{"id":29532,"date":"2024-11-18T02:30:47","date_gmt":"2024-11-18T02:30:47","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=29532"},"modified":"2024-11-18T02:33:17","modified_gmt":"2024-11-18T02:33:17","slug":"%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ru\/%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/","title":{"rendered":"\u0410\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0438 \u043c\u0435\u0442\u043e\u0434\u044b \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u044f"},"content":{"rendered":"<style>\np {\ntext-align:justify;\n}\n<\/style>\n<h1 style=\"text-align:center;\">\u0410\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u041f\u0440\u0435\u0434\u0435\u043b\u044b \u0438 \u041c\u0435\u0442\u043e\u0434\u044b \u0413\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u044f<\/h1>\n<p style=\"text-align:center;\"><em><strong>\u0420\u0435\u0437\u044e\u043c\u0435:<\/strong><br \/>\n\u0412 \u044d\u0442\u043e\u043c \u0443\u0440\u043e\u043a\u0435 \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u044e\u0442\u0441\u044f \u043f\u043e\u043d\u044f\u0442\u0438\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442 \u0438 \u0434\u043e\u043c\u0438\u043d\u0438\u0440\u0443\u044e\u0449\u0438\u0445 \u0447\u043b\u0435\u043d\u043e\u0432 \u0432 \u0430\u043d\u0430\u043b\u0438\u0437\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0439. \u0418\u0441\u0441\u043b\u0435\u0434\u0443\u044e\u0442\u0441\u044f \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u044e\u0442 \u043f\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043a\u043e\u0433\u0434\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0441\u0442\u0440\u0435\u043c\u0438\u0442\u0441\u044f \u043a \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438; \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0443\u043a\u0430\u0437\u044b\u0432\u0430\u044e\u0442 \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b, \u043a\u043e\u0433\u0434\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0435\u0442\u0441\u044f \u043a \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u044b\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u043c; \u0438 \u043d\u0430\u043a\u043b\u043e\u043d\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0430\u043a\u0442\u0443\u0430\u043b\u044c\u043d\u044b \u0432 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u0445, \u043a\u043e\u0433\u0434\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044f \u043f\u0440\u0435\u0432\u044b\u0448\u0430\u0435\u0442 \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044f. \u0422\u0430\u043a\u0436\u0435 \u0430\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u0443\u0435\u0442\u0441\u044f \u0434\u043e\u043c\u0438\u043d\u0438\u0440\u0443\u044e\u0449\u0438\u0439 \u0447\u043b\u0435\u043d \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u043f\u0440\u0435\u0434\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0435 \u0434\u043b\u044f \u0431\u043e\u043b\u044c\u0448\u0438\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0438\u043b\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439, \u0431\u043b\u0438\u0437\u043a\u0438\u0445 \u043a \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u044b\u043c \u0442\u043e\u0447\u043a\u0430\u043c <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span>.<\/em><\/p>\n<p style=\"text-align:center;\"><strong>\u0426\u0435\u043b\u0438 \u041e\u0431\u0443\u0447\u0435\u043d\u0438\u044f<\/strong><br \/>\n\u041f\u043e \u043e\u043a\u043e\u043d\u0447\u0430\u043d\u0438\u0438 \u044d\u0442\u043e\u0433\u043e \u0443\u0440\u043e\u043a\u0430 \u0441\u0442\u0443\u0434\u0435\u043d\u0442 \u0441\u043c\u043e\u0436\u0435\u0442:\n<\/p>\n<ol>\n<li><strong>\u041f\u043e\u043d\u044f\u0442\u044c<\/strong> \u043f\u043e\u043d\u044f\u0442\u0438\u0435 \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0445 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442 \u0438 \u0438\u0445 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0435 \u0432 \u0430\u043d\u0430\u043b\u0438\u0437\u0435 \u043f\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u043a\u043e\u0433\u0434\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0441\u0442\u0440\u0435\u043c\u0438\u0442\u0441\u044f \u043a \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438.<\/li>\n<li><strong>\u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c<\/strong> \u0443\u0441\u043b\u043e\u0432\u0438\u044f \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u043e\u0432\u0430\u043d\u0438\u044f \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442 \u0438 \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0442\u044c \u0438\u0445 \u0434\u043b\u044f \u0438\u0437\u0443\u0447\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0441 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u044b\u043c\u0438 \u043f\u0440\u0435\u0434\u0435\u043b\u0430\u043c\u0438, \u043a\u043e\u0433\u0434\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0435\u0442\u0441\u044f \u043a \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u044b\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u043c.<\/li>\n<li><strong>\u0410\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c<\/strong> \u043f\u043e\u044f\u0432\u043b\u0435\u043d\u0438\u0435 \u043d\u0430\u043a\u043b\u043e\u043d\u043d\u044b\u0445 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442 \u0432 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u0445, \u043a\u043e\u0433\u0434\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044f \u043f\u0440\u0435\u0432\u044b\u0448\u0430\u0435\u0442 \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044f.<\/li>\n<li><strong>\u041f\u0440\u0438\u043c\u0435\u043d\u044f\u0442\u044c<\/strong> \u043f\u043e\u043d\u044f\u0442\u0438\u0435 \u0434\u043e\u043c\u0438\u043d\u0438\u0440\u0443\u044e\u0449\u0435\u0433\u043e \u0447\u043b\u0435\u043d\u0430 \u0434\u043b\u044f \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u044f \u043f\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u043f\u0440\u0438 \u0431\u043e\u043b\u044c\u0448\u0438\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u0445 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0438\u043b\u0438 \u0432\u0431\u043b\u0438\u0437\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u044b\u0445 \u0442\u043e\u0447\u0435\u043a.