{"id":379,"date":"2023-07-04T01:25:58","date_gmt":"2023-07-04T01:25:58","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d0%b2%d0%b5%d1%80%d1%82%d0%b8%d0%ba%d0%b0%d0%bb%d1%8c%d0%bd%d0%b0%d1%8f-%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d0%b0\/"},"modified":"2023-07-04T01:25:58","modified_gmt":"2023-07-04T01:25:58","slug":"%d0%b2%d0%b5%d1%80%d1%82%d0%b8%d0%ba%d0%b0%d0%bb%d1%8c%d0%bd%d0%b0%d1%8f-%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d0%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d0%b2%d0%b5%d1%80%d1%82%d0%b8%d0%ba%d0%b0%d0%bb%d1%8c%d0%bd%d0%b0%d1%8f-%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d0%b0\/","title":{"rendered":"\u0412\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0430\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430"},"content":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \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 (\u0441 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u043c\u0438). \u041c\u044b \u0442\u0430\u043a\u0436\u0435 \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c, \u043a\u0430\u043a \u043d\u0430\u0439\u0442\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, \u0438, \u043a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u0432 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f\u0445, \u0440\u0435\u0448\u0430\u0435\u043c\u044b\u0445 \u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-asintota-vertical\"><\/span> \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0430\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u0412\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0430\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u2014 \u044d\u0442\u043e \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0430\u044f \u043b\u0438\u043d\u0438\u044f, \u0433\u0440\u0430\u0444\u0438\u043a \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u043d\u0435\u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u043e \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0435\u0442\u0441\u044f, \u043d\u0438 \u0440\u0430\u0437\u0443 \u043d\u0435 \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u044f \u0435\u0435.<\/strong> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u043e\u0439 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434 <em>x=k<\/em> , \u0433\u0434\u0435 <em>k<\/em> \u2014 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u043e\u0439 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b.<\/p>\n<p> \u0422\u043e \u0435\u0441\u0442\u044c <strong><em>k<\/em> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u043e\u0439 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u043e\u0439, \u0435\u0441\u043b\u0438 \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0438 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0438 <em>x<\/em> <em>\u043a k<\/em> \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u0435\u043d.<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/asymptote-verticale.webp\" alt=\"\u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b\" class=\"wp-image-1281\" width=\"320\" height=\"255\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-calcular-la-asintota-vertical-de-una-funcion\"><\/span> \u041a\u0430\u043a \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \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=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0427\u0442\u043e\u0431\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \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, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0432\u044b\u043f\u043e\u043b\u043d\u0438\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0448\u0430\u0433\u0438:<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;border:\">\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">\u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0415\u0441\u043b\u0438 \u0432\u0441\u0435 \u0442\u043e\u0447\u043a\u0438 \u043d\u0430\u0445\u043e\u0434\u044f\u0442\u0441\u044f \u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0435 \u0438\u043c\u0435\u0435\u0442 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442.<\/span><\/li>\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">\u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0442\u043e\u0447\u043a\u0430\u0445, \u043d\u0435 \u0432\u0445\u043e\u0434\u044f\u0449\u0438\u0445 \u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f.<\/span><\/li>\n<li> <span style=\"color:#101010;font-weight: normal;\">\u0412\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u043c\u0438 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430\u043c\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0431\u0443\u0434\u0443\u0442 \u0432\u0441\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f, \u043f\u0440\u0438 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b \u0434\u0430\u0435\u0442 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u044c.<\/span><\/li>\n<\/ol>\n<p> \u041e\u0431\u0440\u0430\u0442\u0438\u0442\u0435 \u0432\u043d\u0438\u043c\u0430\u043d\u0438\u0435, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043c\u043e\u0436\u0435\u0442 \u0438\u043c\u0435\u0442\u044c \u0431\u043e\u043b\u0435\u0435 \u043e\u0434\u043d\u043e\u0439 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u043e\u0439 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b. \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, <u style=\"text-decoration-color:#FF9B28;\">\u0433\u0440\u0430\u0444\u0438\u043a \u043a\u0430\u0441\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0438\u043c\u0435\u0435\u0442 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0435 \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442.