{"id":368,"date":"2023-07-04T12:33:10","date_gmt":"2023-07-04T12:33:10","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d0%be%d0%b3%d1%80%d0%b0%d0%bd%d0%b8%d1%87%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d0%b8\/"},"modified":"2023-07-04T12:33:10","modified_gmt":"2023-07-04T12:33:10","slug":"%d0%be%d0%b3%d1%80%d0%b0%d0%bd%d0%b8%d1%87%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d0%b8","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d0%be%d0%b3%d1%80%d0%b0%d0%bd%d0%b8%d1%87%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d0%b8\/","title":{"rendered":"\u041e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438"},"content":{"rendered":"<p>\u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u044b\u0435 (\u0432\u0435\u0440\u0445\u043d\u0438\u0435 \u0438 \u043d\u0438\u0436\u043d\u0438\u0435) \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u043c\u044b \u043f\u043e\u043a\u0430\u0436\u0435\u043c \u0432\u0430\u043c, \u0447\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0442\u043e\u0447\u043a\u0435, \u0438, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u044d\u0442\u043e\u0433\u043e \u0442\u0438\u043f\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-funcion-acotada\"><\/span> \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u041e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f<\/strong> \u2014 \u044d\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u0433\u0440\u0430\u0444\u0438\u043a \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u0432 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u0430\u0445. \u0422\u043e \u0435\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0430 \u0441\u0432\u0435\u0440\u0445\u0443, \u0435\u0441\u043b\u0438 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0447\u0438\u0441\u043b\u043e K \u0442\u0430\u043a\u043e\u0435, \u0447\u0442\u043e \u043d\u0435 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0431\u043e\u043b\u044c\u0448\u0435\u0433\u043e, \u0447\u0435\u043c K (f(x)\u2264K), \u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0430 \u0441\u043d\u0438\u0437\u0443, \u0435\u0441\u043b\u0438 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0447\u0438\u0441\u043b\u043e K \u0442\u0430\u043a\u043e\u0435, \u0447\u0442\u043e \u043e\u043d\u043e \u043c\u0435\u043d\u044c\u0448\u0435 \u0432\u0441\u0435\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 (f(x)\u2265K). \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u2014 \u044d\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u0430\u044f \u0441\u0432\u0435\u0440\u0445\u0443 \u0438 \u0441\u043d\u0438\u0437\u0443. <\/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\/fonction-bornee.webp\" alt=\"\u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f\" class=\"wp-image-427\" width=\"481\" height=\"231\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0441\u0438\u043d\u0443\u0441\u0430, \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u043d\u0430\u044f \u043d\u0430 \u0433\u0440\u0430\u0444\u0438\u043a\u0435 \u0432\u044b\u0448\u0435, \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0430 \u0441\u0432\u0435\u0440\u0445\u0443 f(x)=1 \u0438 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0430 \u0441\u043d\u0438\u0437\u0443 f(x)=-1 (\u043a\u0440\u0430\u0441\u043d\u044b\u0435 \u043f\u0443\u043d\u043a\u0442\u0438\u0440\u043d\u044b\u0435 \u043b\u0438\u043d\u0438\u0438), \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0432\u0441\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u0432 \u044d\u0442\u0438\u0445 \u0434\u0432\u0443\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u0430\u0445. \u0414\u043e\u043f\u043e\u043b\u043d\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u044d\u0442\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u043f\u043e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0441\u0441\u044b\u043b\u043a\u0435:<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0421\u043c.:<\/strong> <span style=\"text-decoration: underline;\"> \u0425\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438 \u0441\u0438\u043d\u0443\u0441\u043e\u0438\u0434\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. <\/span> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"funcion-acotada-superiormente\"><\/span>\u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u0430\u044f \u0441\u0432\u0435\u0440\u0445\u0443<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041e\u0434\u043d\u0430\u043a\u043e \u043d\u0435 \u0432\u0441\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u044b \u0441\u0432\u0435\u0440\u0445\u0443 \u0438 \u0441\u043d\u0438\u0437\u0443, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0430 \u0442\u043e\u043b\u044c\u043a\u043e \u0441\u0432\u0435\u0440\u0445\u0443 \u0438\u043b\u0438 \u0441\u043d\u0438\u0437\u0443.