<\/li>\n<li><strong>\u041e\u0431\u044a\u044f\u0441\u043d\u044f\u0442\u044c<\/strong>, \u043a\u0430\u043a \u0430\u043d\u0430\u043b\u0438\u0437 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442 \u0438 \u0434\u043e\u043c\u0438\u043d\u0438\u0440\u0443\u044e\u0449\u0438\u0445 \u0447\u043b\u0435\u043d\u043e\u0432 \u0441\u043f\u043e\u0441\u043e\u0431\u0441\u0442\u0432\u0443\u0435\u0442 \u043f\u043e\u043d\u0438\u043c\u0430\u043d\u0438\u044e \u043e\u0431\u0449\u0435\u0433\u043e \u043f\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\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\">\u0413\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b \u0438 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438<\/a><br \/>\n<a href=\"#3\">\u0412\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b \u0438 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b<\/a><br \/>\n<a href=\"#4\">\u041d\u0430\u043a\u043b\u043e\u043d\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u043a\u0440\u0438\u0432\u044b\u0435 \u0438 \u0434\u043e\u043c\u0438\u043d\u0438\u0440\u0443\u044e\u0449\u0438\u0435 \u0447\u043b\u0435\u043d\u044b<\/a><br \/>\n<a href=\"#5\">\u0420\u0435\u0448\u0451\u043d\u043d\u044b\u0435 \u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f<\/a><br \/>\n<a href=\"#6\">\u041f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u043d\u044b\u0435 \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\/Ekd0oSvMbfE\" 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=Ekd0oSvMbfE&amp;t=98s\" target=\"_blank\" rel=\"noopener\"><strong>\u041f\u0440\u0435\u0434\u0435\u043b\u044b, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043c\u044b \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u043b\u0438<\/strong><\/a> \u0434\u043e \u0441\u0438\u0445 \u043f\u043e\u0440, \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u044e\u0442 \u043d\u0430\u043c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u043e\u043b\u0435\u0437\u043d\u044b\u0435 \u043f\u043e\u043d\u044f\u0442\u0438\u044f \u0434\u043b\u044f \u043f\u043e\u043d\u0438\u043c\u0430\u043d\u0438\u044f \u043e\u0431\u0449\u0435\u0433\u043e \u043f\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u0442\u0430\u043a\u0438\u0435 \u043a\u0430\u043a \u0434\u043e\u043c\u0438\u043d\u0438\u0440\u0443\u044e\u0449\u0438\u0435 \u0447\u043b\u0435\u043d\u044b \u0438 \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b; \u044d\u0442\u043e, \u0442\u0430\u043a \u0441\u043a\u0430\u0437\u0430\u0442\u044c, \u043a\u0440\u0438\u0432\u044b\u0435, \u043a \u043a\u043e\u0442\u043e\u0440\u044b\u043c \u0433\u0440\u0430\u0444\u0438\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u0442\u0440\u0435\u043c\u0438\u0442\u0441\u044f \u043f\u0440\u0438\u0431\u043b\u0438\u0437\u0438\u0442\u044c\u0441\u044f \u043d\u0430\u0441\u0442\u043e\u043b\u044c\u043a\u043e, \u043d\u0430\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u044d\u0442\u043e \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e, \u043f\u043e \u043c\u0435\u0440\u0435 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0441\u0442\u0440\u0435\u043c\u0438\u0442\u0441\u044f \u043a \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u043e\u043c\u0443 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044e.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u0413\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b \u0438 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=Ekd0oSvMbfE&amp;t=137s\" target=\"_blank\" rel=\"noopener\"><strong>\u0415\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> &#8211; \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u0430\u044f \u043d\u0430<\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">]a,+\\infty[<\/span>, \u0434\u043b\u044f \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e <span class=\"katex-eq\" data-katex-display=\"false\">a\\in\\mathbb{R}<\/span>, \u0442\u043e\u0433\u0434\u0430 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u044c \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043f\u0440\u0435\u0434\u0435\u043b <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span>, \u043a\u043e\u0433\u0434\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0441\u0442\u0440\u0435\u043c\u0438\u0442\u0441\u044f \u043a \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438. \u0415\u0441\u043b\u0438 \u0442\u0430\u043a\u043e\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442, \u0442\u043e \u0438\u0441\u0445\u043e\u0434\u044f \u0438\u0437 \u043d\u0435\u0433\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f <strong>\u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0430\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430 \u0441\u043f\u0440\u0430\u0432\u0430<\/strong> \u043a\u0430\u043a \u043f\u0440\u044f\u043c\u0430\u044f \u0441 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435\u043c<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">A_+(x) = L^+<\/span>\n<p>\u0433\u0434\u0435<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to+\\infty}f(x) = L^+<\/span>\n<p>\u0410\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f <strong>\u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0430\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430 \u0441\u043b\u0435\u0432\u0430<\/strong> \u043a\u0430\u043a \u043f\u0440\u044f\u043c\u0430\u044f \u0441 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435\u043c<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">A_-(x) = L^-<\/span>\n<p>\u043a\u043e\u0433\u0434\u0430<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to-\\infty}f(x) = L^-<\/span>\n<p>\u0413\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b \u043f\u043e\u043c\u043e\u0433\u0430\u044e\u0442 \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u0442\u044c \u043f\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span>, \u043a\u043e\u0433\u0434\u0430 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0440\u0430\u0441\u0442\u0443\u0442 \u0431\u0435\u0437 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0438\u044f.<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-ckBGkFWse2w\/YH1GWClIciI\/AAAAAAAAE6s\/zZ_se7yShqMLiEHKNT_jkgAWuK9cme5wwCLcBGAsYHQ\/s0\/as%25C3%25ADntotahorizontal.PNG\" alt=\"\u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b\" class=\"aligncenter lazyload\" width=\"478\" height=\"290\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-ckBGkFWse2w\/YH1GWClIciI\/AAAAAAAAE6s\/zZ_se7yShqMLiEHKNT_jkgAWuK9cme5wwCLcBGAsYHQ\/s0\/as%25C3%25ADntotahorizontal.PNG\" alt=\"\u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b\" class=\"aligncenter lazyload\" width=\"478\" height=\"290\" \/><\/noscript><\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u0412\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b \u0438 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=Ekd0oSvMbfE&amp;t=277s\" target=\"_blank\" rel=\"noopener\"><strong>\u0410\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u043c \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430\u043c,<\/strong><\/a> \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u044e\u0442\u0441\u044f <strong>\u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b \u0432\u0432\u0435\u0440\u0445<\/strong> \u0434\u043b\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u043a\u0430\u043a \u043f\u0440\u044f\u043c\u0430\u044f \u0441 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435\u043c <span class=\"katex-eq\" data-katex-display=\"false\">x=a<\/span> \u043f\u0440\u0438<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to a}f(x) = +\\infty<\/span>\n<p>\u0418 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430 \u0431\u0443\u0434\u0435\u0442 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u043e\u0439 \u0432\u043d\u0438\u0437, \u0435\u0441\u043b\u0438<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to a}f(x) = -\\infty<\/span>\n<p>\u0418, \u0441\u043b\u0435\u0434\u0443\u044f \u043b\u043e\u0433\u0438\u043a\u0435 \u043e\u0434\u043d\u043e\u0441\u0442\u043e\u0440\u043e\u043d\u043d\u0438\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432, \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b \u0431\u0443\u0434\u0443\u0442 \u0441\u043f\u0440\u0430\u0432\u0430 \u0438\u043b\u0438 \u0441\u043b\u0435\u0432\u0430, \u0432 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 \u043e\u0442 \u0441\u0438\u0442\u0443\u0430\u0446\u0438\u0438.<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-ptEipMpyIhc\/YH1VDclyMxI\/AAAAAAAAE60\/LmzpK2HAU7oLpswJQy5_TLIv9jSf9whDwCLcBGAsYHQ\/s0\/asintotavertical.PNG\" alt=\"\u0412\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0430\u044f \u0410\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430\" class=\" aligncenter lazyload\" width=\"428\" height=\"283\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-ptEipMpyIhc\/YH1VDclyMxI\/AAAAAAAAE60\/LmzpK2HAU7oLpswJQy5_TLIv9jSf9whDwCLcBGAsYHQ\/s0\/asintotavertical.PNG\" alt=\"\u0412\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0430\u044f \u0410\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430\" class=\" aligncenter lazyload\" width=\"428\" height=\"283\" \/><\/noscript><\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u041d\u0430\u043a\u043b\u043e\u043d\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u043a\u0440\u0438\u0432\u044b\u0435 \u0438 \u0434\u043e\u043c\u0438\u043d\u0438\u0440\u0443\u044e\u0449\u0438\u0435 \u0447\u043b\u0435\u043d\u044b<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=Ekd0oSvMbfE&amp;t=400s\" target=\"_blank\" rel=\"noopener\"><strong>\u0421\u0430\u043c\u043e\u0435 \u043f\u0440\u043e\u0441\u0442\u043e\u0435 \u043f\u043e\u044f\u0432\u043b\u0435\u043d\u0438\u0435<\/strong><\/a> <strong>\u043d\u0430\u043a\u043b\u043e\u043d\u043d\u044b\u0445 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442<\/strong> \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0434\u0438\u0442 \u043f\u0440\u0438 \u0440\u0430\u0431\u043e\u0442\u0435 \u0441 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u043c\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u043c\u0438<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\dfrac{P(x)}{Q(x)}<\/span>\n<p>\u0413\u0434\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">Q(x)<\/span> &#8211; \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u044b. \u041a\u043e\u0433\u0434\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u044c <span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span> \u0431\u043e\u043b\u044c\u0448\u0435 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">Q(x)<\/span>, \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u043f\u043e\u043b\u043d\u0438\u0442\u044c \u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432, \u0447\u0442\u043e \u0434\u0430\u0451\u0442 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442 \u0432 \u0432\u0438\u0434\u0435<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\dfrac{P(x)}{Q(x)} = C(x) + \\dfrac{r(x)}{Q(x)}<\/span>\n<p>\u0413\u0434\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span> &#8211; \u044d\u0442\u043e \u0447\u0430\u0441\u0442\u043d\u043e\u0435 \u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u0430 <span class=\"katex-eq\" data-katex-display=\"false\">r(x)<\/span> &#8211; \u043e\u0441\u0442\u0430\u0442\u043e\u043a. \u0415\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span> \u0438\u043c\u0435\u0435\u0442 \u0441\u0442\u0435\u043f\u0435\u043d\u044c, \u043f\u0440\u0435\u0432\u044b\u0448\u0430\u044e\u0449\u0443\u044e \u0441\u0442\u0435\u043f\u0435\u043d\u044c <span class=\"katex-eq\" data-katex-display=\"false\">Q(x)<\/span> \u043d\u0430 \u0435\u0434\u0438\u043d\u0438\u0446\u0443, \u0442\u043e <span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span> \u0431\u0443\u0434\u0435\u0442 \u043f\u0435\u0440\u0432\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438, \u0442\u043e \u0435\u0441\u0442\u044c, \u044d\u0442\u043e \u0431\u0443\u0434\u0435\u0442 \u043f\u0440\u044f\u043c\u0430\u044f, \u0438 \u0435\u0451 \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442 \u043d\u0430\u043a\u043b\u043e\u043d\u043d\u043e\u0439 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span>.<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-wRTmSl2Z3HE\/YH1dSl-noDI\/AAAAAAAAE68\/og2lPX_ydUUGlxYnn5hgj2mNCSeAPoQKACLcBGAsYHQ\/s0\/asintotaoblicua.PNG\" alt=\"\u041d\u0430\u043a\u043b\u043e\u043d\u043d\u0430\u044f \u0410\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430\" class=\" aligncenter lazyload\" width=\"404\" height=\"239\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-wRTmSl2Z3HE\/YH1dSl-noDI\/AAAAAAAAE68\/og2lPX_ydUUGlxYnn5hgj2mNCSeAPoQKACLcBGAsYHQ\/s0\/asintotaoblicua.PNG\" alt=\"\u041d\u0430\u043a\u043b\u043e\u043d\u043d\u0430\u044f \u0410\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430\" class=\" aligncenter lazyload\" width=\"404\" height=\"239\" \/><\/noscript><\/p>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=Ekd0oSvMbfE&amp;t=633s\" target=\"_blank\" rel=\"noopener\"><strong>\u0415\u0441\u043b\u0438 \u0432 \u043e\u0431\u0449\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span> \u0438\u043c\u0435\u0435\u0442 \u0441\u0442\u0435\u043f\u0435\u043d\u044c<\/strong><\/a>, \u043f\u0440\u0435\u0432\u044b\u0448\u0430\u044e\u0449\u0443\u044e \u0441\u0442\u0435\u043f\u0435\u043d\u044c <span class=\"katex-eq\" data-katex-display=\"false\">Q(x)<\/span> \u043d\u0430 \u043b\u044e\u0431\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435, \u0442\u043e\u0433\u0434\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span> \u0431\u0443\u0434\u0435\u0442 \u0438\u043c\u0435\u0442\u044c \u0441\u0442\u0435\u043f\u0435\u043d\u044c, \u0440\u0430\u0432\u043d\u0443\u044e \u0440\u0430\u0437\u043d\u043e\u0441\u0442\u0438 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 <span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">Q(x)<\/span>, \u0438, \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e, \u0431\u0443\u0434\u0435\u0442 \u043e\u0431\u0449\u0435\u0439 \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u043a\u0440\u0438\u0432\u043e\u0439. \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043e\u0431\u044b\u0447\u043d\u043e \u043d\u0435 \u0433\u043e\u0432\u043e\u0440\u044f\u0442, \u0447\u0442\u043e <span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u043e\u0439, \u0445\u043e\u0442\u044f \u043e\u0431\u0449\u0435\u0435 \u043f\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u0431\u0443\u0434\u0435\u0442 \u0442\u0430\u043a\u0438\u043c, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0431\u0443\u0434\u0435\u0442 \u00ab\u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0442\u044c\u0441\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u00bb \u043a <span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span> \u043f\u043e \u043c\u0435\u0440\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">x\\to\\pm\\infty<\/span>. \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0433\u043e\u0432\u043e\u0440\u044f\u0442, \u0447\u0442\u043e <span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span> &#8211; \u044d\u0442\u043e <strong>\u0434\u043e\u043c\u0438\u043d\u0438\u0440\u0443\u044e\u0449\u0438\u0439 \u0447\u043b\u0435\u043d \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u0434\u043b\u044f \u0431\u043e\u043b\u044c\u0448\u0438\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 <span class=\"katex-eq\" data-katex-display=\"false\">x.<\/span><\/strong><\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-IEYO071tTuY\/YH1fjR-WWnI\/AAAAAAAAE7E\/ga2rZ02i8QU5R1IMvQB9rpgFuDknAGfbACLcBGAsYHQ\/s0\/terminoDominante.PNG\" alt=\"\u0414\u043e\u043c\u0438\u043d\u0438\u0440\u0443\u044e\u0449\u0438\u0439 \u0427\u043b\u0435\u043d \u0438 \u0412\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0430\u044f \u0410\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430\" class=\" aligncenter lazyload\" width=\"479\" height=\"437\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-IEYO071tTuY\/YH1fjR-WWnI\/AAAAAAAAE7E\/ga2rZ02i8QU5R1IMvQB9rpgFuDknAGfbACLcBGAsYHQ\/s0\/terminoDominante.PNG\" alt=\"\u0414\u043e\u043c\u0438\u043d\u0438\u0440\u0443\u044e\u0449\u0438\u0439 \u0427\u043b\u0435\u043d \u0438 \u0412\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0430\u044f \u0410\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430\" class=\" aligncenter lazyload\" width=\"479\" height=\"437\" \/><\/noscript><\/p>\n<p>\u0422\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u043d\u043e \u0433\u043e\u0432\u043e\u0440\u0438\u0442\u044c \u043e \u0434\u043e\u043c\u0438\u043d\u0438\u0440\u0443\u044e\u0449\u0435\u043c \u0447\u043b\u0435\u043d\u0435, \u043a\u043e\u0433\u0434\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0431\u043b\u0438\u0437\u043e\u043a \u043a <span class=\"katex-eq\" data-katex-display=\"false\">a\\in\\mathbb{R}<\/span>.<\/p>\n<p>\u0415\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">f(x) = P(x)\/Q(x) = C(x) + r(x)\/Q(x),<\/span>, \u0433\u0434\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">P(x),<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">Q(x),<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">r(x)<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span> &#8211; \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u044b. \u0415\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to a}f(x) = \\infty,<\/span>, \u0442\u043e \u0433\u043e\u0432\u043e\u0440\u044f\u0442, \u0447\u0442\u043e \u0447\u0430\u0441\u0442\u043d\u043e\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">r(x)\/Q(x)<\/span> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f <strong>\u0434\u043e\u043c\u0438\u043d\u0438\u0440\u0443\u044e\u0449\u0438\u043c \u0447\u043b\u0435\u043d\u043e\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u0432\u0431\u043b\u0438\u0437\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">x=a.<\/span><\/strong><\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u0420\u0435\u0448\u0451\u043d\u043d\u044b\u0435 \u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f<\/h2>\n<h3><strong>\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 1:<\/strong><\/h3>\n<p>\u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435 \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0438<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\dfrac{3x + 1}{x - 2}<\/span>\n<p><strong>\u0420\u0435\u0448\u0435\u043d\u0438\u0435:<\/strong><\/p>\n<p>\u0427\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 <strong>\u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0443\u044e \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0443<\/strong>, \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043c \u043f\u0440\u0435\u0434\u0435\u043b <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u043f\u0440\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">x \\to \\pm\\infty<\/span>:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x \\to \\pm\\infty} \\dfrac{3x + 1}{x - 2} = 3<\/span>\n<p>\u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0430\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430 &#8211; <span class=\"katex-eq\" data-katex-display=\"false\">y = 3<\/span>.<\/p>\n<p>\u0414\u043b\u044f <strong>\u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u043e\u0439 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b<\/strong> \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435, \u043f\u0440\u0438 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u043e\u0431\u0440\u0430\u0449\u0430\u0435\u0442\u0441\u044f \u0432 \u043d\u043e\u043b\u044c, \u0442\u043e \u0435\u0441\u0442\u044c, \u043a\u043e\u0433\u0434\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">x = 2<\/span>.<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x \\to 2^\\pm} \\dfrac{3x + 1}{x - 2} = \\pm\\infty<\/span>\n<p>\u042d\u0442\u043e \u0443\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u043d\u0430 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0443\u044e \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0443 \u043f\u0440\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">x = 2<\/span>.<\/p>\n<p><strong>\u0418\u0442\u043e\u0433\u043e\u0432\u044b\u0439 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442:<\/strong> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u043c\u0435\u0435\u0442 \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0443\u044e \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0443 <span class=\"katex-eq\" data-katex-display=\"false\">y = 3<\/span> \u0438 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0443\u044e \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0443 <span class=\"katex-eq\" data-katex-display=\"false\">x = 2<\/span>.