{"id":366,"date":"2023-07-04T13:41:37","date_gmt":"2023-07-04T13:41:37","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%b0%d1%8f-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d1%8f-%d0%ba%d0%be%d1%81%d0%b8%d0%bd%d1%83%d1%81%d0%b0\/"},"modified":"2023-07-04T13:41:37","modified_gmt":"2023-07-04T13:41:37","slug":"%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%b0%d1%8f-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d1%8f-%d0%ba%d0%be%d1%81%d0%b8%d0%bd%d1%83%d1%81%d0%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%b0%d1%8f-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d1%8f-%d0%ba%d0%be%d1%81%d0%b8%d0%bd%d1%83%d1%81%d0%b0\/","title":{"rendered":"\u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430"},"content":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u0432\u0441\u0435 \u043e \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430: \u043a\u0430\u043a\u043e\u0432\u0430 \u0435\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u0430, \u0435\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, \u0435\u0435 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438, \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0441\u0432\u044f\u0437\u0438 \u0441 \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u043c\u0438 \u0438 \u0442. \u0434. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-coseno-hiperbolico\"><\/span> \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0424\u0443\u043d\u043a\u0446\u0438\u044f <strong>\u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430<\/strong> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043e\u0434\u043d\u043e\u0439 \u0438\u0437 \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u0445 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0438 \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442\u0441\u044f \u0441\u0438\u043c\u0432\u043e\u043b\u043e\u043c <strong>cosh(x)<\/strong> . \u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u0440\u0430\u0432\u0435\u043d \u0441\u0443\u043c\u043c\u0435 e <sup>x<\/sup> \u043f\u043b\u044e\u0441 e <sup>-x<\/sup> , \u0440\u0430\u0437\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u043d\u0430 2.<\/p>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434:<\/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-f667377a7e792f2c9f5f5a7a0ecda4e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{cosh}(x)=\\cfrac{e^{x}+e^{-x}}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"149\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0441\u0432\u044f\u0437\u0430\u043d \u0441 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439. \u041f\u043e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0441\u0441\u044b\u043b\u043a\u0435 \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \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<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0421\u043c.:<\/strong> <span style=\"text-decoration: underline;\"> \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\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=\"representacion-grafica-del-coseno-hiperbolico\"><\/span> \u0413\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0413\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0438\u043c\u0435\u0435\u0442 \u0444\u043e\u0440\u043c\u0443 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 (\u0438\u043b\u0438 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b): <\/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\/cosinus-hyperbolique.webp\" alt=\"\u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043a\u043e\u0441\u0438\u043d\u0443\u0441\" class=\"wp-image-376\" width=\"281\" height=\"308\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0421\u043c.:<\/strong> <span style=\"text-decoration: underline;\"> \u0413\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <\/span> .<\/p>\n<p> \u041d\u0430 \u044d\u0442\u043e\u043c \u0433\u0440\u0430\u0444\u0438\u043a\u0435 \u043c\u044b \u044f\u0441\u043d\u043e \u0432\u0438\u0434\u0438\u043c, \u0447\u0442\u043e \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0447\u0435\u0442\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043e\u043d \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u043d \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043e\u0441\u0438 Y.