{"id":29570,"date":"2024-11-18T17:33:55","date_gmt":"2024-11-18T17:33:55","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=29570"},"modified":"2024-11-18T17:33:55","modified_gmt":"2024-11-18T17:33:55","slug":"%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/","title":{"rendered":"\u041f\u0440\u0435\u0434\u0435\u043b \u0438 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c"},"content":{"rendered":"<style>\np {\ntext-align:justify;\n}\n<\/style>\n<p><center><\/p>\n<h1>\u041f\u0440\u0435\u0434\u0435\u043b \u0438 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c<\/h1>\n<p><\/center><\/p>\n<p style=\"text-align:center;\"><em><strong>\u0420\u0435\u0437\u044e\u043c\u0435:<\/strong><\/em><br \/>\n\u041d\u0430 \u044d\u0442\u043e\u043c \u0443\u0440\u043e\u043a\u0435 \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u0435\u0442\u0441\u044f \u0441\u0432\u044f\u0437\u044c \u043c\u0435\u0436\u0434\u0443 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u043c \u0438 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043d\u0430\u0447\u0438\u043d\u0430\u044f \u0441 \u0438\u043d\u0442\u0443\u0438\u0442\u0438\u0432\u043d\u043e\u0433\u043e \u0438 \u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u044f \u0442\u0435\u0440\u043c\u0438\u043d\u0430. \u0420\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u0435\u0442\u0441\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c \u0432 \u0442\u043e\u0447\u043a\u0435 \u0438 \u043d\u0430 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0435, \u043f\u043e\u0434\u0440\u043e\u0431\u043d\u043e \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u044e\u0442\u0441\u044f \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u044b\u0435 \u0443\u0441\u043b\u043e\u0432\u0438\u044f \u0434\u043b\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0422\u0430\u043a\u0436\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u044b \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u0432\u043a\u043b\u044e\u0447\u0430\u044f \u0441\u0443\u043c\u043c\u044b, \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f, \u0447\u0430\u0441\u0442\u043d\u044b\u0435 \u0438 \u043a\u043e\u043c\u043f\u043e\u0437\u0438\u0446\u0438\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0439. \u0412 \u043a\u043e\u043d\u0446\u0435 \u0443\u0440\u043e\u043a\u0430 \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u044e\u0442\u0441\u044f \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0434\u043b\u044f \u0430\u043d\u0430\u043b\u0438\u0437\u0430 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u0438 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0438 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432, \u0441\u0432\u044f\u0437\u0430\u043d\u043d\u044b\u0445 \u0441 \u043f\u043e\u043d\u044f\u0442\u0438\u0435\u043c \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u0438.\n<\/p>\n<p style=\"text-align:center;\"><strong>\u0426\u0435\u043b\u0438 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f:<\/strong><br \/>\n\u041f\u043e\u0441\u043b\u0435 \u0437\u0430\u0432\u0435\u0440\u0448\u0435\u043d\u0438\u044f \u044d\u0442\u043e\u0433\u043e \u0443\u0440\u043e\u043a\u0430 \u0441\u0442\u0443\u0434\u0435\u043d\u0442 \u0441\u043c\u043e\u0436\u0435\u0442:<\/p>\n<ol>\n<li><strong>\u0410\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c<\/strong> \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0442\u043e\u0447\u043a\u0435, \u043f\u0440\u043e\u0432\u0435\u0440\u044f\u044f \u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u043d\u044b\u0435 \u0443\u0441\u043b\u043e\u0432\u0438\u044f.<\/li>\n<li><strong>\u041e\u0446\u0435\u043d\u0438\u0432\u0430\u0442\u044c<\/strong>, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0439 \u043d\u0430 \u0437\u0430\u0434\u0430\u043d\u043d\u043e\u043c \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0435, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u0438.<\/li>\n<li><strong>\u0414\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0442\u044c<\/strong> \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u0435 \u0435\u0451 \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0441\u0432\u043e\u0439\u0441\u0442\u0432.<\/li>\n<li><strong>\u041a\u043b\u0430\u0441\u0441\u0438\u0444\u0438\u0446\u0438\u0440\u043e\u0432\u0430\u0442\u044c<\/strong> \u0442\u043e\u0447\u043a\u0438 \u0440\u0430\u0437\u0440\u044b\u0432\u0430 \u043d\u0430 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0435 \u0442\u0438\u043f\u044b \u0432 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 \u043e\u0442 \u043d\u0435\u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u043d\u044b\u0445 \u0443\u0441\u043b\u043e\u0432\u0438\u0439.