<\/p>\n<p> \u041a \u0443\u043a\u0430\u0437\u0430\u043d\u043d\u044b\u043c <strong>\u0432\u044b\u0448\u0435 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u044b\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u043c<\/strong> \u043e\u0442\u043d\u043e\u0441\u044f\u0442\u0441\u044f \u0442\u0435, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043d\u0435 \u043f\u0440\u0435\u0432\u044b\u0448\u0430\u044e\u0442 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f, \u0442\u043e \u0435\u0441\u0442\u044c \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442\u0441\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435 \u0443\u0441\u043b\u043e\u0432\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-d1b0912c8106b6c93144cda220414684_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\\leq K\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0433\u0434\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 K \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0432\u0435\u0440\u0445\u043d\u0435\u0439 \u0433\u0440\u0430\u043d\u0438\u0446\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n<p> \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0430\u044f <span style=\"text-decoration: underline;\"> \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u0430 <\/span> \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0430 \u0441\u0432\u0435\u0440\u0445\u0443 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u043e\u0439 K=7, \u043d\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0435 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0430 \u0441\u043d\u0438\u0437\u0443, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0435\u0435 \u0432\u0435\u0442\u0432\u0438 \u043f\u0440\u043e\u0441\u0442\u0438\u0440\u0430\u044e\u0442\u0441\u044f \u0434\u043e \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438. <\/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\/exercice-resolu-etape-par-etape-de-la-fonction-quadratique.webp\" alt=\"\" class=\"wp-image-139\" width=\"279\" height=\"334\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u041b\u043e\u0433\u0438\u0447\u043d\u043e, \u0447\u0442\u043e \u0435\u0441\u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0430 K=7, \u043e\u043d\u0430 \u0442\u0430\u043a\u0436\u0435 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0430 K=8 \u0438 \u0431\u043e\u043b\u0435\u0435 \u0432\u044b\u0441\u043e\u043a\u0438\u043c\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u043c\u0438.<\/p>\n<p> \u041d\u0430\u0438\u043c\u0435\u043d\u044c\u0448\u0430\u044f \u0432\u0435\u0440\u0445\u043d\u044f\u044f \u0433\u0440\u0430\u043d\u0438\u0446\u0430 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0432\u0435\u0440\u0445\u043d\u0435\u0439 \u0433\u0440\u0430\u043d\u0438\u0446\u0435\u0439 \u0438 \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442\u0441\u044f \u043a\u0430\u043a <em>sup(f)<\/em> . \u0411\u043e\u043b\u0435\u0435 \u0442\u043e\u0433\u043e, \u0435\u0441\u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0434\u043e\u0441\u0442\u0438\u0433\u0430\u0435\u0442 \u0443\u043a\u0430\u0437\u0430\u043d\u043d\u043e\u0433\u043e \u0432\u0435\u0440\u0445\u043d\u0435\u0433\u043e \u043f\u0440\u0435\u0434\u0435\u043b\u0430 \u0432 \u0441\u0432\u043e\u0435\u0439 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043c\u044b \u0431\u0443\u0434\u0435\u043c \u0433\u043e\u0432\u043e\u0440\u0438\u0442\u044c, \u0447\u0442\u043e \u044d\u0442\u0430 \u0442\u043e\u0447\u043a\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f <strong>\u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u044b\u043c \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u043e\u043c<\/strong> \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0421\u043c\u043e\u0442\u0440\u0438\u0442\u0435:<\/strong> <span style=\"text-decoration: underline;\"> \u043a\u0430\u043a\u043e\u0432\u044b \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u044b \u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0438? <\/span><\/p>\n<p> \u0412 \u043d\u0430\u0448\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0430 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u043e\u0439 K=7, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u044d\u0442\u043e \u0432\u0435\u0440\u0445\u043d\u0438\u0439 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c \u0438 \u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u044b\u0439 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"funcion-acotada-inferiormente\"><\/span>\u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0430 \u043d\u0438\u0436\u0435<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u041d\u0438\u0436\u0435 \u043f\u0435\u0440\u0435\u0447\u0438\u0441\u043b\u0435\u043d\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0438<\/strong> , \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043d\u0435 \u0438\u043c\u0435\u044e\u0442 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043c\u0435\u043d\u044c\u0448\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0433\u043e \u0447\u0438\u0441\u043b\u0430, \u0442\u043e \u0435\u0441\u0442\u044c \u043e\u043d\u0438 \u0443\u0434\u043e\u0432\u043b\u0435\u0442\u0432\u043e\u0440\u044f\u044e\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u043c\u0443 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u043c\u0443 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044e:<\/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-6428bb46a6513be54693aaeb3c70fdc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\\geq K\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0413\u0434\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 K \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043d\u0438\u0436\u043d\u0435\u0439 \u0433\u0440\u0430\u043d\u0438\u0446\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n<p> \u041d\u0438\u0436\u0435 \u0432\u044b \u0432\u0438\u0434\u0438\u0442\u0435 \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u044d\u043a\u0441\u043f\u043e\u043d\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0430 \u043d\u0438\u0436\u0435 K=3: <\/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\/probleme-de-fonction-exponentielle.webp\" alt=\"\" class=\"wp-image-253\" width=\"264\" height=\"321\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u041e\u0447\u0435\u0432\u0438\u0434\u043d\u043e, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0442\u0430\u043a\u0436\u0435 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0430 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u043c\u0438 \u043c\u0435\u043d\u044c\u0448\u0435 K=3.<\/p>\n<p> \u041a\u0430\u043a \u0438 \u043f\u0440\u0435\u0436\u0434\u0435, \u043d\u0430\u0438\u0431\u043e\u043b\u044c\u0448\u0430\u044f \u043d\u0438\u0436\u043d\u044f\u044f \u0433\u0440\u0430\u043d\u0438\u0446\u0430 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043d\u0438\u0436\u043d\u0435\u0439 \u0433\u0440\u0430\u043d\u0438\u0446\u0435\u0439 \u0438 \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442\u0441\u044f <em>inf(f)<\/em> . \u0411\u043e\u043b\u0435\u0435 \u0442\u043e\u0433\u043e, \u0435\u0441\u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0434\u043e\u0441\u0442\u0438\u0433\u0430\u0435\u0442 \u0443\u043a\u0430\u0437\u0430\u043d\u043d\u043e\u0433\u043e \u043d\u0438\u0436\u043d\u0435\u0433\u043e \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u0430 \u0432 \u0441\u0432\u043e\u0435\u0439 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043c\u044b \u0431\u0443\u0434\u0435\u043c \u0433\u043e\u0432\u043e\u0440\u0438\u0442\u044c, \u0447\u0442\u043e \u044d\u0442\u0430 \u0442\u043e\u0447\u043a\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f <strong>\u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u044b\u043c \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u043c<\/strong> \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n<p> \u0412 \u0434\u0430\u043d\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 K=3 \u043d\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u044b\u043c \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0434\u043e\u0441\u0442\u0438\u0433\u0430\u0435\u0442 \u044d\u0442\u043e\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438 \u0438, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u0432\u043d\u0435 \u0441\u0432\u043e\u0435\u0439 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f. \u0414\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, f(x)=3 \u2014 <span style=\"text-decoration: underline;\"> \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0430\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <\/span> .<\/p>\n<p> \u0421\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0442\u0435\u043e\u0440\u0435\u043c\u0430, \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u044e\u0449\u0430\u044f \u0443\u0437\u043d\u0430\u0442\u044c, \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0430 \u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0441\u0432\u0435\u0440\u0445\u0443 \u0438 \u0441\u043d\u0438\u0437\u0443 \u0431\u0435\u0437 \u0435\u0435 \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. \u041d\u0430\u0436\u043c\u0438\u0442\u0435 \u0437\u0434\u0435\u0441\u044c, \u0447\u0442\u043e\u0431\u044b \u0443\u0437\u043d\u0430\u0442\u044c, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u0412\u0435\u0439\u0435\u0440\u0448\u0442\u0440\u0430\u0441\u0441\u0430.