\/span><span style=\"color: #000000\"><strong>\u2192 \u00a03x - 7 - 5\u00a0<\/strong><\/span><span style=\"font-family: 'Times New Roman';line-height: normal;font-size: small\"><span style=\"font-size: xx-small\"><span style=\"color: #000000\"><strong>&lt;\u00a0<\/strong><\/span><\/span><\/span><span style=\"font-family: arial, sans-serif;line-height: 15px;font-size: x-small\"><span style=\"color: #000000\"><strong>\u03b5<\/strong><\/span><\/span><\/pre>\n<pre><span style=\"font-family: arial, sans-serif;line-height: 15px;font-size: x-small\"><span style=\"color: #000000\"><strong>                                       3x - 12 <\/strong><\/span><\/span><span style=\"font-family: 'Times New Roman';line-height: normal;font-size: small\"><span style=\"font-size: xx-small\"><span style=\"color: #000000\"><strong>&lt;\u00a0<\/strong><\/span><\/span><\/span><span style=\"font-family: arial, sans-serif;line-height: 15px;font-size: x-small\"><span style=\"color: #000000\"><strong>\u03b5<\/strong><\/span><\/span><\/pre>\n<pre><span style=\"font-family: arial, sans-serif;line-height: 15px;font-size: x-small\"><span style=\"color: #000000\"><strong>                                       3 (x - 4) <\/strong><\/span><\/span><span style=\"font-family: 'Times New Roman';line-height: normal;font-size: small\"><span style=\"font-size: xx-small\"><span style=\"color: #000000\"><strong>&lt;\u00a0<\/strong><\/span><\/span><\/span><span style=\"font-family: arial, sans-serif;line-height: 15px;font-size: x-small\"><span style=\"color: #000000\"><strong>\u03b5<\/strong><\/span><\/span><\/pre>\n<pre><span style=\"font-family: arial, sans-serif;line-height: 15px;font-size: x-small\"><span style=\"color: #000000\"><strong>                                       x - 4 <\/strong><\/span><\/span><span style=\"font-family: 'Times New Roman';line-height: normal;font-size: small\"><span style=\"font-size: xx-small\"><span style=\"color: #000000\"><strong>&lt;\u00a0<\/strong><\/span><\/span><\/span><span style=\"font-family: arial, sans-serif;line-height: 15px;font-size: x-small\"><span style=\"color: #000000\"><strong>\u03b5\/3<\/strong><\/span><\/span><\/pre>\n<pre><span style=\"line-height: 15px;font-size: x-small\"><span style=\"font-weight: normal;line-height: 19px;font-size: 13px\"><span style=\"font-size: small\"><span style=\"line-height: 19px\"><strong>\r\n<\/strong><\/span><\/span><strong>\r\n<\/strong>\r\n<pre><span style=\"color: #ff0000\"><strong>\u03b4 = <\/strong><\/span><span style=\"line-height: 15px;font-size: x-small\"><span style=\"color: #ff0000\"><strong>\u03b5\/3<\/strong><\/span><\/span><\/pre>\n<p><strong> <\/strong><span style=\"font-size: small\"><span style=\"line-height: 19px\"><strong> <\/strong><\/span><\/span><span style=\"color: #000000\"><strong>3x - 12 <span style=\"line-height: normal;font-size: xx-small\">&lt; \u03b4<\/span><\/strong><\/span><\/p>\n<p><strong> <\/strong><\/p>\n<p><\/span><\/span><\/p>\n<pre><span style=\"line-height: 15px;font-size: x-small\"><span style=\"font-weight: normal;line-height: 19px;font-size: 13px\"><span style=\"color: #000000\"><span style=\"font-size: small\"><span style=\"line-height: 19px\"><strong>3 (x - 4) <\/strong><\/span><\/span><span style=\"font-weight: normal\"><span style=\"font-weight: normal;line-height: 19px;font-size: 13px\"><span style=\"line-height: normal;font-size: xx-small;font-weight: normal\"><strong>&lt;  3\u03b4 = <\/strong><\/span><strong>\u03b5<\/strong><\/span><\/span><\/span><\/span><\/span><\/pre>\n<pre style=\"text-align: right\"><span style=\"line-height: 15px\"><strong><span style=\"color: #000000\"><span style=\"text-decoration: underline\">D E M O S T R A D O<\/span><\/span><\/strong><\/span><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Prove that lim\u00a0(3x - 7) = 5. x\u21924 0\u00a0&lt;\u00a0x - 4\u00a0&lt;\u00a0\u03b4 \u00a0\u2192 \u00a03x - 7 - 5\u00a0&lt;\u00a0\u03b5 3x - 12 &lt;\u00a0\u03b5 3 (x - 4) &lt;\u00a0\u03b5 x - 4 &lt;\u00a0\u03b5\/3 \u03b4 = \u03b5\/3 3x - 12 &lt; \u03b4 3 (x - 4) &lt; 3\u03b4 = \u03b5 D E M O S T R A D [&hellip;]<\/p>\n","protected":false},"author":5402,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-119","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/jloy\/wp-json\/wp\/v2\/posts\/119","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.espol.edu.ec\/jloy\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.espol.edu.ec\/jloy\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/jloy\/wp-json\/wp\/v2\/users\/5402"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/jloy\/wp-json\/wp\/v2\/comments?post=119"}],"version-history":[{"count":10,"href":"https:\/\/blog.espol.edu.ec\/jloy\/wp-json\/wp\/v2\/posts\/119\/revisions"}],"predecessor-version":[{"id":129,"href":"https:\/\/blog.espol.edu.ec\/jloy\/wp-json\/wp\/v2\/posts\/119\/revisions\/129"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/jloy\/wp-json\/wp\/v2\/media?parent=119"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/jloy\/wp-json\/wp\/v2\/categories?post=119"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/jloy\/wp-json\/wp\/v2\/tags?post=119"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}