<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong><u>\u0421\u041e\u0414\u0415\u0420\u0416\u0410\u041d\u0418\u0415:<\/u><\/strong><br \/>\n<a href=\"#1\">\u0412\u0432\u0435\u0434\u0435\u043d\u0438\u0435<\/a><br \/>\n<a href=\"#2\">\u041d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c \u0432 \u0442\u043e\u0447\u043a\u0435<\/a><br \/>\n<a href=\"#3\">\u041d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c \u043d\u0430 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0435<\/a><br \/>\n<a href=\"#4\">\u0421\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439<\/a><br \/>\n<a href=\"#5\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/4kehfJcyPRg\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u0412\u0432\u0435\u0434\u0435\u043d\u0438\u0435<\/h2>\n<p ><a href=\"https:\/\/www.youtube.com\/watch?v=4kehfJcyPRg&amp;t=109s\" target=\"_blank\" rel=\"noopener\"><strong>\u0418\u043d\u0442\u0443\u0438\u0442\u0438\u0432\u043d\u043e \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438<\/strong><\/a> \u043f\u043e\u043d\u0438\u043c\u0430\u0435\u0442\u0441\u044f \u043a\u0430\u043a \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u043e, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u043d\u0430\u0440\u0438\u0441\u043e\u0432\u0430\u0442\u044c \u0435\u0451 \u0433\u0440\u0430\u0444\u0438\u043a \u00ab\u043d\u0435 \u043e\u0442\u0440\u044b\u0432\u0430\u044f \u043a\u0430\u0440\u0430\u043d\u0434\u0430\u0448\u0430 \u043e\u0442 \u0431\u0443\u043c\u0430\u0433\u0438\u00bb. \u041e\u0434\u043d\u0430\u043a\u043e \u044d\u0442\u043e \u043f\u043e\u043d\u044f\u0442\u0438\u0435, \u0445\u043e\u0442\u044f \u0438 \u043b\u0435\u0433\u043a\u043e \u0434\u043b\u044f \u043f\u043e\u043d\u0438\u043c\u0430\u043d\u0438\u044f, \u043d\u0435\u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e \u0434\u043b\u044f \u0441\u0442\u0440\u043e\u0433\u043e\u0433\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043e\u0431\u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f. \u0422\u0440\u0435\u0431\u0443\u0435\u0442\u0441\u044f \u043c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u0430\u044f \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0441\u0442\u0438. \u0421 \u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0438 \u0437\u0440\u0435\u043d\u0438\u044f, \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0442\u0435\u0441\u043d\u043e \u0441\u0432\u044f\u0437\u0430\u043d\u0430 \u0441 \u043f\u043e\u043d\u044f\u0442\u0438\u0435\u043c \u043f\u0440\u0435\u0434\u0435\u043b\u0430, \u0438 \u0438\u043c\u0435\u043d\u043d\u043e \u044d\u0442\u043e \u043c\u044b \u0431\u0443\u0434\u0435\u043c \u0438\u0437\u0443\u0447\u0430\u0442\u044c \u0432 \u0434\u0435\u0442\u0430\u043b\u044f\u0445.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h3>\u041d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c \u0432 \u0442\u043e\u0447\u043a\u0435<\/h3>\n<p ><a href=\"https:\/\/www.youtube.com\/watch?v=4kehfJcyPRg&amp;t=152s\" target=\"_blank\" rel=\"noopener\"><strong>\u0424\u0443\u043d\u043a\u0446\u0438\u044f <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0439 \u0432 \u0442\u043e\u0447\u043a\u0435<\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">x=x_0<\/span>, \u0435\u0441\u043b\u0438 \u0438 \u0442\u043e\u043b\u044c\u043a\u043e \u0435\u0441\u043b\u0438 \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u044e\u0442\u0441\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0443\u0441\u043b\u043e\u0432\u0438\u044f:<\/p>\n<ul >\n<li><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0430 \u0432 <span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/li>\n<li>\u0421\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043f\u0440\u0435\u0434\u0435\u043b <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to x_0} f(x)<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to x_0} f(x) = f(x_0)<\/span><\/li>\n<\/ul>\n<p >\u0412\u0441\u0435 \u044d\u0442\u043e \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0440\u0430\u0437\u0438\u0442\u044c \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0433\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\forall \\epsilon \\gt 0 \\right) \\left(\\exists \\delta \\gt 0 \\right) \\left(0\\lt |x-x_0|\\lt \\delta \\rightarrow |f(x) - f(x_0)|\\lt \\epsilon\\right)<\/span>\n<p >\u042d\u0442\u043e \u0438\u043c\u0435\u043d\u043d\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u0430, \u0433\u0434\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u00abL\u00bb \u0437\u0430\u043c\u0435\u043d\u0435\u043d\u043e \u043d\u0430 \u00abf(<span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span>)\u00bb<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h3>\u041d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c \u043d\u0430 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0435<\/h3>\n<p ><a href=\"https:\/\/www.youtube.com\/watch?v=4kehfJcyPRg&amp;t=462s\" target=\"_blank\" rel=\"noopener\"><strong>\u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u0438<\/strong><\/a> \u0432 \u043e\u0434\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u0440\u0430\u0441\u0448\u0438\u0440\u0435\u043d\u043e \u0434\u043e \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u0438 \u0432\u043e \u0432\u0441\u0435\u0445 \u0442\u043e\u0447\u043a\u0430\u0445 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430. \u041c\u044b \u0433\u043e\u0432\u043e\u0440\u0438\u043c, \u0447\u0442\u043e <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430 \u043d\u0430 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">I\\subseteq Dom(f)<\/span>, \u0435\u0441\u043b\u0438 \u043e\u043d\u0430 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430 \u0432\u043e \u0432\u0441\u0435\u0445 \u0442\u043e\u0447\u043a\u0430\u0445 <span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in I.<\/span> \u042d\u0442\u043e \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0440\u0430\u0437\u0438\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u043c \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435\u043c.<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\forall x_0 \\in I\\subseteq Dom(f) \\right)\\left(\\forall \\epsilon \\gt 0 \\right) \\left(\\exists \\delta \\gt 0 \\right) \\left(0\\lt |x-x_0|\\lt \\delta \\rightarrow |f(x) - f(x_0)|\\lt \\epsilon\\right)<\/span>\n<p><a name=\"4\"><\/a><\/p>\n<h3>\u0421\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439<\/h3>\n<h4>\u0410\u043b\u0433\u0435\u0431\u0440\u0430 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439<\/h4>\n<p ><a href=\"https:\/\/www.youtube.com\/watch?v=4kehfJcyPRg&amp;t=575s\" target=\"_blank\" rel=\"noopener\"><strong>\u0415\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">g<\/span> \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b\u043c\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u043c\u0438 \u043d\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">I\\subseteq Dom(f)\\cap Dom(g)<\/span><\/strong><\/a>, \u0442\u043e \u043c\u044b \u0438\u043c\u0435\u0435\u043c:<\/p>\n<ul >\n<li><span class=\"katex-eq\" data-katex-display=\"false\">f\\pm g<\/span> \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430 \u043d\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">f\\cdot g<\/span> \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430 \u043d\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span><\/li>\n<li>\u0415\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha\\in\\mathbb{R}<\/span>, \u0442\u043e <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha f<\/span> \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430 \u043d\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">f\/g<\/span> \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430 \u043d\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span>, \u0435\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">g\\neq 0<\/span><\/li>\n<li>\u0415\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha,\\beta\\in\\mathbb{R}<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">\\beta\\neq 0<\/span>, \u0442\u043e <span class=\"katex-eq\" data-katex-display=\"false\">f^{\\alpha\/\\beta}<\/span> \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430 \u043d\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span>, \u0435\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">f^{\\alpha\/\\beta}<\/span> \u0445\u043e\u0440\u043e\u0448\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0430 \u043d\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">I.<\/span><\/li>\n<\/ul>\n<p >\u0412\u0441\u0435 \u044d\u0442\u0438 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043c\u043e\u0433\u0443\u0442 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u044c\u0441\u044f \u0441\u043b\u043e\u0436\u043d\u044b\u043c\u0438 \u0434\u043b\u044f \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u0441\u0442\u0432\u0430 \u0441 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u0438, \u043d\u0430 \u0441\u0430\u043c\u043e\u043c \u0434\u0435\u043b\u0435 \u0434\u043e\u0432\u043e\u043b\u044c\u043d\u043e \u043f\u0440\u043e\u0441\u0442\u044b, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043e\u043d\u0438 \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u044b \u0430\u043b\u0433\u0435\u0431\u0440\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043c\u044b <a href=\"https:\/\/toposuranos.com\/la-definicion-de-limite-demostraciones-y-teoremas\/\" rel=\"noopener\" target=\"_blank\">\u0443\u0436\u0435 \u0434\u043e\u043a\u0430\u0437\u0430\u043b\u0438<\/a>, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u043e\u0441\u0432\u043e\u0431\u043e\u0436\u0434\u0435\u043d\u044b \u043e\u0442 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e\u0441\u0442\u0438 \u0438\u0445 \u0434\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0442\u044c \u0441\u043d\u043e\u0432\u0430.