<\/p>\n<p> \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0433\u0440\u0430\u0444\u0438\u043a \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0441\u0438\u043b\u044c\u043d\u043e \u043e\u0442\u043b\u0438\u0447\u0430\u0435\u0442\u0441\u044f \u043e\u0442 \u0433\u0440\u0430\u0444\u0438\u043a\u0430 \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 (\u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438), \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043f\u0435\u0440\u0438\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439. \u0413\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0438 \u0432\u0441\u0435 \u0440\u0430\u0437\u043b\u0438\u0447\u0438\u044f \u0441 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u043c \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u043e\u043c \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;\"> \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430. <\/span> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-del-coseno-hiperbolico\"><\/span> \u0425\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u043e\u0431\u043b\u0430\u0434\u0430\u0435\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> \u041e\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 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \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:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0cd1539b66edeb38040ed80168e1fd9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<ul>\n<li> \u0412\u043c\u0435\u0441\u0442\u043e \u044d\u0442\u043e\u0433\u043e \u0434\u0438\u0430\u043f\u0430\u0437\u043e\u043d (\u0438\u043b\u0438 \u0434\u0438\u0430\u043f\u0430\u0437\u043e\u043d) \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0440\u0430\u0432\u0435\u043d 1 \u0438 \u0432\u0441\u0435 \u0447\u0438\u0441\u043b\u0430 \u0431\u043e\u043b\u044c\u0448\u0435 1:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-60c76341385ea1ebb5f20476cd8226f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Im } f= [1,+\\infty)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"121\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> \u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u2014 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430\u044f \u0438 \u0447\u0435\u0442\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-91f3c4459fc8d8840fd902946c851d1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{cosh}(-x)=\\text{cosh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"152\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u0435\u0442 \u043e\u0441\u044c Y \u0432 \u0442\u043e\u0447\u043a\u0435 x=0.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dd01415f329053c1a450867378fc1582_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(0,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0435 \u0438\u043c\u0435\u0435\u0442 \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u0441 \u043e\u0441\u044c\u044e X.<\/li>\n<\/ul>\n<ul>\n<li> \u0414\u0432\u0430 \u043f\u0440\u0435\u0434\u0435\u043b\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438 (\u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0439 \u0438 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0439) \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0434\u0430\u044e\u0442 \u043f\u043b\u044e\u0441 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u044c.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5a5aadc0c48684e553e9971aefe442d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to+\\infty}\\text{cosh}(x)=+\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"161\" style=\"vertical-align: -13px;\"><\/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-fb2a605c43e81635473abf73554d264f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to-\\infty}\\text{cosh}(x)=+\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"161\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<ul>\n<li> \u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u0443\u043c\u0435\u043d\u044c\u0448\u0430\u0435\u0442\u0441\u044f \u0434\u043e \u0442\u0435\u0445 \u043f\u043e\u0440, \u043f\u043e\u043a\u0430 x = 0, \u0430 \u0437\u0430\u0442\u0435\u043c \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e \u0443\u0432\u0435\u043b\u0438\u0447\u0438\u0432\u0430\u0435\u0442\u0441\u044f, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u043c\u0435\u0435\u0442 \u043c\u0438\u043d\u0438\u043c\u0443\u043c \u043f\u0440\u0438 x = 0.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dd01415f329053c1a450867378fc1582_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(0,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u0432\u044b\u043f\u0443\u043a\u043b\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, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0443 \u043d\u0435\u0435 \u043d\u0435\u0442 \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430.