<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0421\u043c.:<\/strong> <span style=\"text-decoration: underline;\"> \u0422\u0435\u043e\u0440\u0435\u043c\u0430 \u0412\u0435\u0439\u0435\u0440\u0448\u0442\u0440\u0430\u0441\u0441\u0430. <\/span> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"funcion-acotada-en-un-punto\"><\/span> \u0424\u0443\u043d\u043a\u0446\u0438\u044f, \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u0430\u044f \u0432 \u043e\u0434\u043d\u043e\u0439 \u0442\u043e\u0447\u043a\u0435<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041c\u044b \u0442\u043e\u043b\u044c\u043a\u043e \u0447\u0442\u043e \u0438\u0437\u0443\u0447\u0438\u043b\u0438 \u043f\u043e\u043d\u044f\u0442\u0438\u0435 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0446\u0435\u043b\u043e\u043c, \u043d\u043e \u043c\u043e\u0436\u043d\u043e \u0442\u0430\u043a\u0436\u0435 \u043f\u0440\u043e\u0430\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c, \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0430 \u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432 \u043c\u0435\u043d\u044c\u0448\u0435\u0439 \u043e\u043a\u0440\u0435\u0441\u0442\u043d\u043e\u0441\u0442\u0438, \u0442\u043e \u0435\u0441\u0442\u044c \u0432 \u0447\u0430\u0441\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n<p> \u0410\u0433\u0430<\/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-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0442\u043e\u0447\u043a\u043e\u0439 \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 \u0438<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u043b\u044e\u0431\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435, \u0431\u0443\u0434\u0435\u043c \u0433\u043e\u0432\u043e\u0440\u0438\u0442\u044c, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0430 \u0441\u0432\u0435\u0440\u0445\u0443\/\u0441\u043d\u0438\u0437\u0443 \u0432 \u0442\u043e\u0447\u043a\u0435<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0435\u0441\u043b\u0438 \u0435\u0441\u0442\u044c \u043e\u043a\u0440\u0443\u0436\u0435\u043d\u0438\u0435<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-35809b342e97743c17fcf00c8f1fcaa9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V(a,r)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"53\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0433\u0434\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0430 \u0441\u0432\u0435\u0440\u0445\u0443\/\u0441\u043d\u0438\u0437\u0443.<\/p>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, <strong>\u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0430 \u0432 \u0442\u043e\u0447\u043a\u0435<\/strong><\/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-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0435\u0441\u043b\u0438 \u043e\u043d \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d \u0441\u0432\u0435\u0440\u0445\u0443 \u0438 \u0441\u043d\u0438\u0437\u0443 \u0432 \u043e\u043a\u0440\u0435\u0441\u0442\u043d\u043e\u0441\u0442\u0438<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bad21933de1c285515285d51686beea1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V(a,r).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"58\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041e\u0447\u0435\u0432\u0438\u0434\u043d\u043e, \u0447\u0442\u043e \u0435\u0441\u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0430 \u0432\u043e\u043e\u0431\u0449\u0435, \u0442\u043e \u043e\u043d\u0430 \u0431\u0443\u0434\u0435\u0442 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0430 \u0438 \u0432 \u043a\u0430\u0436\u0434\u043e\u0439 \u0441\u0432\u043e\u0435\u0439 \u0442\u043e\u0447\u043a\u0435. \u041e\u0434\u043d\u0430\u043a\u043e \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u0435 \u043d\u0435\u0432\u0435\u0440\u043d\u043e, \u0442\u043e \u0435\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0430 \u0432 \u043a\u0430\u0436\u0434\u043e\u0439 \u0438\u0437 \u0441\u0432\u043e\u0438\u0445 \u0442\u043e\u0447\u0435\u043a \u0438 \u043d\u0435 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0430 \u0432\u043e \u0432\u0441\u0435\u0439 \u0441\u0432\u043e\u0435\u0439 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f.