{"id":365,"date":"2023-07-04T13:53:47","date_gmt":"2023-07-04T13:53:47","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%81%d0%b8%d0%bd%d1%83%d1%81%d0%be%d0%b8%d0%b4%d0%b0%d0%bb%d1%8c%d0%bd%d0%b0%d1%8f-%d1%84%d1%83%d0%bd%d0%ba\/"},"modified":"2023-07-04T13:53:47","modified_gmt":"2023-07-04T13:53:47","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%81%d0%b8%d0%bd%d1%83%d1%81%d0%be%d0%b8%d0%b4%d0%b0%d0%bb%d1%8c%d0%bd%d0%b0%d1%8f-%d1%84%d1%83%d0%bd%d0%ba","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%81%d0%b8%d0%bd%d1%83%d1%81%d0%be%d0%b8%d0%b4%d0%b0%d0%bb%d1%8c%d0%bd%d0%b0%d1%8f-%d1%84%d1%83%d0%bd%d0%ba\/","title":{"rendered":"\u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0441\u0438\u043d\u0443\u0441\u043e\u0438\u0434\u0430\u043b\u044c\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f"},"content":{"rendered":"<p>\u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u0432\u0441\u0435 \u043e \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u043c \u0441\u0438\u043d\u0443\u0441\u0435: \u043a\u0430\u043a\u043e\u0432\u0430 \u0435\u0433\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0430, \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435, \u0432\u0441\u0435 \u0435\u0433\u043e \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438, \u0441\u0432\u044f\u0437\u0438 \u0441 \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u043c\u0438\u2026 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-seno-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 \u0441\u0438\u043d\u0443\u0441\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0441\u0438\u043d\u0443\u0441<\/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>sinh(x)<\/strong> \u0438\u043b\u0438 <strong>sinh(x)<\/strong> . \u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0441\u0438\u043d\u0443\u0441 \u0440\u0430\u0432\u0435\u043d ex <sup>\u043c\u0438\u043d\u0443\u0441<\/sup> e <sup>-x<\/sup> , \u0434\u0435\u043b\u0435\u043d\u043d\u044b\u0439 \u043d\u0430 2.<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\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:<\/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-924551c3d4c8b1d68b0c9a7cf2115ca8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{senh}(x)=\\cfrac{e^{x}-e^{-x}}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"150\" 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 \u0441\u0438\u043d\u0443\u0441 \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.<\/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 \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-seno-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 \u0441\u0438\u043d\u0443\u0441\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0418\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u0443, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043c\u044b \u0432\u0438\u0434\u0435\u043b\u0438 \u0432 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u043c \u0440\u0430\u0437\u0434\u0435\u043b\u0435, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0441\u043e\u0441\u0442\u0430\u0432\u0438\u0442\u044c \u0442\u0430\u0431\u043b\u0438\u0446\u0443 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0441\u0438\u043d\u0443\u0441\u0430 \u0438 \u043f\u043e\u0441\u0442\u0440\u043e\u0438\u0442\u044c \u0433\u0440\u0430\u0444\u0438\u043a \u0444\u0443\u043d\u043a\u0446\u0438\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\/sinus-hyperbolique.webp\" alt=\"\u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0441\u0438\u043d\u0443\u0441\" class=\"wp-image-346\" width=\"281\" height=\"349\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u041d\u0430 \u044d\u0442\u043e\u043c \u0433\u0440\u0430\u0444\u0438\u043a\u0435 \u043c\u044b \u0432\u0438\u0434\u0438\u043c, \u0447\u0442\u043e \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0441\u0438\u043d\u0443\u0441 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f <strong>\u043d\u0435\u0447\u0435\u0442\u043d\u043e\u0439<\/strong> \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439, \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e \u043f\u0440\u043e\u0442\u0438\u0432\u043e\u043f\u043e\u043b\u043e\u0436\u043d\u044b\u0435 x \u0438\u043c\u0435\u044e\u0442 \u043f\u0440\u043e\u0442\u0438\u0432\u043e\u043f\u043e\u043b\u043e\u0436\u043d\u044b\u0435 \u043e\u0431\u0440\u0430\u0437\u044b, \u0438\u043b\u0438, \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u0433\u0440\u0430\u0444\u0438\u043a \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0441\u0438\u043d\u0443\u0441\u0430 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u043d \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043d\u0430\u0447\u0430\u043b\u0430 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442 (0, 0).<\/p>\n<p> \u041a\u0430\u043a \u0432\u0438\u0434\u0438\u0442\u0435, \u0433\u0440\u0430\u0444\u0438\u043a \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\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 \u0441\u0438\u043d\u0443\u0441\u0430, \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 \u0441\u0438\u043d\u0443\u0441\u0430 \u0438 \u0432\u0441\u0435 \u043e\u0442\u043b\u0438\u0447\u0438\u044f \u043e\u0442 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0441\u0438\u043d\u0443\u0441\u0430 \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;\"> \u0413\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \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=\"caracteristicas-del-seno-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 \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 \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 \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> \u0414\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 \u0441\u0438\u043d\u0443\u0441\u0430 \u0442\u0430\u043a\u0436\u0435 \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u043c\u0438 \u0447\u0438\u0441\u043b\u0430\u043c\u0438.