<\/u><\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0421\u043c.:<\/strong> <span style=\"text-decoration: underline;\"> \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430. <\/span> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-asintota-vertical\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u043e\u0439 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0412 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u0430 \u043c\u044b \u043d\u0430\u0439\u0434\u0435\u043c \u0432\u0441\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0447\u0442\u043e\u0431\u044b \u0432\u044b \u043c\u043e\u0433\u043b\u0438 \u0443\u0432\u0438\u0434\u0435\u0442\u044c, \u043a\u0430\u043a \u044d\u0442\u043e \u0434\u0435\u043b\u0430\u0435\u0442\u0441\u044f:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0425f9cc254c22f6e28ad2186732cfdf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{1}{x-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"101\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u0412 \u043e\u0431\u0449\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0442\u043e\u0447\u043a\u0438, \u0432 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u043d\u0435 \u043f\u0440\u0438\u043d\u0430\u0434\u043b\u0435\u0436\u0430\u0442 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043c \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n<p> \u042d\u0442\u043e \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043d\u0430 \u0442\u043e, \u043a\u043e\u0433\u0434\u0430 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u043e\u0431\u0440\u0430\u0449\u0430\u0435\u0442\u0441\u044f \u0432 \u043d\u0443\u043b\u044c, \u0447\u0442\u043e\u0431\u044b \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u0442\u043e\u0447\u043a\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043d\u0435 \u043f\u0440\u0438\u043d\u0430\u0434\u043b\u0435\u0436\u0430\u0442 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e0aacb848a27943fc0e8fba70f545d78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x-2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"73\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c657687cbbf5ea9a7545edb42190e592_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043e\u0431\u043b\u0430\u0441\u0442\u044c\u044e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0432\u0441\u0435 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430, \u043a\u0440\u043e\u043c\u0435 x=2:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-298deba50795b5fc3979441d68ef3ed8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\{2\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c <strong>, x=2 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u043e\u0439 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/strong> \u0427\u0442\u043e\u0431\u044b \u0443\u0431\u0435\u0434\u0438\u0442\u044c\u0441\u044f \u0432 \u044d\u0442\u043e\u043c, \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-acc5425df8da5bffaa5ee31c29284a86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 2} \\frac{1}{x-2}=\\frac{1}{2-2}=\\frac{1}{0}=\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"220\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043b\u0438 \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0441\u0442\u044c \u0447\u0438\u0441\u043b\u0430 \u043c\u0435\u0436\u0434\u0443 \u043d\u0443\u043b\u0435\u043c \u0438, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0434\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043f\u0440\u0435\u0434\u0435\u043b\u0430 \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b, \u0447\u0442\u043e\u0431\u044b \u0443\u0437\u043d\u0430\u0442\u044c, \u0440\u0430\u0432\u043d\u043e \u043b\u0438 \u043e\u043d\u043e \u043f\u043b\u044e\u0441 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438, \u043c\u0438\u043d\u0443\u0441 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438 \u0438\u043b\u0438 \u043f\u0440\u0435\u0434\u0435\u043b \u043d\u0435 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442. \u041e\u0434\u043d\u0430\u043a\u043e, \u043a\u043e\u0433\u0434\u0430 \u043c\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u043d\u0430\u043c \u043d\u0435 \u043d\u0443\u0436\u043d\u043e \u0434\u0435\u043b\u0430\u0442\u044c \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b, \u043d\u043e \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \u044d\u0442\u043e\u0439 \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0441\u0442\u0438 \u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e, \u0447\u0442\u043e\u0431\u044b \u0441\u043a\u0430\u0437\u0430\u0442\u044c, \u0447\u0442\u043e \u044d\u0442\u043e \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0430\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430.<\/p>\n<p> \u041a\u043e\u0440\u043e\u0447\u0435 \u0433\u043e\u0432\u043e\u0440\u044f, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0438 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0438 x \u043a 2 \u0434\u0430\u0435\u0442 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u044c, <strong>x=2 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u043e\u0439 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u043e\u0439.