{"id":29067,"date":"2021-06-26T13:00:18","date_gmt":"2021-06-26T13:00:18","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=29067"},"modified":"2024-09-22T07:41:05","modified_gmt":"2024-09-22T07:41:05","slug":"%d0%be%d0%b1%d0%bb%d0%b0%d1%81%d1%82%d1%8c-%d0%be%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d0%b5%d0%bd%d0%b8%d1%8f-%d0%be%d0%b1%d0%bb%d0%b0%d1%81%d1%82%d1%8c-%d0%b7%d0%bd%d0%b0%d1%87%d0%b5%d0%bd%d0%b8","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/ru\/%d0%be%d0%b1%d0%bb%d0%b0%d1%81%d1%82%d1%8c-%d0%be%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d0%b5%d0%bd%d0%b8%d1%8f-%d0%be%d0%b1%d0%bb%d0%b0%d1%81%d1%82%d1%8c-%d0%b7%d0%bd%d0%b0%d1%87%d0%b5%d0%bd%d0%b8\/","title":{"rendered":"\u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0438 \u0433\u0440\u0430\u0444\u0438\u043a \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439"},"content":{"rendered":"<p><center><\/p>\n<h1>\u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0438 \u0433\u0440\u0430\u0444\u0438\u043a \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439<\/h1>\n<p><em><strong>\u0420\u0435\u0437\u044e\u043c\u0435:<\/strong><br \/>\n\u042d\u0442\u043e\u0442 \u0443\u0440\u043e\u043a \u0432\u0432\u043e\u0434\u0438\u0442 \u043f\u043e\u043d\u044f\u0442\u0438\u044f \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0438 \u0433\u0440\u0430\u0444\u0438\u043a\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u044f \u0438\u0445 \u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435 \u0434\u043b\u044f \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439. \u0420\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u044e\u0442\u0441\u044f \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0438 \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043c\u0435\u0442\u043e\u0434\u044b \u0434\u043b\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u044d\u0442\u0438\u0445 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u043e\u0432.<br \/>\n<\/em><br \/>\n<strong>\u0423\u0447\u0435\u0431\u043d\u044b\u0435 \u0446\u0435\u043b\u0438:<\/strong><br \/>\n\u041a \u043a\u043e\u043d\u0446\u0443 \u044d\u0442\u043e\u0433\u043e \u0443\u0440\u043e\u043a\u0430 \u0443\u0447\u0430\u0449\u0438\u0435\u0441\u044f \u0441\u043c\u043e\u0433\u0443\u0442:<\/p>\n<ol style=\"text-align:left;\">\n<li><strong>\u041f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c<\/strong> \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0438 \u0433\u0440\u0430\u0444\u0438\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/li>\n<li><strong>\u041f\u0440\u0438\u043c\u0435\u043d\u044f\u0442\u044c<\/strong> \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043c\u0435\u0442\u043e\u0434\u044b \u0434\u043b\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0438 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439.<\/li>\n<li><strong>\u0421\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u0442\u044c<\/strong> \u0442\u0430\u0431\u043b\u0438\u0446\u044b \u0437\u043d\u0430\u043a\u043e\u0432 \u0434\u043b\u044f \u0430\u043d\u0430\u043b\u0438\u0437\u0430 \u043f\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0439.<\/li>\n<\/ol>\n<p><\/center><\/p>\n<p><center><br \/>\n<iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/zhb8GKlcdA8\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><br \/>\n<\/center><\/p>\n<h2>\u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0438 \u0433\u0440\u0430\u0444\u0438\u043a\u0430<\/h2>\n<p style=\"text-align: justify;\">\u041d\u0430 \u0434\u0430\u043d\u043d\u044b\u0439 \u043c\u043e\u043c\u0435\u043d\u0442 \u043c\u044b \u0443\u0436\u0435 \u043f\u0440\u043e\u0432\u0435\u043b\u0438 \u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e \u043f\u043e\u0434\u0440\u043e\u0431\u043d\u043e\u0435 \u0438\u0437\u0443\u0447\u0435\u043d\u0438\u0435 \u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0445, \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u044b\u0445 \u0438 \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439. \u041c\u044b \u0442\u0430\u043a\u0436\u0435 \u0438\u0437\u0443\u0447\u0438\u043b\u0438 \u0442\u0430\u043a\u0438\u0435 \u043a\u0440\u0438\u0432\u044b\u0435, \u043a\u0430\u043a \u043f\u0440\u044f\u043c\u044b\u0435, \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b, \u044d\u043b\u043b\u0438\u043f\u0441\u044b \u0438 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u044b, \u0430 \u0442\u0430\u043a\u0436\u0435 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438 \u0441 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430\u043c\u0438 \u0438 \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u043c\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u043c\u0438 \u0432 \u0446\u0435\u043b\u043e\u043c. \u0421 \u044d\u0442\u0438\u043c\u0438 \u0437\u043d\u0430\u043d\u0438\u044f\u043c\u0438 \u0442\u0435\u043f\u0435\u0440\u044c \u0431\u0443\u0434\u0435\u0442 \u0433\u043e\u0440\u0430\u0437\u0434\u043e \u043b\u0435\u0433\u0447\u0435 \u0443\u0433\u043b\u0443\u0431\u0438\u0442\u044c\u0441\u044f \u0432 \u0431\u043e\u043b\u0435\u0435 \u0444\u0443\u043d\u0434\u0430\u043c\u0435\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0430\u0441\u043f\u0435\u043a\u0442\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u0442\u0430\u043a\u0438\u0435 \u043a\u0430\u043a <strong>\u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0438 \u0433\u0440\u0430\u0444\u0438\u043a.<\/strong><\/p>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=zhb8GKlcdA8&amp;t=306s\" target=\"_blank\" rel=\"noopener\"><strong>\u041f\u0443\u0441\u0442\u044c <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u0431\u0443\u0434\u0435\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439,<\/strong><\/a> \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u043c\u0435\u0436\u0434\u0443 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430\u043c\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{matrix}f &amp; : &amp; A &amp; \\longrightarrow &amp; B \\\\ &amp; &amp; x &amp; \\longmapsto &amp; y=f(x)\n\n\\end{matrix}<\/span>\n<p style=\"text-align: justify;\">\u041c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442\u0441\u044f \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430\u043c\u0438 \u00ab\u0432\u0445\u043e\u0434\u043d\u044b\u0445\u00bb \u0438 \u00ab\u0432\u044b\u0445\u043e\u0434\u043d\u044b\u0445\u00bb \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439, \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e. \u041d\u0430 \u043e\u0441\u043d\u043e\u0432\u0435 \u044d\u0442\u0438\u0445 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u044e\u0442\u0441\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430:<\/p>\n<p style=\"text-align: justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">Dom(f) = \\{x\\in A\\;|\\; (\\exists y \\in B)(y=f(x))\\}<\/span>\n<p style=\"text-align: justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">Rec(f) = \\{y\\in B\\;|\\; (\\exists ! x \\in Dom(f))(y=f(x))\\}<\/span>\n<p style=\"text-align: justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">Graf(f) = \\{(x,y)\\in A\\times B\\;|\\; x\\in Dom(f) \\wedge y=f(x) \\}<\/span>\n<h2>\u0410\u043d\u0430\u043b\u0438\u0437 \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432<\/h2>\n<p style=\"text-align: justify;\">\u0425\u043e\u0442\u044f \u043f\u043e\u043d\u044f\u0442\u0438\u044f \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0438 \u0433\u0440\u0430\u0444\u0438\u043a\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u043f\u043e \u0441\u0443\u0442\u0438 \u0442\u0435\u043e\u0440\u0435\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435, \u0438\u0445 \u043f\u043e\u043d\u0438\u043c\u0430\u043d\u0438\u0435 \u043b\u0443\u0447\u0448\u0435 \u0432\u0441\u0435\u0433\u043e \u043f\u0440\u0438\u0445\u043e\u0434\u0438\u0442 \u0447\u0435\u0440\u0435\u0437 \u0430\u043d\u0430\u043b\u0438\u0437 \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432. \u0421\u0435\u0439\u0447\u0430\u0441 \u043c\u044b \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0442\u0440\u0438 \u0441\u043b\u0443\u0447\u0430\u044f \u0434\u043b\u044f \u0430\u043d\u0430\u043b\u0438\u0437\u0430 \u044d\u0442\u0438\u0445 \u043f\u043e\u043d\u044f\u0442\u0438\u0439:<\/p>\n<h3>\u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0438 \u0433\u0440\u0430\u0444\u0438\u043a: <span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\sqrt{1-x^2}<\/span><\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=zhb8GKlcdA8&amp;t=560s\" target=\"_blank\" rel=\"noopener\"><strong>\u041d\u0430\u0447\u043d\u0435\u043c \u044d\u0442\u043e\u0442 \u0430\u043d\u0430\u043b\u0438\u0437<\/strong><\/a> \u0441 \u0437\u0430\u043f\u0438\u0441\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">y=f(x).