{"id":29347,"date":"2024-10-22T13:00:21","date_gmt":"2024-10-22T13:00:21","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=29347"},"modified":"2024-10-23T14:37:47","modified_gmt":"2024-10-23T14:37:47","slug":"%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%bd%d0%b0-%d0%b1%d0%b5%d1%81%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d0%be%d1%81%d1%82%d0%b8-%d0%be%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d0%b5%d0%bd%d0%b8%d1%8f","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb-%d0%bd%d0%b0-%d0%b1%d0%b5%d1%81%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d0%be%d1%81%d1%82%d0%b8-%d0%be%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d0%b5%d0%bd%d0%b8%d1%8f\/","title":{"rendered":"\u041f\u0440\u0435\u0434\u0435\u043b \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438: \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0438 \u043f\u0440\u0438\u043c\u0435\u0440\u044b"},"content":{"rendered":"<p><center><\/p>\n<h1>\u041f\u0440\u0435\u0434\u0435\u043b \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438: \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0438 \u043f\u0440\u0438\u043c\u0435\u0440\u044b<\/h1>\n<p><em><\/p>\n<p><strong>\u0420\u0435\u0437\u044e\u043c\u0435:<\/strong><br \/>\n\u041d\u0430 \u044d\u0442\u043e\u043c \u0443\u0440\u043e\u043a\u0435 \u0431\u0443\u0434\u0443\u0442 \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u043d\u044b \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438, \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u044e\u0449\u0438\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\">f(x)<\/span> \u043f\u0440\u0438 \u0441\u0442\u0440\u0435\u043c\u043b\u0435\u043d\u0438\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u043a \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438. \u0411\u0443\u0434\u0443\u0442 \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u044b \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b, \u0442\u0430\u043a\u0438\u0435 \u043a\u0430\u043a <span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x\\to \\infty} \\frac{1}{x} = 0<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x\\to \\infty} k = k<\/span>, \u0430 \u0442\u0430\u043a\u0436\u0435 \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430, \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u044b\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430\u043c \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432.\n<\/p>\n<p><\/em><\/p>\n<p><strong>\u0423\u0447\u0435\u0431\u043d\u044b\u0435 \u0446\u0435\u043b\u0438:<\/strong><br \/>\n\u041a \u043a\u043e\u043d\u0446\u0443 \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 style=\"text-align:left;\">\n<li><strong>\u041e\u043f\u0438\u0441\u0430\u0442\u044c<\/strong> \u043f\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u043f\u0440\u0438 \u0441\u0442\u0440\u0435\u043c\u043b\u0435\u043d\u0438\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \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> \u043f\u0440\u0435\u0434\u0435\u043b \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u043d\u043e\u0442\u0430\u0446\u0438\u044e.<\/li>\n<li><strong>\u041f\u0440\u0438\u043c\u0435\u043d\u044f\u0442\u044c<\/strong> \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u043f\u0440\u0438 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0438 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432 \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438.<\/li>\n<li><strong>\u0420\u0430\u0437\u043b\u0438\u0447\u0430\u0442\u044c<\/strong> \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0435 \u0441\u043b\u0443\u0447\u0430\u0438 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432 \u0432 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u0445 \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438.<\/li>\n<li><strong>\u0414\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0442\u044c<\/strong> \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u0441\u043b\u043e\u0436\u0435\u043d\u0438\u044f, \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u044f, \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044f, \u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0438 \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0432 \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432 \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438.<\/li>\n<li><strong>\u0420\u0435\u0448\u0430\u0442\u044c<\/strong> \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043d\u0430 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438 \u0432 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u0445.