<\/p>\n<h3><strong>\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 2:<\/strong><\/h3>\n<p>\u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u043d\u0430\u043a\u043b\u043e\u043d\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u0435\u0441\u043b\u0438 \u043e\u043d\u0438 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442, \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">g(x) = \\frac{2x^2 + 3x + 4}{x + 1}<\/span>.<\/p>\n<p><strong>\u0420\u0435\u0448\u0435\u043d\u0438\u0435:<\/strong><\/p>\n<p>\u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u0438\u0449\u0435\u043c <strong>\u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0443\u044e \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0443<\/strong>, \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u044f \u043f\u0440\u0435\u0434\u0435\u043b \u043f\u0440\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">x \\to \\pm\\infty<\/span>. \u0422\u0430\u043a \u043a\u0430\u043a \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044f \u0431\u043e\u043b\u044c\u0448\u0435 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044f, \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0430\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430 \u043e\u0442\u0441\u0443\u0442\u0441\u0442\u0432\u0443\u0435\u0442.<\/p>\n<p>\u0414\u043b\u044f <strong>\u043d\u0430\u043a\u043b\u043e\u043d\u043d\u043e\u0439 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b<\/strong> \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u043c \u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432, \u043f\u043e\u043b\u0443\u0447\u0430\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{2x^2 + 3x + 4}{x + 1} = 2x + 1 + \\dfrac{3}{x + 1}<\/span>\n<p>\u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043d\u0430\u043a\u043b\u043e\u043d\u043d\u0430\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430 &#8211; \u043f\u0440\u044f\u043c\u0430\u044f <span class=\"katex-eq\" data-katex-display=\"false\">y = 2x + 1<\/span>, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0434\u043e\u043c\u0438\u043d\u0438\u0440\u0443\u044e\u0449\u0438\u043c \u0447\u043b\u0435\u043d\u043e\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n<p><strong>\u0418\u0442\u043e\u0433\u043e\u0432\u044b\u0439 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442:<\/strong> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0435 \u0438\u043c\u0435\u0435\u0442 \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u043e\u0439 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u043d\u043e \u0438\u043c\u0435\u0435\u0442 \u043d\u0430\u043a\u043b\u043e\u043d\u043d\u0443\u044e \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0443, \u0440\u0430\u0432\u043d\u0443\u044e \u043f\u0440\u044f\u043c\u043e\u0439 <span class=\"katex-eq\" data-katex-display=\"false\">y = 2x + 1<\/span>.<\/p>\n<h3><strong>\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 3:<\/strong><\/h3>\n<p>\u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0443\u044e \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">h(x) = \\frac{5}{x^2 - 4}<\/span>.<\/p>\n<p><strong>\u0420\u0435\u0448\u0435\u043d\u0438\u0435:<\/strong><\/p>\n<p>\u0427\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 <strong>\u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0443\u044e \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0443<\/strong>, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f, \u043f\u0440\u0438 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u043e\u0431\u0440\u0430\u0449\u0430\u0435\u0442\u0441\u044f \u0432 \u043d\u043e\u043b\u044c, \u0442\u043e \u0435\u0441\u0442\u044c, <span class=\"katex-eq\" data-katex-display=\"false\">x^2 - 4 = 0<\/span>. \u042d\u0442\u043e \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0434\u0438\u0442 \u043f\u0440\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">x = \\pm 2<\/span>.<\/p>\n<p>\u0412\u044b\u0447\u0438\u0441\u043b\u0438\u043c \u043e\u0434\u043d\u043e\u0441\u0442\u043e\u0440\u043e\u043d\u043d\u0438\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0434\u043b\u044f \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x \\to 2^\\pm} \\dfrac{5}{x^2 - 4} = \\pm\\infty<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x \\to -2^\\pm} \\dfrac{5}{x^2 - 4} = \\pm\\infty<\/span>\n<p><strong>\u0418\u0442\u043e\u0433\u043e\u0432\u044b\u0439 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442:<\/strong> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u043c\u0435\u0435\u0442 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b \u043f\u0440\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">x = 2<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">x = -2<\/span>.<\/p>\n<p><a name=\"6\"><\/a><\/p>\n<h2>\u041f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u043d\u044b\u0435 \u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f<\/h2>\n<ol>\n<li>\u0410\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u0443\u0439\u0442\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044e <span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\frac{2x^2 - 3x + 1}{x^2 + x - 2}<\/span>. \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435 \u0435\u0451 \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435, \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u043d\u0430\u043a\u043b\u043e\u043d\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u0435\u0441\u043b\u0438 \u043e\u043d\u0438 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442. \u041e\u0431\u044a\u044f\u0441\u043d\u0438\u0442\u0435 \u043a\u0430\u0436\u0434\u044b\u0439 \u0448\u0430\u0433, \u0447\u0442\u043e\u0431\u044b \u0443\u043a\u0440\u0435\u043f\u0438\u0442\u044c \u043f\u043e\u043d\u0438\u043c\u0430\u043d\u0438\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442 \u0438 \u0440\u0430\u0441\u0447\u0451\u0442\u0430 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432.<\/li>\n<li>\u041e\u0446\u0435\u043d\u0438\u0442\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044e <span class=\"katex-eq\" data-katex-display=\"false\">g(x) = \\frac{3x^3 + 2x}{x^2 + 1}<\/span>. \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435 \u0434\u043e\u043c\u0438\u043d\u0438\u0440\u0443\u044e\u0449\u0438\u0439 \u0447\u043b\u0435\u043d, \u043a\u043e\u0433\u0434\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0441\u0442\u0440\u0435\u043c\u0438\u0442\u0441\u044f \u043a \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438. \u0417\u0430\u0442\u0435\u043c \u043f\u0440\u043e\u0432\u0435\u0440\u044c\u0442\u0435, \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043b\u0438 \u043d\u0430\u043a\u043b\u043e\u043d\u043d\u0430\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430, \u043e\u0431\u043e\u0441\u043d\u043e\u0432\u044b\u0432\u0430\u044f \u0441\u0432\u043e\u0439 \u043e\u0442\u0432\u0435\u0442.