<\/li>\n<\/ul>\n<ul>\n<li> \u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0441\u0438\u043d\u0443\u0441:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9a7a982aae764353843a57652f9a6797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{cosh}(x) \\ \\longrightarrow \\ f'(x)=\\text{senh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"286\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> \u0418\u043d\u0442\u0435\u0433\u0440\u0430\u043b \u043e\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0441\u0438\u043d\u0443\u0441:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a509c96c515bb7115359764e7e4451df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\int \\text{cosh}(x) \\ dx= \\text{senh}(x) + C\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"221\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<ul>\n<li> \u041f\u043e\u043b\u0438\u043d\u043e\u043c \u0422\u0435\u0439\u043b\u043e\u0440\u0430 (\u0438\u043b\u0438 \u0440\u044f\u0434 \u041c\u0430\u043a\u043b\u043e\u0440\u0435\u043d\u0430) \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0432\u044b\u0433\u043b\u044f\u0434\u0438\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cdbe87b63234b62e226371256f8a6c8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{cosh}(x)=1+\\cfrac{x^2}{2!}+\\cfrac{x^4}{4!}+\\cfrac{x^6}{6!}+\\dots=\\sum_{n=0}^\\infty\\cfrac{x^{2n}}{(2n)!}\" title=\"Rendered by QuickLaTeX.com\" height=\"50\" width=\"350\" style=\"vertical-align: -21px;\"><\/p>\n<\/p>\n<ul>\n<li> \u041f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u041b\u0430\u043f\u043b\u0430\u0441\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0432\u044b\u0433\u043b\u044f\u0434\u0438\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c: <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ee373a19450972f0c4cccc3a273770e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mathcal{L}\\bigl[\\text{cosh}(at)\\bigr]=\\cfrac{s}{s^2-a^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"171\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"relaciones-matematicas-del-coseno-hiperbolico\"><\/span> \u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0441\u043e\u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u044f \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0414\u0430\u043b\u0435\u0435 \u043c\u044b \u0443\u0432\u0438\u0434\u0438\u043c, \u043a\u0430\u043a \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0438\u0437 \u0434\u0440\u0443\u0433\u0438\u0445 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0432\u0441\u0435 \u043e\u043d\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0441\u0432\u044f\u0437\u0430\u043d\u044b.<\/p>\n<p> \u0424\u0443\u043d\u0434\u0430\u043c\u0435\u043d\u0442\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0441\u0432\u044f\u0437\u044b\u0432\u0430\u0435\u0442 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u0441 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u043c \u0441\u0438\u043d\u0443\u0441\u043e\u043c:<\/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-4317a445a90e4d139b47db7cf4a49a1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cosh}^2(x)-\\text{senh}^2(x)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"185\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0421\u043c.:<\/strong>  <span style=\"text-decoration: underline;\">\u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0441\u0438\u043d\u0443\u0441.<\/span> <\/p>\n<p> \u0422\u0440\u0438 \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 (\u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0441\u0438\u043d\u0443\u0441, \u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u0438 \u0442\u0430\u043d\u0433\u0435\u043d\u0441) \u043c\u043e\u0433\u0443\u0442 \u0431\u044b\u0442\u044c \u0441\u0432\u044f\u0437\u0430\u043d\u044b \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435\u043c:<\/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-12f286528bc0635705aadbe510b6ceb7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{tanh}(x)=\\cfrac{\\text{senh}(x)}{\\text{cosh}(x)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"144\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u0441\u043b\u043e\u0436\u0435\u043d\u0438\u044f (\u0438\u043b\u0438 \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u044f) \u0434\u0432\u0443\u0445 \u0440\u0430\u0437\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b \u043c\u043e\u0436\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u043f\u043e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u0430\u043c:<\/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-75dff3fbdfd533e08cf581767a0d9b7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cosh}(x+y)=\\text{cosh}(x)\\text{cosh}(y)+\\text{senh}(y)\\text{senh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"363\" style=\"vertical-align: -5px;\"><\/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-3762e67762eecb02ed3d30c39febca9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cosh}(x-y)=\\text{cosh}(x)\\text{cosh}(y)-\\text{senh}(y)\\text{senh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"363\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u0443\u0434\u0432\u043e\u0435\u043d\u043d\u043e\u0433\u043e \u0447\u0438\u0441\u043b\u0430 \u0440\u0430\u0432\u0435\u043d \u0441\u0443\u043c\u043c\u0435 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0438 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0441\u0438\u043d\u0443\u0441\u0430 \u044d\u0442\u043e\u0433\u043e \u0447\u0438\u0441\u043b\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-be5e2f8a1f407e6dce0c53932575d545_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cosh}(2x)=\\text{cosh}^2(x)+\\text{senh}^2(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"242\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0421\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u0438\u043b\u0438 \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u043e\u0432 \u043c\u043e\u0436\u043d\u043e \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0442\u044c, \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u044b:<\/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-02b9d1c798f2639e6503add69dcdb401_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{cosh}(x)+\\text{cosh}(y)=2\\text{cosh}\\left(\\frac{x+y}{2}\\right)\\text{cosh}\\left(\\frac{x-y}{2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"384\" style=\"vertical-align: -17px;\"><\/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-0ec9d613adc720e383f1c3c0c9c8ca5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{cosh}(x)-\\text{cosh}(y)=2\\text{senh}\\left(\\frac{x+y}{2}\\right)\\text{senh}\\left(\\frac{x-y}{2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"386\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043f\u043e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0444\u043e\u0440\u043c\u0443\u043b\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-33c90357c8680ebd2ca5725aad7703f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cosh}^2(x)=\\cfrac{1}{2}\\Bigl(\\text{cosh}(2x)+1\\Bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"215\" style=\"vertical-align: -12px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u0432\u0441\u0435 \u043e \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430: \u043a\u0430\u043a\u043e\u0432\u0430 \u0435\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u0430, \u0435\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, \u0435\u0435 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438, \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0441\u0432\u044f\u0437\u0438 \u0441 \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u043c\u0438 \u0438 \u0442. \u0434. \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043e\u0434\u043d\u043e\u0439 \u0438\u0437 \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u0445 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0438 \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442\u0441\u044f \u0441\u0438\u043c\u0432\u043e\u043b\u043e\u043c cosh(x) . \u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u0440\u0430\u0432\u0435\u043d \u0441\u0443\u043c\u043c\u0435 e x \u043f\u043b\u044e\u0441 e -x , \u0440\u0430\u0437\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u043d\u0430 2. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ru\/%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%b0%d1%8f-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d1%8f-%d0%ba%d0%be%d1%81%d0%b8%d0%bd%d1%83%d1%81%d0%b0\/\"> <span class=\"screen-reader-text\">\u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043a\u043e\u0441\u0438\u043d\u0443\u0441\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":[17],"tags":[],"class_list":["post-366","post","type-post","status-publish","format-standard","hentry","category-17"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 - \u041c\u0430\u0442\u043e\u0440\u043d\u043e\u0441\u0442\u044c<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/ru\/\u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0430\u044f-\u0444\u0443\u043d\u043a\u0446\u0438\u044f-\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430\/\" \/>\n<meta property=\"og:locale\" content=\"ru_RU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 - \u041c\u0430\u0442\u043e\u0440\u043d\u043e\u0441\u0442\u044c\" \/>\n<meta property=\"og:description\" content=\"\u0417\u0434\u0435\u0441\u044c \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u0432\u0441\u0435 \u043e \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430: \u043a\u0430\u043a\u043e\u0432\u0430 \u0435\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u0430, \u0435\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, \u0435\u0435 