{"id":4677,"date":"2019-02-04T06:00:19","date_gmt":"2019-02-04T04:00:19","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=4677"},"modified":"2019-02-11T09:24:44","modified_gmt":"2019-02-11T07:24:44","slug":"limites-de-sucesiones","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/limites-de-sucesiones\/","title":{"rendered":"L\u00edmites de sucesiones"},"content":{"rendered":"<p>El l\u00edmite de una sucesi\u00f3n, con una aproximaci\u00f3n a y una amplitud n, es el primer t\u00e9rmino x de la sucesi\u00f3n tal que el valor absoluto de x y cualquiera de sus n siguentes elementos es menor que a.<\/p>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\"> \n   limite :: [Double] -> Double -> Int -> Double\n<\/pre>\n<p>tal que (limite xs a n) es el l\u00edmite de xs xon aproximaci\u00f3n a y amplitud n. Por ejemplo,<\/p>\n<pre lang=\"text\"> \n   \u03bb> limite [(2*n+1)\/(n+5) | n <- [1..]] 0.001 300\n   1.993991989319092\n   \u03bb> limite [(2*n+1)\/(n+5) | n <- [1..]] 1e-6 300\n   1.9998260062637745\n   \u03bb> limite [(1+1\/n)**n | n <- [1..]] 0.001 300\n   2.7155953364173175\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (tails)\n\nlimite :: [Double] -> Double -> Int -> Double\nlimite xs a n = \n  head [ x | (x:ys) <- segmentos xs n\n       , all (\\y ->  abs (y - x) < a) ys]\n\n-- (segmentos xs n) es la lista de los segmentos de la lista infinita xs\n-- con n elementos. Por ejemplo,   \n--    \u03bb> take 5 (segmentos [1..] 3)\n--    [[1,2,3],[2,3,4],[3,4,5],[4,5,6],[5,6,7]]\nsegmentos :: [a] -> Int -> [[a]]\nsegmentos xs n = map (take n) (tails xs)\n<\/pre>\n<h4>Pensamiento<\/h4>\n<blockquote><p>\nDe diez cabezas, nueve<br \/>\nembisten y una piensa.<br \/>\nNunca extra\u00f1\u00e9is que un bruto<br \/>\nse descuerne luchando por la idea.<\/p>\n<p>Antonio Machado\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>El l\u00edmite de una sucesi\u00f3n, con una aproximaci\u00f3n a y una amplitud n, es el primer t\u00e9rmino x de la sucesi\u00f3n tal que el valor absoluto de x y cualquiera de sus n siguentes elementos es menor que a. Definir la funci\u00f3n limite :: [Double] -> Double -> Int -> Double tal que (limite xs&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"footnotes":"","_jetpack_memberships_contains_paid_content":false},"categories":[5],"tags":[130,41,8,415,10,11,75,47],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4677"}],"collection":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/comments?post=4677"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4677\/revisions"}],"predecessor-version":[{"id":4718,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4677\/revisions\/4718"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=4677"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=4677"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=4677"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}