<\/p>\n<h5>\u041a\u043e\u043c\u043f\u043e\u0437\u0438\u0446\u0438\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439<\/h5>\n<p >\u0415\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430 \u043d\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">I\\subseteq Dom(f)<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">g<\/span> \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430 \u043d\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">f(I)<\/span>, \u0442\u043e\u0433\u0434\u0430 \u043a\u043e\u043c\u043f\u043e\u0437\u0438\u0446\u0438\u044f <span class=\"katex-eq\" data-katex-display=\"false\">(g\\circ f)(x) = g(f(x))<\/span> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0439 \u043d\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span>. \u042d\u0442\u043e, \u043a\u0430\u043a \u0443\u0436\u0435 \u043c\u043e\u0436\u043d\u043e \u043f\u0440\u0435\u0434\u043f\u043e\u043b\u043e\u0436\u0438\u0442\u044c, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043f\u0440\u044f\u043c\u044b\u043c \u0441\u043b\u0435\u0434\u0441\u0442\u0432\u0438\u0435\u043c \u0437\u0430\u043a\u043e\u043d\u043e\u0432 \u043a\u043e\u043c\u043f\u043e\u0437\u0438\u0446\u0438\u0438 \u0434\u043b\u044f \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432 \u0444\u0443\u043d\u043a\u0446\u0438\u0439.<\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f<\/h2>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/R91vswfQT_Q\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<ol >\n<li>\u0410\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u0443\u0439\u0442\u0435 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439<br \/>\n<table>\n<tbody>\n<tr>\n<td width=\"30\">a.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y=\\dfrac{1}{x-2} - 3x<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=33s\" target=\"_blank\" rel=\"noopener\"><strong>\u0420\u0415\u0428\u0415\u041d\u0418\u0415<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>b.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y=\\dfrac{x+1}{x^2-4x+3}<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=97s\" target=\"_blank\" rel=\"noopener\"><strong>\u0420\u0415\u0428\u0415\u041d\u0418\u0415<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>c.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y=|x-1| + \\sin(x)<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=215s\" target=\"_blank\" rel=\"noopener\"><strong>\u0420\u0415\u0428\u0415\u041d\u0418\u0415<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>d.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y=\\dfrac{\\cos(x)}{x}<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=450s\" target=\"_blank\" rel=\"noopener\"><strong>\u0420\u0415\u0428\u0415\u041d\u0418\u0415<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>e.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y=csc(2x)<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=564s\" target=\"_blank\" rel=\"noopener\"><strong>\u0420\u0415\u0428\u0415\u041d\u0418\u0415<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>f.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y=\\dfrac{x\\tan(x)}{x^2 + 1}<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=666s\" target=\"_blank\" rel=\"noopener\"><strong>\u0420\u0415\u0428\u0415\u041d\u0418\u0415<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>g.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y=\\sqrt{2x + 3}<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=784s\" target=\"_blank\" rel=\"noopener\"><strong>\u0420\u0415\u0428\u0415\u041d\u0418\u0415<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>h.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y=\\dfrac{x+2}{\\cos(x)}<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=917s\" target=\"_blank\" rel=\"noopener\"><strong>\u0420\u0415\u0428\u0415\u041d\u0418\u0415<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>i.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y=\\dfrac{\\sqrt{x^4 + 1}}{1+\\sin^2(x)}<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=952s\" target=\"_blank\" rel=\"noopener\"><strong>\u0420\u0415\u0428\u0415\u041d\u0418\u0415<\/strong><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>\u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b. \u042f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b\u043c\u0438 \u0432 \u0442\u043e\u0447\u043a\u0430\u0445, \u043a \u043a\u043e\u0442\u043e\u0440\u044b\u043c \u043e\u043d\u0438 \u0441\u0442\u0440\u0435\u043c\u044f\u0442\u0441\u044f?<br \/>\n<table>\n<tbody>\n<tr>\n<td width=\"30\">a.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to\\pi} \\sin(x -\\sin(x))<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=1033s\" target=\"_blank\" rel=\"noopener\"><strong>\u0420\u0415\u0428\u0415\u041d\u0418\u0415<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>b.