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438, \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0441\u0432\u044f\u0437\u0438 \u0441 \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u043c\u0438 \u0438 \u0442. \u0434. \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043e\u0434\u043d\u043e\u0439 \u0438\u0437 \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u0445 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0438 \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442\u0441\u044f \u0441\u0438\u043c\u0432\u043e\u043b\u043e\u043c cosh(x) . \u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u0440\u0430\u0432\u0435\u043d \u0441\u0443\u043c\u043c\u0435 e x \u043f\u043b\u044e\u0441 e -x , \u0440\u0430\u0437\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u043d\u0430 2. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, &hellip; \u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/ru\/\u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0430\u044f-\u0444\u0443\u043d\u043a\u0446\u0438\u044f-\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-04T13:41:37+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f667377a7e792f2c9f5f5a7a0ecda4e9_l3.png\" \/>\n<meta name=\"author\" content=\"Mathority \u041a\u043e\u043c\u0430\u043d\u0434\u0430\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u041d\u0430\u043f\u0438\u0441\u0430\u043d\u043e \u0430\u0432\u0442\u043e\u0440\u043e\u043c\" \/>\n\t<meta name=\"twitter:data1\" content=\"Mathority \u041a\u043e\u043c\u0430\u043d\u0434\u0430\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/ru\/%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%b0%d1%8f-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d1%8f-%d0%ba%d0%be%d1%81%d0%b8%d0%bd%d1%83%d1%81%d0%b0\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/ru\/%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%b0%d1%8f-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d1%8f-%d0%ba%d0%be%d1%81%d0%b8%d0%bd%d1%83%d1%81%d0%b0\/\"},\"author\":{\"name\":\"Mathority \u041a\u043e\u043c\u0430\u043d\u0434\u0430\",\"@id\":\"https:\/\/mathority.org\/ru\/#\/schema\/person\/69fe5e2ffd89c6227f6a42153bb3655b\"},\"headline\":\"\u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430\",\"datePublished\":\"2023-07-04T13:41:37+00:00\",\"dateModified\":\"2023-07-04T13:41:37+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/ru\/%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%b0%d1%8f-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d1%8f-%d0%ba%d0%be%d1%81%d0%b8%d0%bd%d1%83%d1%81%d0%b0\/\"},\"wordCount\":391,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/ru\/#organization\"},\"articleSection\":[\"\u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438\"],\"inLanguage\":\"ru-RU\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/ru\/%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%b0%d1%8f-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d1%8f-%d0%ba%d0%be%d1%81%d0%b8%d0%bd%d1%83%d1%81%d0%b0\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/ru\/%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%b0%d1%8f-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d1%8f-%d0%ba%d0%be%d1%81%d0%b8%d0%bd%d1%83%d1%81%d0%b0\/\",\"url\":\"https:\/\/mathority.org\/ru\/%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%b0%d1%8f-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d1%8f-%d0%ba%d0%be%d1%81%d0%b8%d0%bd%d1%83%d1%81%d0%b0\/\",\"name\":\"\u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 - \u041c\u0430\u0442\u043e\u0440\u043d\u043e\u0441\u0442\u044c\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/ru\/#website\"},\"datePublished\":\"2023-07-04T13:41:37+00:00\",\"dateModified\":\"2023-07-04T13:41:37+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathority.org\/ru\/%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%b0%d1%8f-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d1%8f-%d0%ba%d0%be%d1%81%d0%b8%d0%bd%d1%83%d1%81%d0%b0\/#breadcrumb\"},\"inLanguage\":\"ru-RU\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathority.org\/ru\/%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%b0%d1%8f-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d1%8f-%d0%ba%d0%be%d1%81%d0%b8%d0%bd%d1%83%d1%81%d0%b0\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathority.org\/ru\/%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%b0%d1%8f-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d1%8f-%d0%ba%d0%be%d1%81%d0%b8%d0%bd%d1%83%d1%81%d0%b0\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathority.org\/ru\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathority.org\/ru\/#website\",\"url\":\"https:\/\/mathority.org\/ru\/\",\"name\":\"Mathority\",\"description\":\"\u0413\u0434\u0435 \u043b\u044e\u0431\u043e\u043f\u044b\u0442\u0441\u0442\u0432\u043e \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u0435\u0442\u0441\u044f \u0441 \u0440\u0430\u0441\u0447\u0435\u0442\u043e\u043c!