<\/strong><\/p>\n<p> \u041d\u0438\u0436\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0430 \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u0438. \u041a\u0430\u043a \u0432\u0438\u0434\u0438\u0442\u0435, \u043e\u043d\u0430 \u043e\u0447\u0435\u043d\u044c \u0431\u043b\u0438\u0437\u043a\u043e \u043f\u043e\u0434\u0445\u043e\u0434\u0438\u0442 \u043a \u043b\u0438\u043d\u0438\u0438 x=2 (\u043a\u0430\u043a \u0441\u043b\u0435\u0432\u0430, \u0442\u0430\u043a \u0438 \u0441\u043f\u0440\u0430\u0432\u0430), \u043d\u043e \u043d\u0438\u043a\u043e\u0433\u0434\u0430 \u043d\u0435 \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u0435\u0442 \u0435\u0435, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u043e\u0439 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u043e\u0439: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-dasymptote-verticale.webp\" alt=\"\u043f\u0440\u0438\u043c\u0435\u0440 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u043e\u0439 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b\" class=\"wp-image-1294\" width=\"431\" height=\"382\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u043f\u043e \u0433\u0440\u0430\u0444\u0438\u043a\u0443 \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0432\u0435\u0441\u0442\u0438 \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0442\u043e\u0447\u043a\u0435 x=2: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bae3e5d8a91ed8bfd4d59e8cf2b2e046_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 2^-} \\frac{1}{x-2} = -\\infty \\qquad  \\lim_{x \\to 2^+} \\frac{1}{x-2} = +\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"320\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-asintotas-verticales\"><\/span> \u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043e \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430\u0445<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> \u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 1<\/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 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-911fac1ac9244ceb5c6bff7e4bd14633_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\frac{3x-1}{2x-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"110\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u041d\u0435 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u0434\u043b\u044f \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0445 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043d\u043e \u0432\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u043d\u0430\u0439\u0442\u0438 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0438 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c, \u0432 \u043a\u0430\u043a\u0438\u0445 \u0442\u043e\u0447\u043a\u0430\u0445, \u0433\u0434\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0430, \u043f\u0440\u0435\u0434\u0435\u043b \u0434\u0430\u0435\u0442 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u044c.<\/p>\n<p class=\"has-text-align-left\"> \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043f\u043e\u043b\u043e\u0436\u0438\u043c \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0440\u0430\u0432\u043d\u044b\u043c 0, \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u0442\u043e\u0447\u043a\u0438, \u043d\u0435 \u043f\u0440\u0438\u043d\u0430\u0434\u043b\u0435\u0436\u0430\u0449\u0438\u0435 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-eda4c745b07ad63c3060964038aebf0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x -1 =0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"82\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0323089c11e731c307ef7664ecb6710b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x= 1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-971df94c9decb86065329338ff4b81ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x = \\cfrac{1}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"45\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043e\u0431\u043b\u0430\u0441\u0442\u044c\u044e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0432\u0441\u0435 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430, \u043a\u0440\u043e\u043c\u0435 x=1\/2:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d45cfed65d2da3a61311dce298a529a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\left\\{ \\cfrac{1}{2} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"149\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, x=1\/2 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u043e\u0439 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u043e\u0439. \u0427\u0442\u043e\u0431\u044b \u044d\u0442\u043e \u043f\u0440\u043e\u0432\u0435\u0440\u0438\u0442\u044c, \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043c \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-55047465393cc2a65a7214fa64eac93d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to \\frac{1}{2} } \\cfrac{3x-1}{2x-1} = \\cfrac{3\\cdot\\cfrac{1}{2}-1}{2\\cdot\\cfrac{1}{2}-1} = \\cfrac{ \\cfrac{3}{2} -1 }{\\cfrac{2}{2} -1 } = \\cfrac{ \\cfrac{1}{2} }{1-1}=\\cfrac{\\cfrac{1}{2}}{0} =\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"84\" width=\"383\" style=\"vertical-align: -39px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418\u0442\u0430\u043a <strong>, x=1\/2 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u043e\u0439 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u043e\u0439<\/strong> , \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u0434\u0430\u0435\u0442 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u044c.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> \u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 2<\/h3>\n<p> \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u0432\u0441\u0435 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0434\u0440\u043e\u0431\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cc3badbfcece4b7976d30989606ca685_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\frac{2x+1}{x^2-9}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"110\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u0443\u0441\u0442\u0430\u043d\u0430\u0432\u043b\u0438\u0432\u0430\u0435\u043c \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u0434\u0440\u043e\u0431\u0438 \u0440\u0430\u0432\u043d\u044b\u043c \u043d\u0443\u043b\u044e, \u0447\u0442\u043e\u0431\u044b \u0443\u0432\u0438\u0434\u0435\u0442\u044c, \u043a\u0430\u043a\u0438\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043d\u0435 \u0432\u0445\u043e\u0434\u044f\u0442 \u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ce55adbc277e9378607d68bce8ef19fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2-9=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"81\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0420\u0435\u0448\u0430\u0435\u043c \u043d\u0435\u043f\u043e\u043b\u043d\u043e\u0435 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-05112cb5a98f653cd1920fb40e5ef9a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2=9\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"50\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0505454de5d542ace3e698cb903893ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\pm 3\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043e\u0431\u043b\u0430\u0441\u0442\u044c\u044e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c91231eb4c883e8c625dba58f070307f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\left\\{3, -3\\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"168\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418\u0442\u0430\u043a, \u0447\u0442\u043e\u0431\u044b \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c, \u043a\u0430\u043a\u043e\u0435 \u0438\u0437 \u044d\u0442\u0438\u0445 \u0434\u0432\u0443\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u043c\u0438 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430\u043c\u0438, \u043c\u044b \u043d\u0430\u0445\u043e\u0434\u0438\u043c \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u043a\u0430\u0436\u0434\u043e\u0439 \u0442\u043e\u0447\u043a\u0435: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1a56d9ceafa2628b7a80603109ceafc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 3}\\frac{2x+1}{x^2-9}=\\frac{2\\cdot3+1}{3^2-9}=\\frac{7}{9-9}=\\frac{7}{0}=\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"317\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-944d84ad3ab51829df2623a4467cc16a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to -3}\\frac{2x+1}{x^2-9}=\\frac{2\\cdot(-3)+1}{(-3)^2-9}=\\frac{-5}{9-9}=\\frac{-5}{0}=\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"369\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0414\u0432\u0430 \u043f\u0440\u0435\u0434\u0435\u043b\u0430 \u0434\u0430\u044e\u0442 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u044c, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 <strong>x=3 \u0438 x=-3 \u2014 \u0434\u0432\u0435 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438<\/strong> .<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> \u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 3<\/h3>\n<p> \u041d\u0430\u0439\u0434\u0438\u0442\u0435, \u0435\u0441\u043b\u0438 \u043e\u043d\u0438 \u0443 \u0432\u0430\u0441 \u0435\u0441\u0442\u044c, \u0432\u0441\u0435 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1dd8356a2f682824a334f15826b31c89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\frac{x+3}{x^2+2x-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"150\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0421\u043c.:<\/strong> <span style=\"text-decoration: underline;\"> \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0441\u0442\u044c \u043d\u043e\u043b\u044c \u043c\u0435\u0436\u0434\u0443 \u043d\u0443\u043b\u0435\u043c. <\/span> <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u0440\u0435\u0448\u0430\u0435\u043c \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044f, \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f, \u0441\u043e\u043a\u0440\u0430\u0449\u0430\u044e\u0449\u0438\u0435 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u0434\u0440\u043e\u0431\u0438: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d5c5fd813f4a2456efa315766ad90ced_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+2x-3=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"122\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9b2170358d5d1719077695aba5afa02e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle x&amp;=\\cfrac{-b\\pm\\sqrt{b^2-4ac}}{2a}=\\cfrac{-2\\pm\\sqrt{2^2-4\\cdot1\\cdot(-3)}}{2\\cdot1}=\\\\[3ex]\\displaystyle &amp;=\\cfrac{-2\\pm\\sqrt{16}}{2}=\\cfrac{-2\\pm 4}{2}=\\begin{cases}\\cfrac{-2+4}{2}=1\\\\[3ex]\\cfrac{-2-4}{2}=-3\\end{cases}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"172\" width=\"396\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418\u0442\u0430\u043a, \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fd230a1caa7456bca8746870a6d0264a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\left\\{1, -3\\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"168\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418\u0442\u0430\u043a, \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0438 x=1:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3784526cad2b36766a213c13a5938c6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 1}\\frac{x+3}{x^2+2x-3}=\\frac{1+3}{1^2+2\\cdot 1-3}=\\frac{4}{0}=\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"328\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418, \u0441 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u043c\u044b \u0440\u0435\u0448\u0430\u0435\u043c \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043a\u043e\u0433\u0434\u0430 x \u0441\u0442\u0440\u0435\u043c\u0438\u0442\u0441\u044f \u043a -3:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f0e96a48986cd110e04058e3545290a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle\\lim_{x \\to -3}\\frac{x+3}{x^2+2x-3}=\\frac{-3+3}{(-3)^2+2\\cdot(-3)-3}=\\frac{0}{0}=\\\\[3ex]\\displaystyle =\\lim_{x \\to -3}\\frac{\\cancel{x+3}}{(x-1)\\cancel{(x+3)}}=\\lim_{x \\to -3}\\frac{1}{x-1}=\\frac{1}{-3-1}=-\\frac{1}{4}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"94\" width=\"413\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0438\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u0434\u0430\u0435\u0442 \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u0443\u044e \u0444\u043e\u0440\u043c\u0443 \u043e\u0442 \u043d\u0443\u043b\u044f \u0434\u043e \u043d\u0443\u043b\u044f, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0434\u043b\u044f \u0435\u0433\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u043e\u0432\u0430\u0442\u044c \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u044b. <u style=\"text-decoration-color:#FF9B28;\">\u0415\u0441\u043b\u0438 \u0443 \u0432\u0430\u0441 \u0435\u0441\u0442\u044c \u043a\u0430\u043a\u0438\u0435-\u043b\u0438\u0431\u043e \u0441\u043e\u043c\u043d\u0435\u043d\u0438\u044f \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u043c\u044b \u0440\u0435\u0448\u0438\u043b\u0438 \u043f\u0440\u0435\u0434\u0435\u043b, \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u043f\u043e\u043b\u043d\u043e\u0435 \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u0435 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u0440\u0435\u0448\u0438\u0442\u044c \u044d\u0442\u043e\u0442 \u0442\u0438\u043f \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0441\u0442\u0438, \u043f\u043e \u0441\u0441\u044b\u043b\u043a\u0435 \u043d\u0430 \u043e\u043f\u0435\u0440\u0430\u0442\u043e\u0440 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f.<\/u><\/p>\n<p class=\"has-text-align-left\"> \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0442\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0442\u043e\u0447\u043a\u0435 x=1 \u0434\u0430\u0435\u0442 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u044c, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 <strong>x=1 \u2014 \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0430\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438<\/strong> .<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \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 (\u0441 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u043c\u0438). \u041c\u044b \u0442\u0430\u043a\u0436\u0435 \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c, \u043a\u0430\u043a \u043d\u0430\u0439\u0442\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, \u0438, \u043a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u0432 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f\u0445, \u0440\u0435\u0448\u0430\u0435\u043c\u044b\u0445 \u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c. \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0430\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430? \u0412\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0430\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u2014 \u044d\u0442\u043e \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0430\u044f \u043b\u0438\u043d\u0438\u044f, \u0433\u0440\u0430\u0444\u0438\u043a \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u043d\u0435\u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u043e \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0435\u0442\u0441\u044f, \u043d\u0438 \u0440\u0430\u0437\u0443 \u043d\u0435 \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u044f \u0435\u0435. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u043e\u0439 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b \u0438\u043c\u0435\u0435\u0442 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ru\/%d0%b2%d0%b5%d1%80%d1%82%d0%b8%d0%ba%d0%b0%d0%bb%d1%8c%d0%bd%d0%b0%d1%8f-%d0%b0%d1%81%d0%b8%d0%bc%d0%bf%d1%82%d0%be%d1%82%d0%b0\/\"> <span class=\"screen-reader-text\">\u0412\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0430\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430<\/span> \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[11],"tags":[],"class_list":["post-379","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"<!-- This site is optimized 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content=\"\u0417\u0434\u0435\u0441\u044c \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \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 (\u0441 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u043c\u0438). \u041c\u044b \u0442\u0430\u043a\u0436\u0435 \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c, \u043a\u0430\u043a \u043d\u0430\u0439\u0442\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, \u0438, \u043a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u0432 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f\u0445, \u0440\u0435\u0448\u0430\u0435\u043c\u044b\u0445 \u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c. \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0430\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430? \u0412\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0430\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u2014 \u044d\u0442\u043e \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0430\u044f \u043b\u0438\u043d\u0438\u044f, \u0433\u0440\u0430\u0444\u0438\u043a \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u043d\u0435\u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u043e \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0435\u0442\u0441\u044f, \u043d\u0438 \u0440\u0430\u0437\u0443 \u043d\u0435 \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u044f \u0435\u0435. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u043e\u0439 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b \u0438\u043c\u0435\u0435\u0442 &hellip; \u0412\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0430\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430 \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/ru\/\u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0430\u044f-\u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-04T01:25:58+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/asymptote-verticale.webp\" \/>\n<meta name=\"author\" content=\"Mathority 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