<\/li>\n<\/ol>\n<p><u>\u0421\u043e\u0434\u0435\u0440\u0436\u0430\u043d\u0438\u0435:<\/u><br \/>\n<a href=\"#1\">\u0412\u0432\u0435\u0434\u0435\u043d\u0438\u0435<\/a><br \/>\n<a href=\"#2\">\u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u0430 \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438<\/a><br \/>\n<a href=\"#3\">\u041e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \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=\"#4\">\u0410\u043b\u0433\u0435\u0431\u0440\u0430 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432 \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438<\/a><br \/>\n<a href=\"#5\">\u041f\u0440\u0435\u0434\u0435\u043b \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438 \u0432 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u0445<\/a><br \/>\n<a href=\"#6\">\u041f\u0440\u0438\u043c\u0435\u0440\u044b \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432 \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438<\/a><br \/>\n<\/center><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/MjjSAQLeNBE\" 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 style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=41s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u041e\u0434\u043d\u0438\u043c \u0438\u0437 \u0441\u0430\u043c\u044b\u0445 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u043d\u044b\u0445 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u043e\u0432 \u0430\u043d\u0430\u043b\u0438\u0437\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u044c \u0438 \u043f\u0440\u0435\u0434\u0435\u043b \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438.<\/span><\/strong><\/a> \u041f\u043e\u043d\u044f\u0442\u0438\u0435 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438 \u043d\u0435 \u0443\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u043d\u0430 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e, \u0430 \u0441\u043a\u043e\u0440\u0435\u0435 \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u0442 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0443, \u043f\u0440\u0435\u0432\u044b\u0448\u0430\u044e\u0449\u0443\u044e \u043b\u044e\u0431\u0443\u044e \u0440\u0435\u0430\u043b\u044c\u043d\u0443\u044e \u0433\u0440\u0430\u043d\u0438\u0446\u0443. \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u043f\u0440\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">f(x) = 1\/x<\/span> \u0438 \u0432\u043e\u043f\u0440\u043e\u0441\u0435 \u043e \u0435\u0451 \u043f\u043e\u0432\u0435\u0434\u0435\u043d\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 (<span class=\"katex-eq\" data-katex-display=\"false\">x\\to \\infty<\/span>), \u043c\u043e\u0436\u043d\u043e \u043d\u0430\u0431\u043b\u044e\u0434\u0430\u0442\u044c, \u0447\u0442\u043e <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u043c\u043e\u0436\u0435\u0442 \u043d\u0435\u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u043e \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0442\u044c\u0441\u044f \u043a \u043d\u0443\u043b\u044e. \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043f\u0438\u0448\u0435\u043c:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to + \\infty}\\dfrac{1}{x} = 0<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u0413\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u0438 \u044d\u0442\u043e \u0432\u044b\u0433\u043b\u044f\u0434\u0438\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c:<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-fX0lg2ICTTU\/YGD0hNJWI6I\/AAAAAAAAEwQ\/0v8hW6ARkQYDIzT_eG5WVgZ0-pPwwPBwgCLcBGAsYHQ\/s0\/limiteAlinfinito.PNG\" alt=\"\u043f\u0440\u0435\u0434\u0435\u043b \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438\" class=\"alignnone size-full lazyload\" width=\"400\" height=\"300\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-fX0lg2ICTTU\/YGD0hNJWI6I\/AAAAAAAAEwQ\/0v8hW6ARkQYDIzT_eG5WVgZ0-pPwwPBwgCLcBGAsYHQ\/s0\/limiteAlinfinito.PNG\" alt=\"\u043f\u0440\u0435\u0434\u0435\u043b \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438\" class=\"alignnone size-full lazyload\" width=\"400\" height=\"300\" \/><\/noscript><\/center><\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u0430 \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=144s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0418\u0441\u0445\u043e\u0434\u044f \u0438\u0437 \u044d\u0442\u043e\u0439 \u0438\u0434\u0435\u0438, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0441\u0444\u043e\u0440\u043c\u0443\u043b\u0438\u0440\u043e\u0432\u0430\u0442\u044c \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 \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438:<\/span><\/strong><\/a><\/p>\n<p style=\"text-align: justify; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}f(x) = L := (\\forall\\epsilon\\gt 0) (\\exists M\\in\\mathbb{R})(M\\lt x \\rightarrow |f(x) - L|\\lt \\epsilon )<\/span>\n<p style=\"text-align: justify; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to -\\infty}f(x) = L := (\\forall\\epsilon\\gt 0) (\\exists N\\in\\mathbb{R})(x\\lt N \\rightarrow |f(x) - L|\\lt \\epsilon )<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u0418\u043d\u0442\u0443\u0438\u0442\u0438\u0432\u043d\u043e\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u044d\u0442\u043e\u0433\u043e \u043f\u0440\u0435\u0434\u0435\u043b\u0430 \u0443\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u043d\u0430 \u043f\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span>, \u043a\u043e\u0433\u0434\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0443\u0434\u0430\u043b\u044f\u0435\u0442\u0441\u044f \u043e\u0442 \u043d\u0430\u0447\u0430\u043b\u0430 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442 \u0432 \u043b\u044e\u0431\u043e\u043c \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0438. \u0421\u0442\u0440\u0430\u0442\u0435\u0433\u0438\u044f \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432 \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438 \u043d\u0435 \u0441\u0438\u043b\u044c\u043d\u043e \u043e\u0442\u043b\u0438\u0447\u0430\u0435\u0442\u0441\u044f \u043e\u0442 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0430\u043b\u0433\u0435\u0431\u0440\u0430 \u043e\u0441\u0442\u0430\u0435\u0442\u0441\u044f \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0442\u043e\u0439 \u0436\u0435, \u0437\u0430 \u0438\u0441\u043a\u043b\u044e\u0447\u0435\u043d\u0438\u0435\u043c \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e\u0441\u0442\u0438 \u0443\u0447\u0438\u0442\u044b\u0432\u0430\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u044b:<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u041e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \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=MjjSAQLeNBE&amp;t=450s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u041d\u0430 \u043e\u0441\u043d\u043e\u0432\u0435 \u044d\u0442\u0438\u0445 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0439 \u043c\u043e\u0436\u043d\u043e \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b:<\/span><\/strong><\/a><\/p>\n<ol style=\"text-align: justify; color: #000000;\">\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm\\infty}k = k <\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm\\infty}\\dfrac{1}{x} = 0 <\/span><\/li>\n<\/ol>\n<p style=\"text-align: justify; color: #000000;\"><span style=\"color: #000080;\">\u0414\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u0441\u0442\u0432\u043e:<\/span><\/p>\n<ol style=\"text-align: justify; color: #000000;\">\n<li>\u0421\u043e\u0433\u043b\u0430\u0441\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044e \u043f\u0440\u0435\u0434\u0435\u043b\u0430 \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438, <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}k = k <\/span> \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u043e \u0443\u0442\u0432\u0435\u0440\u0436\u0434\u0435\u043d\u0438\u044e: <span class=\"katex-eq\" data-katex-display=\"false\">(\\forall\\epsilon\\gt 0) (\\exists M\\in\\mathbb{R})\\left(M\\lt x \\rightarrow \\left|k-k\\right|\\lt \\epsilon \\right)<\/span>. \u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 <span class=\"katex-eq\" data-katex-display=\"false\">\\left|k-k\\right|=0\\lt \\epsilon<\/span> \u0434\u043b\u044f \u043b\u044e\u0431\u043e\u0433\u043e <span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon \\gt 0<\/span> \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442\u0441\u044f \u0432\u0441\u0435\u0433\u0434\u0430 \u0438 \u0434\u043b\u044f \u043b\u044e\u0431\u043e\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f <span class=\"katex-eq\" data-katex-display=\"false\">M<\/span>, \u043f\u0440\u0435\u0434\u0435\u043b \u043f\u043e\u0434\u0442\u0432\u0435\u0440\u0436\u0434\u0430\u0435\u0442\u0441\u044f.\n<p>&nbsp;<\/li>\n<li>\u0418\u0437 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}k = k <\/span> \u0441\u043b\u0435\u0434\u0443\u0435\u0442: <span class=\"katex-eq\" data-katex-display=\"false\">(\\forall\\epsilon\\gt 0) (\\exists M\\in\\mathbb{R})\\left(M\\lt x \\rightarrow \\left|\\dfrac{1}{x}\\right|\\lt \\epsilon \\right)<\/span>. \u042d\u0442\u0430 \u0438\u043c\u043f\u043b\u0438\u043a\u0430\u0446\u0438\u044f \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442\u0441\u044f \u0441\u0440\u0430\u0437\u0443, \u0435\u0441\u043b\u0438 \u043c\u044b \u0431\u0435\u0440\u0435\u043c <span class=\"katex-eq\" data-katex-display=\"false\">M=1\/\\epsilon<\/span>, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043f\u0440\u0435\u0434\u0435\u043b \u043f\u043e\u0434\u0442\u0432\u0435\u0440\u0436\u0434\u0430\u0435\u0442\u0441\u044f.\n<p>&nbsp;<\/li>\n<\/ol>\n<p style=\"text-align: justify; color: #000000;\">\u042d\u0442\u0438 \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u0441\u0442\u0432\u0430 \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u044b \u0434\u043b\u044f \u0441\u043b\u0443\u0447\u0430\u044f <span class=\"katex-eq\" data-katex-display=\"false\">x\\to+\\infty<\/span>.<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u0410\u043b\u0433\u0435\u0431\u0440\u0430 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432 \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=620s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0410\u043b\u0433\u0435\u0431\u0440\u0430 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432 \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438 \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u0430 \u0430\u043b\u0433\u0435\u0431\u0440\u0435 \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432.