{"id":1472,"date":"2010-10-21T13:11:00","date_gmt":"2010-10-21T11:11:00","guid":{"rendered":"http:\/\/laaventuradelasmatematicas.jesussoto.es\/?p=1472"},"modified":"2010-10-21T13:11:00","modified_gmt":"2010-10-21T11:11:00","slug":"un-limite-sencillo","status":"publish","type":"post","link":"http:\/\/pimedios.jesussoto.es\/?p=1472","title":{"rendered":"Un l\u00edmite sencillo"},"content":{"rendered":"<p>De vez de en cuando nos surge en clase una pregunta que no suele aparecer en las mentes de los alumnos: &iquest;por qu&eacute;? Es curioso, verdad. Bueno, pues una respuesta a la afirmaci&oacute;n de que<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" width=\"96\" height=\"43\" alt=\"\" src=\"http:\/\/laaventuradelasmatematicas.jesussoto.es\/wp-content\/uploads\/lim1.png\" \/><\/p>\n<p>utilizando geometr&iacute;a y el &quot;teorema del s&aacute;ndwich de los l&iacute;mites&quot;, podr&iacute;a ser esta.<\/p>\n<p>Utilizamos la circunferencia de radio unidad, tomando x, en radianes, el &aacute;ngulo <em>COB<\/em>, tal que $0&lt;x&lt;\\frac{\\pi}{2}$.<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" width=\"183\" height=\"182\" alt=\"\" src=\"http:\/\/laaventuradelasmatematicas.jesussoto.es\/wp-content\/uploads\/lim2.png\" \/><\/p>\n<p>Entonces, se cumple que<\/p>\n<p style=\"text-align: center;\">&aacute;rea tri&aacute;ngulo <em>OAB <\/em>&lt; &aacute;rea sector <em>OAB <\/em>&lt; &aacute;rea triangular <em>OED<\/em>.<\/p>\n<p>A partir de aqu&iacute; obtenemos<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" width=\"359\" height=\"285\" alt=\"\" src=\"http:\/\/laaventuradelasmatematicas.jesussoto.es\/wp-content\/uploads\/lim3.png\" \/><\/p>\n<p>La &uacute;ltima igualdad nos implica directamente el resultado que buscamos.<\/p>\n<h3>Enlaces de inter&eacute;s:<\/h3>\n<ul>\n<li><a href=\"http:\/\/books.google.es\/books?id=DEW2TeAjhhYC&amp;lpg=PA249&amp;dq=limites%20de%20funciones&amp;pg=PA258#v=onepage&amp;q&amp;f=false\">Problemas de c&aacute;lculo infinitesimal<\/a>, E. T&eacute;bar Flores<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>De vez de en cuando nos surge en clase una pregunta que no suele aparecer en las mentes de los alumnos: &iquest;por qu&eacute;? Es curioso, verdad. Bueno, pues una respuesta a la afirmaci&oacute;n de que utilizando geometr&iacute;a y el &quot;teorema del s&aacute;ndwich de los l&iacute;mites&quot;, podr&iacute;a ser esta. Utilizamos la circunferencia de radio unidad, tomando&hellip; <a class=\"more-link\" href=\"http:\/\/pimedios.jesussoto.es\/?p=1472\">Seguir leyendo <span class=\"screen-reader-text\">Un l\u00edmite sencillo<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[],"class_list":["post-1472","post","type-post","status-publish","format-standard","hentry","category-ocio","entry"],"_links":{"self":[{"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/1472","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1472"}],"version-history":[{"count":0,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/1472\/revisions"}],"wp:attachment":[{"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1472"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1472"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1472"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}