<\/li>\n<li>\u0421\u043e\u0441\u0442\u0430\u0432\u044c\u0442\u0435 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0451\u043d\u043d\u044b\u0439 \u0433\u0440\u0430\u0444\u0438\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">h(x) = \\frac{5x - 4}{x + 1}<\/span>. \u0412\u043a\u043b\u044e\u0447\u0438\u0442\u0435 \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435, \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u043d\u0430\u043a\u043b\u043e\u043d\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b (\u0435\u0441\u043b\u0438 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442) \u0438 \u043f\u0440\u043e\u0430\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u0443\u0439\u0442\u0435 \u043f\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">h(x)<\/span> \u043f\u0440\u0438 \u043a\u0440\u0430\u0439\u043d\u0438\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u0445 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span>.<\/li>\n<li>\u041f\u0440\u043e\u0432\u0435\u0440\u044c\u0442\u0435, \u0435\u0441\u0442\u044c \u043b\u0438 \u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">k(x) = \\frac{x^2 - 4x + 3}{x^2 - 1}<\/span> \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b. \u041e\u0431\u0441\u0443\u0434\u0438\u0442\u0435 \u0440\u043e\u043b\u044c \u0434\u043e\u043c\u0438\u043d\u0438\u0440\u0443\u044e\u0449\u0438\u0445 \u0447\u043b\u0435\u043d\u043e\u0432 \u0432 \u0430\u043d\u0430\u043b\u0438\u0437\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">k(x)<\/span> \u043f\u0440\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u0445, \u0433\u0434\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0441\u0442\u0440\u0435\u043c\u0438\u0442\u0441\u044f \u043a \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438.<\/li>\n<li>\u0418\u0441\u0441\u043b\u0435\u0434\u0443\u0439\u0442\u0435 \u0434\u043e\u043c\u0438\u043d\u0438\u0440\u0443\u044e\u0449\u0438\u0435 \u0447\u043b\u0435\u043d\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">m(x) = \\frac{2x^4 + 3x^2 - x + 5}{x^3 - x^2 + 2}<\/span>. \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435 \u043f\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">m(x)<\/span>, \u043a\u043e\u0433\u0434\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">x \\to \\pm\\infty<\/span>, \u0438 \u0441\u0434\u0435\u043b\u0430\u0439\u0442\u0435 \u0432\u044b\u0432\u043e\u0434, \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0435\u0442\u0441\u044f \u043b\u0438 \u043e\u043d\u0430 \u043a \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u043a\u0440\u0438\u0432\u043e\u0439, \u0430 \u043d\u0435 \u043a \u043f\u0440\u044f\u043c\u043e\u0439.<\/li>\n<li>\u0421\u0444\u043e\u0440\u043c\u0443\u043b\u0438\u0440\u0443\u0439\u0442\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u043f\u043e \u0432\u0430\u0448\u0435\u043c\u0443 \u0432\u044b\u0431\u043e\u0440\u0443 \u0438 \u043f\u043e\u0434\u0440\u043e\u0431\u043d\u043e \u043e\u043f\u0438\u0448\u0438\u0442\u0435, \u043a\u0430\u043a \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0435\u0451 \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435, \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u043d\u0430\u043a\u043b\u043e\u043d\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u0430 \u0442\u0430\u043a\u0436\u0435 \u0434\u043e\u043c\u0438\u043d\u0438\u0440\u0443\u044e\u0449\u0438\u0435 \u0447\u043b\u0435\u043d\u044b. \u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u044c\u0442\u0435 \u0441\u0432\u043e\u0438 \u0432\u044b\u0432\u043e\u0434\u044b \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0433\u0440\u0430\u0444\u0438\u043a\u043e\u0432 \u0434\u043b\u044f \u0432\u0438\u0437\u0443\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438 \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0442\u0438\u043f\u0430 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u0410\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u041f\u0440\u0435\u0434\u0435\u043b\u044b \u0438 \u041c\u0435\u0442\u043e\u0434\u044b \u0413\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u0420\u0435\u0437\u044e\u043c\u0435: \u0412 \u044d\u0442\u043e\u043c \u0443\u0440\u043e\u043a\u0435 \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u044e\u0442\u0441\u044f \u043f\u043e\u043d\u044f\u0442\u0438\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442 \u0438 \u0434\u043e\u043c\u0438\u043d\u0438\u0440\u0443\u044e\u0449\u0438\u0445 \u0447\u043b\u0435\u043d\u043e\u0432 \u0432 \u0430\u043d\u0430\u043b\u0438\u0437\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0439. \u0418\u0441\u0441\u043b\u0435\u0434\u0443\u044e\u0442\u0441\u044f \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u044e\u0442 \u043f\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043a\u043e\u0433\u0434\u0430 \u0441\u0442\u0440\u0435\u043c\u0438\u0442\u0441\u044f \u043a \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438; \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0443\u043a\u0430\u0437\u044b\u0432\u0430\u044e\u0442 \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b, \u043a\u043e\u0433\u0434\u0430 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0435\u0442\u0441\u044f \u043a \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u044b\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u043c; \u0438 \u043d\u0430\u043a\u043b\u043e\u043d\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0430\u043a\u0442\u0443\u0430\u043b\u044c\u043d\u044b \u0432 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u0445, \u043a\u043e\u0433\u0434\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044f \u043f\u0440\u0435\u0432\u044b\u0448\u0430\u0435\u0442 \u0441\u0442\u0435\u043f\u0435\u043d\u044c [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":29511,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":108,"footnotes":""},"categories":[864,573],"tags":[],"class_list":["post-29532","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>\u0410\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0438 \u043c\u0435\u0442\u043e\u0434\u044b \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u044f - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u042d\u0442\u043e \u0440\u0443\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u043e \u043f\u043e\u043c\u043e\u0436\u0435\u0442 \u0432\u0430\u043c \u043f\u043e\u043d\u044f\u0442\u044c \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435, \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u043d\u0430\u043a\u043b\u043e\u043d\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u0430 \u0442\u0430\u043a\u0436\u0435 \u043a\u0430\u043a \u0438\u0445 \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c, \u0438\u0437\u0443\u0447\u0430\u044f \u043f\u0440\u0435\u0434\u0435\u043b\u044b.