<\/span><\/strong><\/a> \u0415\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm \\infty}f(x) = L<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm \\infty}g(x) = M<\/span>, \u0442\u043e \u0441\u043f\u0440\u0430\u0432\u0435\u0434\u043b\u0438\u0432\u044b \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u0430:<\/p>\n<ol style=\"text-align: justify; color: #000000;\">\n<li><strong>\u0421\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u0438 \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432:<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm\\infty}(f(x)\\pm g(x)) = L \\pm M<\/span><\/li>\n<li><strong>\u0423\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435 \u043d\u0430 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u0443:<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm\\infty}cf(x) = cL<\/span><\/li>\n<li><strong>\u041f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432:<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm\\infty}f(x)g(x) = LM<\/span><\/li>\n<li><strong>\u0427\u0430\u0441\u0442\u043d\u043e\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432:<\/strong> \u041f\u0440\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">M\\neq 0<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm\\infty}f(x)\/g(x)=L\/M<\/span><\/li>\n<li><strong>\u0412\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0432 \u0441\u0442\u0435\u043f\u0435\u043d\u044c:<\/strong> \u0415\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">p,q \\in\\mathbb{Z}<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">q\\neq 0<\/span>, \u0442\u043e <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm\\infty}[f(x)]^{p\/q} = L^{p\/q}<\/span>. \u0415\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">q<\/span> \u0447\u0435\u0442\u043d\u043e\u0435, \u043f\u0440\u0435\u0434\u043f\u043e\u043b\u0430\u0433\u0430\u0435\u0442\u0441\u044f, \u0447\u0442\u043e <span class=\"katex-eq\" data-katex-display=\"false\">L\\geq 0<\/span>.<\/li>\n<\/ol>\n<p style=\"text-align: justify; color: #000000;\">\u041d\u0430 \u0441\u0430\u043c\u043e\u043c \u0434\u0435\u043b\u0435, \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u0441\u0442\u0432\u0430 \u0432\u0441\u0435\u0445 \u044d\u0442\u0438\u0445 \u0441\u0432\u043e\u0439\u0441\u0442\u0432 \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u044b \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u0441\u0442\u0432\u0430\u043c <a href=\"https:\/\/toposuranos.com\/la-definicion-de-limite-demostraciones-y-teoremas\/\" target=\"_blank\" rel=\"noopener\">\u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432<\/a>.<\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u041f\u0440\u0435\u0434\u0435\u043b \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438 \u0432 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u0445<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=792s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0420\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u2014 \u044d\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0430 \u043a\u0430\u043a \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432.<\/span><\/strong><\/a> \u041f\u0440\u0438 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0438 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432 \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438 \u0434\u043b\u044f \u0442\u0430\u043a\u043e\u0433\u043e \u0442\u0438\u043f\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0434\u0435\u043b\u0438\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u043f\u043e\u043b\u0435\u0437\u043d\u0443\u044e \u0437\u0430\u043a\u043e\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u044c:<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u041f\u0440\u0435\u0434\u043f\u043e\u043b\u043e\u0436\u0438\u043c, \u0447\u0442\u043e \u043c\u044b \u0445\u043e\u0442\u0438\u043c \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\infty}P(x)\/Q(x)<\/span>:<\/p>\n<ul style=\"text-align: justify; color: #000000;\">\n<li>\u0415\u0441\u043b\u0438 \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>, \u0442\u043e <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u0431\u0443\u0434\u0435\u0442 \u0440\u0430\u0441\u0442\u0438 \u0431\u0435\u0437\u0433\u0440\u0430\u043d\u0438\u0447\u043d\u043e \u043f\u0440\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">x\\to\\infty<\/span> (\u043f\u0440\u0435\u0434\u0435\u043b \u043d\u0435 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442).<\/li>\n<li>\u0415\u0441\u043b\u0438 \u0441\u0442\u0435\u043f\u0435\u043d\u044c <span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span> \u043c\u0435\u043d\u044c\u0448\u0435 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">Q(x)<\/span>, \u0442\u043e \u043f\u0440\u0435\u0434\u0435\u043b \u0431\u0443\u0434\u0435\u0442 \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\u044e.<\/li>\n<li>\u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u0435\u0441\u043b\u0438 \u0441\u0442\u0435\u043f\u0435\u043d\u044c <span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span> \u0440\u0430\u0432\u043d\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">Q(x)<\/span>, \u0442\u043e \u043f\u0440\u0435\u0434\u0435\u043b \u0431\u0443\u0434\u0435\u0442 \u0440\u0430\u0432\u0435\u043d \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u044e \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u043e\u0432 \u043f\u0440\u0438 \u0441\u0442\u0430\u0440\u0448\u0438\u0445 \u0441\u0442\u0435\u043f\u0435\u043d\u044f\u0445.<\/li>\n<\/ul>\n<p style=\"text-align: justify; color: #000000;\">\u0421\u0430\u043c\u043e\u0435 \u043b\u0443\u0447\u0448\u0435\u0435 \u0432 \u044d\u0442\u043e\u043c \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0435 \u0442\u043e, \u0447\u0442\u043e, \u043a\u0430\u043a \u043c\u044b \u0443\u0432\u0438\u0434\u0438\u043c \u0432 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0445 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u0445, \u043e\u043d \u0440\u0430\u0431\u043e\u0442\u0430\u0435\u0442 \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e, \u0434\u0430\u0436\u0435 \u0435\u0441\u043b\u0438 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u043d\u0435 \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0446\u0435\u043b\u044b\u043c\u0438 \u0447\u0438\u0441\u043b\u0430\u043c\u0438.