<\/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-5a954b5c192478c3b7b14428ac8d5cbc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Im } f= \\mathbb{R}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"74\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<ul>\n<li> \u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0441\u0438\u043d\u0443\u0441 \u2014 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430\u044f \u0438 \u043d\u0435\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-5b37f1a110d810d8dbf0b5a52a1175c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{senh}(-x) =- \\text{senh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"167\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> \u041f\u0435\u0440\u0435\u0445\u0432\u0430\u0442\u044b\u0432\u0430\u0435\u0442 \u043e\u0441\u0438 X \u0438 \u043e\u0441\u0438 Y \u0432 \u043e\u0434\u043d\u043e\u0439 \u0438 \u0442\u043e\u0439 \u0436\u0435 \u0442\u043e\u0447\u043a\u0435 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f, \u043d\u0430\u0447\u0430\u043b\u0435 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442:<\/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-9cf2000c782cfe94be6df5f499cd3e24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> \u041f\u0440\u0435\u0434\u0435\u043b \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0441\u0438\u043d\u0443\u0441\u043e\u0438\u0434\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0438 \u0441\u0442\u0440\u0435\u043c\u043b\u0435\u043d\u0438\u0438 x \u043a \u043f\u043b\u044e\u0441\/\u043c\u0438\u043d\u0443\u0441 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438 \u0440\u0430\u0432\u0435\u043d \u043f\u043b\u044e\u0441\/\u043c\u0438\u043d\u0443\u0441 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438:<\/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-14c1cd1cfcf12880c94a1a992fca6636_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to+\\infty}\\text{senh}(x)=+\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"162\" 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-d3bad505c476b08f8494c9d4a558ca46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to-\\infty}\\text{senh}(x)=-\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"162\" 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 \u0441\u0438\u043d\u0443\u0441 \u0441\u0442\u0440\u043e\u0433\u043e \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u0435\u0442 \u0432\u043e \u0432\u0441\u0435\u0439 \u043e\u0431\u043b\u0430\u0441\u0442\u0438, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043d\u0435 \u0438\u043c\u0435\u0435\u0442 \u043d\u0438 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u043e\u0432, \u043d\u0438 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u043e\u0432.<\/li>\n<\/ul>\n<ul>\n<li> \u041e\u0434\u043d\u0430\u043a\u043e \u043e\u043d\u0430 \u043c\u0435\u043d\u044f\u0435\u0442 \u0441\u0432\u043e\u044e \u043a\u0440\u0438\u0432\u0438\u0437\u043d\u0443 \u0432 \u0442\u043e\u0447\u043a\u0435 x = 0, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u044d\u0442\u043e \u0442\u043e\u0447\u043a\u0430 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0414\u043b\u044f \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u043c\u0435\u043d\u044c\u0448\u0435 x=0 \u044d\u0442\u043e \u0432\u043e\u0433\u043d\u0443\u0442\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u0430 \u0434\u043b\u044f \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0431\u043e\u043b\u044c\u0448\u0435 x=0 \u044d\u0442\u043e \u0432\u044b\u043f\u0443\u043a\u043b\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f.<\/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 \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 \u043a\u043e\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-c47c54bd2abef41b1660f7779cd51cc1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\text{senh}(x) \\ \\longrightarrow \\ f'(x)=\\text{cosh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"286\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> \u0422\u043e\u0447\u043d\u043e \u0442\u0430\u043a \u0436\u0435 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b \u043e\u0442 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\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 \u043a\u043e\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-fb5ef4d6ad0649cda51f73b558814b45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\int \\text{senh}(x) \\ dx= \\text{cosh}(x) + C\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"221\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<ul>\n<li> \u0420\u044f\u0434 \u0422\u0435\u0439\u043b\u043e\u0440\u0430 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0441\u0438\u043d\u0443\u0441\u043e\u0438\u0434\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u0435\u043d \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u043c\u0443 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044e:<\/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-3db771459579b232c860bb1276f1d665_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{senh}(x)=x+\\cfrac{x^3}{3!}+\\cfrac{x^5}{5!}+\\cfrac{x^7}{7!}+\\dots=\\sum_{n=0}^\\infty\\cfrac{x^{2n+1}}{(2n+1)!}\" title=\"Rendered by QuickLaTeX.com\" height=\"50\" width=\"382\" 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 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0441\u0438\u043d\u0443\u0441\u043e\u0438\u0434\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \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-e3e6b1c1d82a639269c25218155f4019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mathcal{L}\\bigl[\\text{senh}(at)\\bigr]=\\cfrac{a}{s^2-a^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"172\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"relaciones-matematicas-del-seno-hiperbolico\"><\/span> \u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \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 \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 \u0441\u0438\u043d\u0443\u0441 \u0441\u0432\u044f\u0437\u0430\u043d \u0441 \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u043c\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u043c\u0438 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f\u043c\u0438:<\/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 \u0441\u0438\u043d\u0443\u0441 \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:<\/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> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u0438\u043d\u0443\u0441 \u0438 \u043a\u043e\u0441\u0438\u043d\u0443\u0441 \u0441\u0432\u044f\u0437\u0430\u043d\u044b \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435\u043c \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u044b, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434 x <sup>2<\/sup> -y <sup>2<\/sup> =1. \u0412 \u043e\u0442\u043b\u0438\u0447\u0438\u0435 \u043e\u0442 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0441\u0438\u043d\u0443\u0441\u0430 \u0438 \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0441\u0432\u044f\u0437\u0430\u043d\u044b \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435\u043c \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438 (x <sup>2<\/sup> +y <sup>2<\/sup> =1).