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to 0} \\sin\\left(\\dfrac{\\pi}{2}\\cos(\\tan(x)) \\right)<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=1092s\" target=\"_blank\" rel=\"noopener\"><strong>\u0420\u0415\u0428\u0415\u041d\u0418\u0415<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>c.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to 1} \\sec\\left(x\\sec^2(x) - \\tan^2(x) -1 \\right)<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=1162s\" target=\"_blank\" rel=\"noopener\"><strong>\u0420\u0415\u0428\u0415\u041d\u0418\u0415<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>d.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to 0} \\tan\\left(\\dfrac{\\pi}{4}\\cos\\left(\\sin\\left(x^{1\/3}\\right)\\right) \\right)<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=1274s\" target=\"_blank\" rel=\"noopener\"><strong>\u0420\u0415\u0428\u0415\u041d\u0418\u0415<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>e.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to 0} \\cos\\left(\\dfrac{\\pi}{\\sqrt{19 - 3\\sec{2x}}} \\right)<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=1424s\" target=\"_blank\" rel=\"noopener\"><strong>\u0420\u0415\u0428\u0415\u041d\u0418\u0415<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>f.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to \\pi\/6} \\sqrt{\\csc^2(x) + 5\\sqrt{3}\\tan(x)}<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=1505s\" target=\"_blank\" rel=\"noopener\"><strong>\u0420\u0415\u0428\u0415\u041d\u0418\u0415<\/strong><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u041f\u0440\u0435\u0434\u0435\u043b \u0438 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c \u0420\u0435\u0437\u044e\u043c\u0435: \u041d\u0430 \u044d\u0442\u043e\u043c \u0443\u0440\u043e\u043a\u0435 \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u0435\u0442\u0441\u044f \u0441\u0432\u044f\u0437\u044c \u043c\u0435\u0436\u0434\u0443 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u043c \u0438 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043d\u0430\u0447\u0438\u043d\u0430\u044f \u0441 \u0438\u043d\u0442\u0443\u0438\u0442\u0438\u0432\u043d\u043e\u0433\u043e \u0438 \u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u044f \u0442\u0435\u0440\u043c\u0438\u043d\u0430. \u0420\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u0435\u0442\u0441\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c \u0432 \u0442\u043e\u0447\u043a\u0435 \u0438 \u043d\u0430 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0435, \u043f\u043e\u0434\u0440\u043e\u0431\u043d\u043e \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u044e\u0442\u0441\u044f \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u044b\u0435 \u0443\u0441\u043b\u043e\u0432\u0438\u044f \u0434\u043b\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0422\u0430\u043a\u0436\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u044b \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u0432\u043a\u043b\u044e\u0447\u0430\u044f \u0441\u0443\u043c\u043c\u044b, \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f, \u0447\u0430\u0441\u0442\u043d\u044b\u0435 \u0438 \u043a\u043e\u043c\u043f\u043e\u0437\u0438\u0446\u0438\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0439. \u0412 \u043a\u043e\u043d\u0446\u0435 \u0443\u0440\u043e\u043a\u0430 \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u044e\u0442\u0441\u044f \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0434\u043b\u044f [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":29557,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":1,"footnotes":""},"categories":[864,573],"tags":[],"class_list":["post-29570","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-864","category-573"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u041f\u0440\u0435\u0434\u0435\u043b \u0438 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c \u0438 \u043a\u0430\u043a \u043e\u043d\u0430 \u0441\u0432\u044f\u0437\u0430\u043d\u0430 \u0441 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u043c? \u0417\u0434\u0435\u0441\u044c \u0432\u044b \u043f\u043e\u0439\u043c\u0435\u0442\u0435 \u044d\u0442\u0438 \u0438\u0434\u0435\u0438 \u0438\u0437 \u0430\u043d\u0430\u043b\u0438\u0437\u0430 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 \u0438 \u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u044b\u0445 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0439.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/toposuranos.com\/material\/ru\/\u043f\u0440\u0435\u0434\u0435\u043b-\u0438-\u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u041f\u0440\u0435\u0434\u0435\u043b \u0438 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c\" \/>\n<meta property=\"og:description\" content=\"\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c \u0438 \u043a\u0430\u043a \u043e\u043d\u0430 \u0441\u0432\u044f\u0437\u0430\u043d\u0430 \u0441 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u043c? \u0417\u0434\u0435\u0441\u044c \u0432\u044b \u043f\u043e\u0439\u043c\u0435\u0442\u0435 \u044d\u0442\u0438 \u0438\u0434\u0435\u0438 \u0438\u0437 \u0430\u043d\u0430\u043b\u0438\u0437\u0430 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 \u0438 \u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u044b\u0445 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0439.