\" \/>\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\/\u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b-\u043f\u0440\u0435\u0434\u0435\u043b\u044b-\u0438-\u043c\u0435\u0442\u043e\u0434\u044b-\u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0410\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0438 \u043c\u0435\u0442\u043e\u0434\u044b \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u044f\" \/>\n<meta property=\"og:description\" content=\"\u042d\u0442\u043e \u0440\u0443\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u043e \u043f\u043e\u043c\u043e\u0436\u0435\u0442 \u0432\u0430\u043c \u043f\u043e\u043d\u044f\u0442\u044c \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435, \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u043d\u0430\u043a\u043b\u043e\u043d\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u0430 \u0442\u0430\u043a\u0436\u0435 \u043a\u0430\u043a \u0438\u0445 \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c, \u0438\u0437\u0443\u0447\u0430\u044f \u043f\u0440\u0435\u0434\u0435\u043b\u044b.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/toposuranos.com\/material\/ru\/\u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b-\u043f\u0440\u0435\u0434\u0435\u043b\u044b-\u0438-\u043c\u0435\u0442\u043e\u0434\u044b-\u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\/\" \/>\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=\"2024-11-18T02:30:47+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-11-18T02:33:17+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/11\/asintotas-1024x550.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"\u0410\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0438 \u043c\u0435\u0442\u043e\u0434\u044b \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u044f\" \/>\n<meta name=\"twitter:description\" content=\"\u042d\u0442\u043e \u0440\u0443\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u043e \u043f\u043e\u043c\u043e\u0436\u0435\u0442 \u0432\u0430\u043c \u043f\u043e\u043d\u044f\u0442\u044c \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435, \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u043d\u0430\u043a\u043b\u043e\u043d\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u0430 \u0442\u0430\u043a\u0436\u0435 \u043a\u0430\u043a \u0438\u0445 \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c, \u0438\u0437\u0443\u0447\u0430\u044f \u043f\u0440\u0435\u0434\u0435\u043b\u044b.\" \/>\n<meta name=\"twitter:image\" content=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/11\/asintotas.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=\"6 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"https:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"\u0410\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0438 \u043c\u0435\u0442\u043e\u0434\u044b \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u044f\",\"datePublished\":\"2024-11-18T02:30:47+00:00\",\"dateModified\":\"2024-11-18T02:33:17+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/\"},\"wordCount\":1258,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/toposuranos.com\/material\/#organization\"},\"image\":{\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/11\/asintotas.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%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/\",\"url\":\"https:\/\/toposuranos.com\/material\/ru\/%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/\",\"name\":\"\u0410\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0438 \u043c\u0435\u0442\u043e\u0434\u044b \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u044f - toposuranos.com\/material\",\"isPartOf\":{\"@id\":\"https:\/\/toposuranos.com\/material\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/11\/asintotas.jpg\",\"datePublished\":\"2024-11-18T02:30:47+00:00\",\"dateModified\":\"2024-11-18T02:33:17+00:00\",\"description\":\"\u042d\u0442\u043e \u0440\u0443\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u043e \u043f\u043e\u043c\u043e\u0436\u0435\u0442 \u0432\u0430\u043c \u043f\u043e\u043d\u044f\u0442\u044c \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435, \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u043d\u0430\u043a\u043b\u043e\u043d\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u0430 \u0442\u0430\u043a\u0436\u0435 \u043a\u0430\u043a \u0438\u0445 \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c, \u0438\u0437\u0443\u0447\u0430\u044f \u043f\u0440\u0435\u0434\u0435\u043b\u044b.\",\"breadcrumb\":{\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/#breadcrumb\"},\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/toposuranos.com\/material\/ru\/%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/#primaryimage\",\"url\":\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/11\/asintotas.jpg\",\"contentUrl\":\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/11\/asintotas.jpg\",\"width\":1792,\"height\":963,\"caption\":\"As\u00edntotas y L\u00edmites\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/toposuranos.com\/material\/ru\/%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"https:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u0410\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0438 \u043c\u0435\u0442\u043e\u0434\u044b \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u044f\"}]},{\"@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":"\u0410\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0438 \u043c\u0435\u0442\u043e\u0434\u044b \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u044f - toposuranos.com\/material","description":"\u042d\u0442\u043e \u0440\u0443\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u043e \u043f\u043e\u043c\u043e\u0436\u0435\u0442 \u0432\u0430\u043c \u043f\u043e\u043d\u044f\u0442\u044c \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435, \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u043d\u0430\u043a\u043b\u043e\u043d\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u0430 \u0442\u0430\u043a\u0436\u0435 \u043a\u0430\u043a \u0438\u0445 \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c, \u0438\u0437\u0443\u0447\u0430\u044f \u043f\u0440\u0435\u0434\u0435\u043b\u044b.","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\/\u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b-\u043f\u0440\u0435\u0434\u0435\u043b\u044b-\u0438-\u043c\u0435\u0442\u043e\u0434\u044b-\u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\/","og_locale":"es_ES","og_type":"article","og_title":"\u0410\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0438 \u043c\u0435\u0442\u043e\u0434\u044b \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u044f","og_description":"\u042d\u0442\u043e \u0440\u0443\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u043e \u043f\u043e\u043c\u043e\u0436\u0435\u0442 \u0432\u0430\u043c \u043f\u043e\u043d\u044f\u0442\u044c \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435, \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u043d\u0430\u043a\u043b\u043e\u043d\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u0430 \u0442\u0430\u043a\u0436\u0435 \u043a\u0430\u043a \u0438\u0445 \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c, \u0438\u0437\u0443\u0447\u0430\u044f \u043f\u0440\u0435\u0434\u0435\u043b\u044b.","og_url":"https:\/\/toposuranos.com\/material\/ru\/\u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b-\u043f\u0440\u0435\u0434\u0435\u043b\u044b-\u0438-\u043c\u0435\u0442\u043e\u0434\u044b-\u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\/","og_site_name":"toposuranos.com\/material","article_publisher":"https:\/\/www.facebook.com\/groups\/toposuranos","article_published_time":"2024-11-18T02:30:47+00:00","article_modified_time":"2024-11-18T02:33:17+00:00","og_image":[{"url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/11\/asintotas-1024x550.jpg","type":"","width":"","height":""}],"author":"giorgio.reveco","twitter_card":"summary_large_image","twitter_title":"\u0410\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0438 \u043c\u0435\u0442\u043e\u0434\u044b \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u044f","twitter_description":"\u042d\u0442\u043e \u0440\u0443\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u043e \u043f\u043e\u043c\u043e\u0436\u0435\u0442 \u0432\u0430\u043c \u043f\u043e\u043d\u044f\u0442\u044c \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435, \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u043d\u0430\u043a\u043b\u043e\u043d\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u0430 \u0442\u0430\u043a\u0436\u0435 \u043a\u0430\u043a \u0438\u0445 \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c, \u0438\u0437\u0443\u0447\u0430\u044f \u043f\u0440\u0435\u0434\u0435\u043b\u044b.","twitter_image":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/11\/asintotas.jpg","twitter_creator":"@topuranos","twitter_site":"@topuranos","twitter_misc":{"Escrito por":"giorgio.reveco","Tiempo de lectura":"6 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/toposuranos.com\/material\/ru\/%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/#article","isPartOf":{"@id":"https:\/\/toposuranos.com\/material\/ru\/%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/"},"author":{"name":"giorgio.reveco","@id":"https:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1"},"headline":"\u0410\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0438 \u043c\u0435\u0442\u043e\u0434\u044b \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u044f","datePublished":"2024-11-18T02:30:47+00:00","dateModified":"2024-11-18T02:33:17+00:00","mainEntityOfPage":{"@id":"https:\/\/toposuranos.com\/material\/ru\/%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/"},"wordCount":1258,"commentCount":0,"publisher":{"@id":"https:\/\/toposuranos.com\/material\/#organization"},"image":{"@id":"https:\/\/toposuranos.com\/material\/ru\/%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/#primaryimage"},"thumbnailUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/11\/asintotas.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%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/toposuranos.com\/material\/ru\/%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/","url":"https:\/\/toposuranos.com\/material\/ru\/%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/","name":"\u0410\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0438 \u043c\u0435\u0442\u043e\u0434\u044b \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u044f - toposuranos.com\/material","isPartOf":{"@id":"https:\/\/toposuranos.com\/material\/#website"},"primaryImageOfPage":{"@id":"https:\/\/toposuranos.com\/material\/ru\/%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/#primaryimage"},"image":{"@id":"https:\/\/toposuranos.com\/material\/ru\/%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/#primaryimage"},"thumbnailUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/11\/asintotas.jpg","datePublished":"2024-11-18T02:30:47+00:00","dateModified":"2024-11-18T02:33:17+00:00","description":"\u042d\u0442\u043e \u0440\u0443\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u043e \u043f\u043e\u043c\u043e\u0436\u0435\u0442 \u0432\u0430\u043c \u043f\u043e\u043d\u044f\u0442\u044c \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435, \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u043d\u0430\u043a\u043b\u043e\u043d\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u0430 \u0442\u0430\u043a\u0436\u0435 \u043a\u0430\u043a \u0438\u0445 \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c, \u0438\u0437\u0443\u0447\u0430\u044f \u043f\u0440\u0435\u0434\u0435\u043b\u044b.","breadcrumb":{"@id":"https:\/\/toposuranos.com\/material\/ru\/%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/#breadcrumb"},"inLanguage":"es","potentialAction":[{"@type":"ReadAction","target":["https:\/\/toposuranos.com\/material\/ru\/%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/"]}]},{"@type":"ImageObject","inLanguage":"es","@id":"https:\/\/toposuranos.com\/material\/ru\/%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/#primaryimage","url":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/11\/asintotas.jpg","contentUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/11\/asintotas.jpg","width":1792,"height":963,"caption":"As\u00edntotas y L\u00edmites"},{"@type":"BreadcrumbList","@id":"https:\/\/toposuranos.com\/material\/ru\/%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d1%8b-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b-%d0%b8-%d0%bc%d0%b5%d1%82%d0%be%d0%b4%d1%8b-%d0%b3%d1%80%d0%b0%d1%84%d0%b8%d1%87%d0%b5%d1%81%d0%ba\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"https:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/"},{"@type":"ListItem","position":2,"name":"\u0410\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0438 \u043c\u0435\u0442\u043e\u0434\u044b \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u044f"}]},{"@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\/29532","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=29532"}],"version-history":[{"count":0,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/29532\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media\/29511"}],"wp:attachment":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media?parent=29532"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/categories?post=29532"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/tags?post=29532"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}