<\/p>\n<p><a name=\"6\"><\/a><\/p>\n<h2>\u041f\u0440\u0438\u043c\u0435\u0440\u044b \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432 \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438<\/h2>\n<ol style=\"text-align: justify; color: #000000;\">\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}\\dfrac{x+1}{x^2+3}<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=907s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u0420\u0415\u0428\u0415\u041d\u0418\u0415]<\/span><\/strong><\/a><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to -\\infty}\\dfrac{2x^3 + 7}{x^3 - x^2 + x + 7}<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=986s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u0420\u0415\u0428\u0415\u041d\u0418\u0415]<\/span><\/strong><\/a><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}\\dfrac{9x^4 + x}{2x^4 + 5x^2 - x + 6}<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=1049s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u0420\u0415\u0428\u0415\u041d\u0418\u0415]<\/span><\/strong><\/a><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}\\dfrac{10x^5 + x4 + 31}{x^4 - 7x^3 + 7x^2 + 9}<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=1111s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u0420\u0415\u0428\u0415\u041d\u0418\u0415]<\/span><\/strong><\/a><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}\\dfrac{2\\sqrt{x}+x^{-1}}{3x - 7}<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=1220s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u0420\u0415\u0428\u0415\u041d\u0418\u0415]<\/span><\/strong><\/a><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to -\\infty}\\dfrac{2x^{5\/3} - x^{1\/3} + 7}{x^{8\/5}+3x + \\sqrt{x}}<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=1284s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u0420\u0415\u0428\u0415\u041d\u0418\u0415]<\/span><\/strong><\/a><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}\\dfrac{\\sqrt[3]{x}-5x+3}{2x + x^{2\/3} - 4}<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=1406s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u0420\u0415\u0428\u0415\u041d\u0418\u0415]<\/span><\/strong><\/a><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}\\dfrac{x^{8\/3}+2x + \\sqrt{x}}{x^2+x-3}<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=1521s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u0420\u0415\u0428\u0415\u041d\u0418\u0415]<\/span><\/strong><\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u041f\u0440\u0435\u0434\u0435\u043b \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438: \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0438 \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0420\u0435\u0437\u044e\u043c\u0435: \u041d\u0430 \u044d\u0442\u043e\u043c \u0443\u0440\u043e\u043a\u0435 \u0431\u0443\u0434\u0443\u0442 \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u043d\u044b \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438, \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u044e\u0449\u0438\u0435 \u043f\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0438 \u0441\u0442\u0440\u0435\u043c\u043b\u0435\u043d\u0438\u0438 \u043a \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438. \u0411\u0443\u0434\u0443\u0442 \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u044b \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b, \u0442\u0430\u043a\u0438\u0435 \u043a\u0430\u043a \u0438 , \u0430 \u0442\u0430\u043a\u0436\u0435 \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430, \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u044b\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430\u043c \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432. \u0423\u0447\u0435\u0431\u043d\u044b\u0435 \u0446\u0435\u043b\u0438: \u041a \u043a\u043e\u043d\u0446\u0443 \u044d\u0442\u043e\u0433\u043e \u0443\u0440\u043e\u043a\u0430 \u0441\u0442\u0443\u0434\u0435\u043d\u0442 \u0441\u043c\u043e\u0436\u0435\u0442: \u041e\u043f\u0438\u0441\u0430\u0442\u044c \u043f\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u043f\u0440\u0438 \u0441\u0442\u0440\u0435\u043c\u043b\u0435\u043d\u0438\u0438 \u043a \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438. \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u043f\u0440\u0435\u0434\u0435\u043b \u043d\u0430 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":29336,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":21,"footnotes":""},"categories":[864,573],"tags":[],"class_list":["post-29347","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 v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u041f\u0440\u0435\u0434\u0435\u043b \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438: \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0438 \u043f\u0440\u0438\u043c\u0435\u0440\u044b - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u041d\u0435\u043f\u043e\u043d\u0438\u043c\u0430\u043d\u0438\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432 \u043d\u0430 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