\",\"publisher\":{\"@id\":\"https:\/\/mathority.org\/ru\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathority.org\/ru\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"ru-RU\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathority.org\/ru\/#organization\",\"name\":\"Mathority\",\"url\":\"https:\/\/mathority.org\/ru\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"ru-RU\",\"@id\":\"https:\/\/mathority.org\/ru\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/mathority.org\/ru\/wp-content\/uploads\/2023\/10\/mathority-logo.png\",\"contentUrl\":\"https:\/\/mathority.org\/ru\/wp-content\/uploads\/2023\/10\/mathority-logo.png\",\"width\":703,\"height\":151,\"caption\":\"Mathority\"},\"image\":{\"@id\":\"https:\/\/mathority.org\/ru\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathority.org\/ru\/#\/schema\/person\/69fe5e2ffd89c6227f6a42153bb3655b\",\"name\":\"Mathority \u041a\u043e\u043c\u0430\u043d\u0434\u0430\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"ru-RU\",\"@id\":\"https:\/\/mathority.org\/ru\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"caption\":\"Mathority \u041a\u043e\u043c\u0430\u043d\u0434\u0430\"},\"sameAs\":[\"http:\/\/mathority.org\/ru\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 - \u041c\u0430\u0442\u043e\u0440\u043d\u043e\u0441\u0442\u044c","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathority.org\/ru\/\u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0430\u044f-\u0444\u0443\u043d\u043a\u0446\u0438\u044f-\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430\/","og_locale":"ru_RU","og_type":"article","og_title":"\u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 - \u041c\u0430\u0442\u043e\u0440\u043d\u043e\u0441\u0442\u044c","og_description":"\u0417\u0434\u0435\u0441\u044c \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u0432\u0441\u0435 \u043e \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430: \u043a\u0430\u043a\u043e\u0432\u0430 \u0435\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u0430, \u0435\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, \u0435\u0435 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438, \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0441\u0432\u044f\u0437\u0438 \u0441 \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u043c\u0438 \u0438 \u0442. \u0434. \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043e\u0434\u043d\u043e\u0439 \u0438\u0437 \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u0445 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0438 \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442\u0441\u044f \u0441\u0438\u043c\u0432\u043e\u043b\u043e\u043c cosh(x) . \u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u0440\u0430\u0432\u0435\u043d \u0441\u0443\u043c\u043c\u0435 e x \u043f\u043b\u044e\u0441 e -x , \u0440\u0430\u0437\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u043d\u0430 2. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, &hellip; \u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 &raquo;","og_url":"https:\/\/mathority.org\/ru\/\u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0430\u044f-\u0444\u0443\u043d\u043a\u0446\u0438\u044f-\u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430\/","article_published_time":"2023-07-04T13:41:37+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f667377a7e792f2c9f5f5a7a0ecda4e9_l3.png"}],"author":"Mathority \u041a\u043e\u043c\u0430\u043d\u0434\u0430","twitter_card":"summary_large_image","twitter_misc":{"\u041d\u0430\u043f\u0438\u0441\u0430\u043d\u043e \u0430\u0432\u0442\u043e\u0440\u043e\u043c":"Mathority \u041a\u043e\u043c\u0430\u043d\u0434\u0430"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/ru\/%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%b0%d1%8f-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d1%8f-%d0%ba%d0%be%d1%81%d0%b8%d0%bd%d1%83%d1%81%d0%b0\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/ru\/%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%b0%d1%8f-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d1%8f-%d0%ba%d0%be%d1%81%d0%b8%d0%bd%d1%83%d1%81%d0%b0\/"},"author":{"name":"Mathority \u041a\u043e\u043c\u0430\u043d\u0434\u0430","@id":"https:\/\/mathority.org\/ru\/#\/schema\/person\/69fe5e2ffd89c6227f6a42153bb3655b"},"headline":"\u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430","datePublished":"2023-07-04T13:41:37+00:00","dateModified":"2023-07-04T13:41:37+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/ru\/%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%b0%d1%8f-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d1%8f-%d0%ba%d0%be%d1%81%d0%b8%d0%bd%d1%83%d1%81%d0%b0\/"},"wordCount":391,"commentCount":0,"publisher":{"@id":"https:\/\/mathority.org\/ru\/#organization"},"articleSection":["\u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438"],"inLanguage":"ru-RU","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathority.org\/ru\/%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%b0%d1%8f-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d1%8f-%d0%ba%d0%be%d1%81%d0%b8%d0%bd%d1%83%d1%81%d0%b0\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/ru\/%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%b0%d1%8f-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d1%8f-%d0%ba%d0%be%d1%81%d0%b8%d0%bd%d1%83%d1%81%d0%b0\/","url":"https:\/\/mathority.org\/ru\/%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%b0%d1%8f-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d1%8f-%d0%ba%d0%be%d1%81%d0%b8%d0%bd%d1%83%d1%81%d0%b0\/","name":"\u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 - \u041c\u0430\u0442\u043e\u0440\u043d\u043e\u0441\u0442\u044c","isPartOf":{"@id":"https:\/\/mathority.org\/ru\/#website"},"datePublished":"2023-07-04T13:41:37+00:00","dateModified":"2023-07-04T13:41:37+00:00","breadcrumb":{"@id":"https:\/\/mathority.org\/ru\/%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%b0%d1%8f-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d1%8f-%d0%ba%d0%be%d1%81%d0%b8%d0%bd%d1%83%d1%81%d0%b0\/#breadcrumb"},"inLanguage":"ru-RU","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathority.org\/ru\/%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%b0%d1%8f-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d1%8f-%d0%ba%d0%be%d1%81%d0%b8%d0%bd%d1%83%d1%81%d0%b0\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathority.org\/ru\/%d0%b3%d0%b8%d0%bf%d0%b5%d1%80%d0%b1%d0%be%d0%bb%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%b0%d1%8f-%d1%84%d1%83%d0%bd%d0%ba%d1%86%d0%b8%d1%8f-%d0%ba%d0%be%d1%81%d0%b8%d0%bd%d1%83%d1%81%d0%b0\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathority.org\/ru\/"},{"@type":"ListItem","position":2,"name":"\u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430"}]},{"@type":"WebSite","@id":"https:\/\/mathority.org\/ru\/#website","url":"https:\/\/mathority.org\/ru\/","name":"Mathority","description":"\u0413\u0434\u0435 \u043b\u044e\u0431\u043e\u043f\u044b\u0442\u0441\u0442\u0432\u043e \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u0435\u0442\u0441\u044f \u0441 \u0440\u0430\u0441\u0447\u0435\u0442\u043e\u043c!","publisher":{"@id":"https:\/\/mathority.org\/ru\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathority.org\/ru\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"ru-RU"},{"@type":"Organization","@id":"https:\/\/mathority.org\/ru\/#organization","name":"Mathority","url":"https:\/\/mathority.org\/ru\/","logo":{"@type":"ImageObject","inLanguage":"ru-RU","@id":"https:\/\/mathority.org\/ru\/#\/schema\/logo\/image\/","url":"https:\/\/mathority.org\/ru\/wp-content\/uploads\/2023\/10\/mathority-logo.png","contentUrl":"https:\/\/mathority.org\/ru\/wp-content\/uploads\/2023\/10\/mathority-logo.png","width":703,"height":151,"caption":"Mathority"},"image":{"@id":"https:\/\/mathority.org\/ru\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/mathority.org\/ru\/#\/schema\/person\/69fe5e2ffd89c6227f6a42153bb3655b","name":"Mathority \u041a\u043e\u043c\u0430\u043d\u0434\u0430","image":{"@type":"ImageObject","inLanguage":"ru-RU","@id":"https:\/\/mathority.org\/ru\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","caption":"Mathority \u041a\u043e\u043c\u0430\u043d\u0434\u0430"},"sameAs":["http:\/\/mathority.org\/ru"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/mathority.org\/ru\/wp-json\/wp\/v2\/posts\/366","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathority.org\/ru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathority.org\/ru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathority.org\/ru\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathority.org\/ru\/wp-json\/wp\/v2\/comments?post=366"}],"version-history":[{"count":0,"href":"https:\/\/mathority.org\/ru\/wp-json\/wp\/v2\/posts\/366\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathority.org\/ru\/wp-json\/wp\/v2\/media?parent=366"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathority.org\/ru\/wp-json\/wp\/v2\/categories?post=366"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathority.org\/ru\/wp-json\/wp\/v2\/tags?post=366"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}