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/toposuranos.com\/material\/ru\/\u043f\u0440\u0435\u0434\u0435\u043b-\u0438-\u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c\/\" \/>\n<meta property=\"og:site_name\" content=\"toposuranos.com\/material\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/groups\/toposuranos\" \/>\n<meta property=\"article:published_time\" content=\"2024-11-18T17:33:55+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/11\/limitecontinuidad-1024x585.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"\u041f\u0440\u0435\u0434\u0435\u043b \u0438 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c\" \/>\n<meta name=\"twitter:description\" content=\"\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c \u0438 \u043a\u0430\u043a \u043e\u043d\u0430 \u0441\u0432\u044f\u0437\u0430\u043d\u0430 \u0441 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u043c? \u0417\u0434\u0435\u0441\u044c \u0432\u044b \u043f\u043e\u0439\u043c\u0435\u0442\u0435 \u044d\u0442\u0438 \u0438\u0434\u0435\u0438 \u0438\u0437 \u0430\u043d\u0430\u043b\u0438\u0437\u0430 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 \u0438 \u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u044b\u0445 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0439.\" \/>\n<meta name=\"twitter:image\" content=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/11\/limitecontinuidad.jpg\" \/>\n<meta name=\"twitter:creator\" content=\"@topuranos\" \/>\n<meta name=\"twitter:site\" content=\"@topuranos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"giorgio.reveco\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tiempo de lectura\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minuto\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"https:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"\u041f\u0440\u0435\u0434\u0435\u043b \u0438 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c\",\"datePublished\":\"2024-11-18T17:33:55+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/\"},\"wordCount\":776,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/toposuranos.com\/material\/#organization\"},\"image\":{\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/11\/limitecontinuidad.jpg\",\"articleSection\":[\"\u0414\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0438\u0441\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435\",\"\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/\",\"url\":\"https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/\",\"name\":\"\u041f\u0440\u0435\u0434\u0435\u043b \u0438 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c - toposuranos.com\/material\",\"isPartOf\":{\"@id\":\"https:\/\/toposuranos.com\/material\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/11\/limitecontinuidad.jpg\",\"datePublished\":\"2024-11-18T17:33:55+00:00\",\"description\":\"\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c \u0438 \u043a\u0430\u043a \u043e\u043d\u0430 \u0441\u0432\u044f\u0437\u0430\u043d\u0430 \u0441 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u043c? \u0417\u0434\u0435\u0441\u044c \u0432\u044b \u043f\u043e\u0439\u043c\u0435\u0442\u0435 \u044d\u0442\u0438 \u0438\u0434\u0435\u0438 \u0438\u0437 \u0430\u043d\u0430\u043b\u0438\u0437\u0430 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 \u0438 \u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u044b\u0445 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0439.\",\"breadcrumb\":{\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/#breadcrumb\"},\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/#primaryimage\",\"url\":\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/11\/limitecontinuidad.jpg\",\"contentUrl\":\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/11\/limitecontinuidad.jpg\",\"width\":1792,\"height\":1024,\"caption\":\"limite y continuidad\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"https:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u041f\u0440\u0435\u0434\u0435\u043b \u0438 