{"id":114003,"date":"2020-01-29T18:19:02","date_gmt":"2020-01-29T17:19:02","guid":{"rendered":"https:\/\/www.superprof.es\/diccionario\/calculo\/teorema-bolzano.html"},"modified":"2020-01-29T18:19:02","modified_gmt":"2020-01-29T17:19:02","slug":"teorema-bolzano","status":"publish","type":"post","link":"https:\/\/www.superprof.es\/diccionario\/matematicas\/calculo\/teorema-bolzano.html","title":{"rendered":"Teorema de bolzano"},"content":{"rendered":"<section id=\"sec\" style=\"\">\n<p class=\"\"><strong>Sea f una funci\u00f3n continua en un intervalo cerrado [a, b] y toma valores de signo contrario en los extremos, entonces existe al menos un c <img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/teorema-de-bolzano-1.gif\" alt=\"Explicaciones y ejemplos de teorema de bolzano - 1\" \/> (a, b) tal que f(c) = 0.<\/strong><\/p>\n<p class=\"actividades_2\"><img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/teorema-de-bolzano-2.gif\" alt=\"Explicaciones y ejemplos de teorema de bolzano - 2\"  ><\/p>\n<p><\/p>\n<p class=\"\">Comprobar que la ecuaci\u00f3n x<sup>3<\/sup> + x \u2212 1 = 0 tiene al menos una soluci\u00f3n real en el intervalo [0,1].<\/p>\n<p class=\"\">Consideramos la funci\u00f3n f(x) =  x<sup>3<\/sup> + x \u2212 1, que es continua en [0,1] por ser polin\u00f3mica. Estudiamos el signo en los extremos del intervalo:<\/p>\n<p class=\"\">f(0) = -1  &lt; 0<\/p>\n<p class=\"\">f(1) = 1 &gt; 0<\/p>\n<p class=\"\">Como los signos son distintos se cumple el <strong>teorema de Bolzano<\/strong>, por tanto existe un <strong>c <img decoding=\"async\" src=\"https:\/\/www.superprof.es\/diccionario\/wp-content\/uploads\/2020\/01\/teorema-de-bolzano-3.gif\" alt=\"Explicaciones y ejemplos de teorema de bolzano - 3\" \/> (0. 1)<\/strong> tal que <strong>f(c) = 0<\/strong>. Lo que demuestra que tiene una soluci\u00f3n en ese intervalo.<\/p>\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>Sea f una funci\u00f3n continua en un intervalo cerrado [a, b] y toma valores de signo contrario en los extremos, entonces existe al menos un c (a, b) tal que f(c) = 0. Comprobar que la ecuaci\u00f3n x3 + x \u2212 1 = 0 tiene al menos una soluci\u00f3n real en el intervalo [0,1]. Consideramos [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_seopress_robots_primary_cat":"","_seopress_titles_title":"","_seopress_titles_desc":"","_seopress_robots_index":"","advgb_blocks_editor_width":"","advgb_blocks_columns_visual_guide":"","footnotes":""},"categories":[366],"tags":[364],"class_list":["post-114003","post","type-post","status-publish","format-standard","hentry","category-calculo","tag-t"],"acf":[],"author_meta":{"display_name":"Andra","author_link":"https:\/\/www.superprof.es\/diccionario\/author\/andra"},"featured_img":null,"coauthors":[],"tax_additional":{"categories":{"linked":["<a href=\"https:\/\/www.superprof.es\/diccionario\/matematicas\/calculo\" class=\"advgb-post-tax-term\">C\u00e1lculo<\/a>"],"unlinked":["<span class=\"advgb-post-tax-term\">C\u00e1lculo<\/span>"]},"tags":{"linked":["<a href=\"https:\/\/www.superprof.es\/diccionario\/matematicas\/calculo\" class=\"advgb-post-tax-term\">t<\/a>"],"unlinked":["<span class=\"advgb-post-tax-term\">t<\/span>"]}},"comment_count":"0","relative_dates":{"created":"Publicado 6 a\u00f1os hace","modified":"Actualizado 6 a\u00f1os hace"},"absolute_dates":{"created":"Publicado el 29 enero 2020","modified":"Actualizado el 29 enero 2020"},"absolute_dates_time":{"created":"Publicado el 29 enero 2020 18 h 19 min","modified":"Actualizado el 29 enero 2020 18 h 19 min"},"featured_img_caption":"","series_order":"","_links":{"self":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/114003","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/comments?post=114003"}],"version-history":[{"count":0,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/114003\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/media?parent=114003"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/categories?post=114003"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/tags?post=114003"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}