<\/p>\n<p> \u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u0438\u043d\u0443\u0441\u0430, \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0438 \u0442\u0430\u043d\u0433\u0435\u043d\u0441\u0430 \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 \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 \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\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-d0b2492cbc95b27046485a6d7d9cd08c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{senh}(x+y)=\\text{senh}(x)\\text{cosh}(y)+\\text{senh}(y)\\text{cosh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"364\" 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-9a2205899042608a33bd61b158526026_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{senh}(x-y)=\\text{senh}(x)\\text{cosh}(y)-\\text{senh}(y)\\text{cosh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"364\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0441\u0438\u043d\u0443\u0441 \u0443\u0434\u0432\u043e\u0435\u043d\u043d\u043e\u0433\u043e \u0447\u0438\u0441\u043b\u0430 \u043c\u043e\u0436\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c, \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0432 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0441\u043e\u043e\u0442\u043d\u043e\u0448\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-f0d5c63a53de957eac1f69a4fb209f96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{senh}(2x)=2\\text{senh}(x)\\text{cosh}(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"215\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0421\u0443\u043c\u043c\u0443 \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 \u0441\u0438\u043d\u0443\u0441\u043e\u0432 \u043c\u043e\u0436\u043d\u043e \u043d\u0430\u0439\u0442\u0438 \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-9d3598ef49dbf33b925a73edc773a85d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{senh}(x)+\\text{senh}(y)=2\\text{senh}\\left(\\frac{x+y}{2}\\right)\\text{cosh}\\left(\\frac{x-y}{2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"387\" 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-00ee545f4866d13406bc3d5de7de528a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{senh}(x)-\\text{senh}(y)=2\\text{senh}\\left(\\frac{x-y}{2}\\right)\\text{cosh}\\left(\\frac{x+y}{2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"387\" 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 \u0441\u0438\u043d\u0443\u0441\u0430 \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c, \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0432 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u0443:<\/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-2e3e8284b95e317f876a4f8802ebf5fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{senh}^2(x)=\\cfrac{1}{2}\\Bigl(\\text{cosh}(2x)-1\\Bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"216\" style=\"vertical-align: -12px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u0432\u0441\u0435 \u043e \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u043c \u0441\u0438\u043d\u0443\u0441\u0435: \u043a\u0430\u043a\u043e\u0432\u0430 \u0435\u0433\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0430, \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435, \u0432\u0441\u0435 \u0435\u0433\u043e \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438, \u0441\u0432\u044f\u0437\u0438 \u0441 \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u043c\u0438\u2026 \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0441\u0438\u043d\u0443\u0441\u0430 \u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0441\u0438\u043d\u0443\u0441 \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 sinh(x) \u0438\u043b\u0438 sinh(x) . \u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0441\u0438\u043d\u0443\u0441 \u0440\u0430\u0432\u0435\u043d ex \u043c\u0438\u043d\u0443\u0441 e -x , \u0434\u0435\u043b\u0435\u043d\u043d\u044b\u0439 \u043d\u0430 2. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0441\u0438\u043d\u0443\u0441\u0430 &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%81%d0%b8%d0%bd%d1%83%d1%81%d0%be%d0%b8%d0%b4%d0%b0%d0%bb%d1%8c%d0%bd%d0%b0%d1%8f-%d1%84%d1%83%d0%bd%d0%ba\/\"> <span class=\"screen-reader-text\">\u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0441\u0438\u043d\u0443\u0441\u043e\u0438\u0434\u0430\u043b\u044c\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f<\/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-365","post","type-post","status-publish","format-standard","hentry","category-17"],"yoast_head":"<!-- This site is optimized 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\u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0441\u0438\u043d\u0443\u0441\u0430 \u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0441\u0438\u043d\u0443\u0441 \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 sinh(x) \u0438\u043b\u0438 sinh(x) . \u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0441\u0438\u043d\u0443\u0441 \u0440\u0430\u0432\u0435\u043d ex \u043c\u0438\u043d\u0443\u0441 e -x , \u0434\u0435\u043b\u0435\u043d\u043d\u044b\u0439 \u043d\u0430 2. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0441\u0438\u043d\u0443\u0441\u0430 &hellip; \u0413\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0441\u0438\u043d\u0443\u0441\u043e\u0438\u0434\u0430\u043b\u044c\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \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-\u0441\u0438\u043d\u0443\u0441\u043e\u0438\u0434\u0430\u043b\u044c\u043d\u0430\u044f-\u0444\u0443\u043d\u043a\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-04T13:53:47+00:00\" \/>\n<meta property=\"og:image\" 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