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/toposuranos.com\/material\/#website\",\"url\":\"https:\/\/toposuranos.com\/material\/\",\"name\":\"toposuranos.com\/material\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\/\/toposuranos.com\/material\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/toposuranos.com\/material\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"es\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/toposuranos.com\/material\/#organization\",\"name\":\"toposuranos.com\/material\",\"url\":\"https:\/\/toposuranos.com\/material\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"https:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/\",\"url\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png\",\"contentUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png\",\"width\":2400,\"height\":2059,\"caption\":\"toposuranos.com\/material\"},\"image\":{\"@id\":\"https:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/groups\/toposuranos\",\"https:\/\/x.com\/topuranos\",\"https:\/\/www.youtube.com\/channel\/UC16yDm12cPcrwsE0fAM7X1g\",\"https:\/\/www.linkedin.com\/company\/69429190\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\",\"name\":\"giorgio.reveco\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"https:\/\/toposuranos.com\/material\/#\/schema\/person\/image\/\",\"url\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg\",\"contentUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg\",\"caption\":\"giorgio.reveco\"},\"description\":\"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.\",\"sameAs\":[\"http:\/\/toposuranos.com\/material\"],\"url\":\"https:\/\/toposuranos.com\/material\/author\/giorgio-reveco\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u041f\u0440\u0435\u0434\u0435\u043b \u0438 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c - toposuranos.com\/material","description":"\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c \u0438 \u043a\u0430\u043a \u043e\u043d\u0430 \u0441\u0432\u044f\u0437\u0430\u043d\u0430 \u0441 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u043c? \u0417\u0434\u0435\u0441\u044c \u0432\u044b \u043f\u043e\u0439\u043c\u0435\u0442\u0435 \u044d\u0442\u0438 \u0438\u0434\u0435\u0438 \u0438\u0437 \u0430\u043d\u0430\u043b\u0438\u0437\u0430 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 \u0438 \u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u044b\u0445 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0439.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/toposuranos.com\/material\/ru\/\u043f\u0440\u0435\u0434\u0435\u043b-\u0438-\u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c\/","og_locale":"es_ES","og_type":"article","og_title":"\u041f\u0440\u0435\u0434\u0435\u043b \u0438 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c","og_description":"\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c \u0438 \u043a\u0430\u043a \u043e\u043d\u0430 \u0441\u0432\u044f\u0437\u0430\u043d\u0430 \u0441 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u043c? \u0417\u0434\u0435\u0441\u044c \u0432\u044b \u043f\u043e\u0439\u043c\u0435\u0442\u0435 \u044d\u0442\u0438 \u0438\u0434\u0435\u0438 \u0438\u0437 \u0430\u043d\u0430\u043b\u0438\u0437\u0430 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 \u0438 \u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u044b\u0445 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0439.","og_url":"https:\/\/toposuranos.com\/material\/ru\/\u043f\u0440\u0435\u0434\u0435\u043b-\u0438-\u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c\/","og_site_name":"toposuranos.com\/material","article_publisher":"https:\/\/www.facebook.com\/groups\/toposuranos","article_published_time":"2024-11-18T17:33:55+00:00","og_image":[{"url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/11\/limitecontinuidad-1024x585.jpg","type":"","width":"","height":""}],"author":"giorgio.reveco","twitter_card":"summary_large_image","twitter_title":"\u041f\u0440\u0435\u0434\u0435\u043b \u0438 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c","twitter_description":"\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c \u0438 \u043a\u0430\u043a \u043e\u043d\u0430 \u0441\u0432\u044f\u0437\u0430\u043d\u0430 \u0441 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u043c? \u0417\u0434\u0435\u0441\u044c \u0432\u044b \u043f\u043e\u0439\u043c\u0435\u0442\u0435 \u044d\u0442\u0438 \u0438\u0434\u0435\u0438 \u0438\u0437 \u0430\u043d\u0430\u043b\u0438\u0437\u0430 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 \u0438 \u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u044b\u0445 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0439.","twitter_image":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/11\/limitecontinuidad.jpg","twitter_creator":"@topuranos","twitter_site":"@topuranos","twitter_misc":{"Escrito por":"giorgio.reveco","Tiempo de lectura":"1 minuto"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/#article","isPartOf":{"@id":"https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/"},"author":{"name":"giorgio.reveco","@id":"https:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1"},"headline":"\u041f\u0440\u0435\u0434\u0435\u043b \u0438 