<\/p>\n<p> \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0430\u044f \u0430\u0444\u0444\u0438\u043d\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0447\u0430\u0441\u0442\u0438\u0447\u043d\u043e \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0430 \u0432 \u043a\u0430\u0436\u0434\u043e\u0439 \u0438\u0437 \u0441\u0432\u043e\u0438\u0445 \u0442\u043e\u0447\u0435\u043a, \u043d\u043e \u043d\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\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-de-representation-d-une-fonction-lineaire-ou-affine.webp\" alt=\"\" class=\"wp-image-104\" width=\"263\" height=\"265\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-las-funciones-acotadas\"><\/span> \u0421\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043e\u0431\u043b\u0430\u0434\u0430\u044e\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c\u0438 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430\u043c\u0438:<\/p>\n<ul>\n<li> \u0410\u0433\u0430\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a7ee323bc5a3f73ad5e066b13bed5504_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0418<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6a5054ad96fb0978182340eb214bb125_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"32\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0434\u0432\u0435 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0441\u043b\u043e\u0436\u0435\u043d\u0438\u0435 (\u0438\u043b\u0438 \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u0435) \u0434\u0432\u0443\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e24299805ed877ea052cd135c96e7c28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\\pm g(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0442\u0430\u043a\u0436\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439.<\/li>\n<li> \u0410\u0433\u0430\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a7ee323bc5a3f73ad5e066b13bed5504_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0418<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6a5054ad96fb0978182340eb214bb125_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"32\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0434\u0432\u0435 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d47b381826b8c5e901bf202b6d4b14c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\\cdot g(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"79\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0442\u0430\u043a\u0436\u0435 \u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439.<\/li>\n<li> \u0415\u0441\u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u043c\u0435\u0435\u0442 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0443\u044e \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0443, \u043e\u043d\u0430 \u043d\u0435 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u043f\u043e\u043b\u043d\u043e\u0441\u0442\u044c\u044e \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0430. \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0430 \u0441\u0432\u0435\u0440\u0445\u0443 \u0438\u043b\u0438 \u0441\u043d\u0438\u0437\u0443.<\/li>\n<li> \u041b\u044e\u0431\u0430\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430\u044f \u0438 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u0430\u044f \u043d\u0430 \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u0443\u0435\u043c\u0430.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u044b\u0435 (\u0432\u0435\u0440\u0445\u043d\u0438\u0435 \u0438 \u043d\u0438\u0436\u043d\u0438\u0435) \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u043c\u044b \u043f\u043e\u043a\u0430\u0436\u0435\u043c \u0432\u0430\u043c, \u0447\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0442\u043e\u0447\u043a\u0435, \u0438, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u044d\u0442\u043e\u0433\u043e \u0442\u0438\u043f\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f? \u041e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u2014 \u044d\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u0433\u0440\u0430\u0444\u0438\u043a \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u0432 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u0430\u0445. \u0422\u043e \u0435\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0430 \u0441\u0432\u0435\u0440\u0445\u0443, \u0435\u0441\u043b\u0438 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0447\u0438\u0441\u043b\u043e K &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ru\/%d0%be%d0%b3%d1%80%d0%b0%d0%bd%d0%b8%d1%87%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d0%b8\/\"> <span class=\"screen-reader-text\">\u041e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438<\/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":[17],"tags":[],"class_list":["post-368","post","type-post","status-publish","format-standard","hentry","category-17"],"yoast_head":"<!-- This site is optimized 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