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c","datePublished":"2024-11-18T17:33:55+00:00","mainEntityOfPage":{"@id":"https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/"},"wordCount":776,"commentCount":0,"publisher":{"@id":"https:\/\/toposuranos.com\/material\/#organization"},"image":{"@id":"https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/#primaryimage"},"thumbnailUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/11\/limitecontinuidad.jpg","articleSection":["\u0414\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0438\u0441\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435","\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430"],"inLanguage":"es","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/","url":"https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/","name":"\u041f\u0440\u0435\u0434\u0435\u043b \u0438 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c - toposuranos.com\/material","isPartOf":{"@id":"https:\/\/toposuranos.com\/material\/#website"},"primaryImageOfPage":{"@id":"https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/#primaryimage"},"image":{"@id":"https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/#primaryimage"},"thumbnailUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/11\/limitecontinuidad.jpg","datePublished":"2024-11-18T17:33:55+00:00","description":"\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c \u0438 \u043a\u0430\u043a \u043e\u043d\u0430 \u0441\u0432\u044f\u0437\u0430\u043d\u0430 \u0441 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u043c? \u0417\u0434\u0435\u0441\u044c \u0432\u044b \u043f\u043e\u0439\u043c\u0435\u0442\u0435 \u044d\u0442\u0438 \u0438\u0434\u0435\u0438 \u0438\u0437 \u0430\u043d\u0430\u043b\u0438\u0437\u0430 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 \u0438 \u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u044b\u0445 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0439.","breadcrumb":{"@id":"https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/#breadcrumb"},"inLanguage":"es","potentialAction":[{"@type":"ReadAction","target":["https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/"]}]},{"@type":"ImageObject","inLanguage":"es","@id":"https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/#primaryimage","url":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/11\/limitecontinuidad.jpg","contentUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/11\/limitecontinuidad.jpg","width":1792,"height":1024,"caption":"limite y continuidad"},{"@type":"BreadcrumbList","@id":"https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%b8-%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d0%be%d1%81%d1%82%d1%8c\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"https:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/"},{"@type":"ListItem","position":2,"name":"\u041f\u0440\u0435\u0434\u0435\u043b \u0438 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c"}]},{"@type":"WebSite","@id":"https:\/\/toposuranos.com\/material\/#website","url":"https:\/\/toposuranos.com\/material\/","name":"toposuranos.com\/material","description":"","publisher":{"@id":"https:\/\/toposuranos.com\/material\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/toposuranos.com\/material\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"es"},{"@type":"Organization","@id":"https:\/\/toposuranos.com\/material\/#organization","name":"toposuranos.com\/material","url":"https:\/\/toposuranos.com\/material\/","logo":{"@type":"ImageObject","inLanguage":"es","@id":"https:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","width":2400,"height":2059,"caption":"toposuranos.com\/material"},"image":{"@id":"https:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/groups\/toposuranos","https:\/\/x.com\/topuranos","https:\/\/www.youtube.com\/channel\/UC16yDm12cPcrwsE0fAM7X1g","https:\/\/www.linkedin.com\/company\/69429190"]},{"@type":"Person","@id":"https:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1","name":"giorgio.reveco","image":{"@type":"ImageObject","inLanguage":"es","@id":"https:\/\/toposuranos.com\/material\/#\/schema\/person\/image\/","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","caption":"giorgio.reveco"},"description":"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.","sameAs":["http:\/\/toposuranos.com\/material"],"url":"https:\/\/toposuranos.com\/material\/author\/giorgio-reveco\/"}]}},"_links":{"self":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/29570","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/comments?post=29570"}],"version-history":[{"count":0,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/29570\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media\/29557"}],"wp:attachment":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media?parent=29570"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/categories?post=29570"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/tags?post=29570"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}