<\/span> \u0415\u0441\u043b\u0438 \u043c\u044b \u044d\u0442\u043e \u0441\u0434\u0435\u043b\u0430\u0435\u043c, \u0442\u043e \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">y = \\sqrt{1-x^2}<\/span>\n<p style=\"text-align: justify;\">\u0415\u0441\u043b\u0438 \u0432\u043e\u0437\u0432\u0435\u0441\u0442\u0438 \u044d\u0442\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442, \u043c\u044b \u0431\u044b\u0441\u0442\u0440\u043e \u043f\u0440\u0438\u0434\u0435\u043c \u043a \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044e, \u043f\u0440\u0438\u0432\u043e\u0434\u044f\u0449\u0435\u043c\u0443 \u043a \u0443\u0436\u0435 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u043c \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0430\u043c:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n&amp; y^2 = 1-x^2 \\\\\n\n\\equiv &amp; x^2 + y^2 = 1 \\end{array}<\/span>\n<p style=\"text-align: justify;\">\u042d\u0442\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0435\u0434\u0438\u043d\u0438\u0447\u043d\u043e\u0439 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438.<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-DQGthMyBY6g\/YNVVrnVQEfI\/AAAAAAAAFOQ\/6_lf8fRQdDIT9NMqstyLOJ2F7nQM9pc8ACLcBGAsYHQ\/s0\/circulounitario.PNG\" alt=\"\u0415\u0434\u0438\u043d\u0438\u0447\u043d\u0430\u044f \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u044c \u0438 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0438 \u0433\u0440\u0430\u0444\u0438\u043a\" class=\"aligncenter lazyload\" width=\"245\" height=\"249\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-DQGthMyBY6g\/YNVVrnVQEfI\/AAAAAAAAFOQ\/6_lf8fRQdDIT9NMqstyLOJ2F7nQM9pc8ACLcBGAsYHQ\/s0\/circulounitario.PNG\" alt=\"\u0415\u0434\u0438\u043d\u0438\u0447\u043d\u0430\u044f \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u044c \u0438 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0438 \u0433\u0440\u0430\u0444\u0438\u043a\" class=\"aligncenter lazyload\" width=\"245\" height=\"249\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u041e\u0434\u043d\u0430\u043a\u043e \u043d\u0443\u0436\u043d\u043e \u0431\u044b\u0442\u044c \u043e\u0441\u0442\u043e\u0440\u043e\u0436\u043d\u044b\u043c, \u0442\u0430\u043a \u043a\u0430\u043a \u043f\u0440\u0438 \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0438 \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u043c\u044b \u00ab\u0434\u043e\u0431\u0430\u0432\u0438\u043b\u0438 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u0443\u044e \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u044e\u00bb. \u0410\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438 \u0434\u0432\u0430 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0443\u0434\u043e\u0432\u043b\u0435\u0442\u0432\u043e\u0440\u044f\u044e\u0442 \u0443\u0441\u043b\u043e\u0432\u0438\u044e \u00ab\u0431\u044b\u0442\u044c \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u043c \u043a\u043e\u0440\u043d\u0435\u043c\u00bb, \u043e\u0434\u043d\u0430\u043a\u043e \u043d\u0430 \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u043e\u043c \u044d\u0442\u0430\u043f\u0435 \u0430\u043d\u0430\u043b\u0438\u0437\u0430 \u043a\u043e\u0440\u0435\u043d\u044c \u0437\u0430\u0434\u0430\u043d \u043a\u0430\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0438\u043c\u0435\u044e\u0442 \u0442\u043e\u043b\u044c\u043a\u043e \u043e\u0434\u0438\u043d \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442. \u041c\u044b \u0433\u043e\u0432\u043e\u0440\u0438\u043c \u043e \u0433\u043b\u0430\u0432\u043d\u043e\u043c \u043a\u043e\u0440\u043d\u0435. \u041f\u043e \u044d\u0442\u043e\u0439 \u043f\u0440\u0438\u0447\u0438\u043d\u0435 \u0438\u0441\u0445\u043e\u0434\u043d\u0430\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u0438\u0440\u043e\u0432\u043a\u0430 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0441\u044f \u0442\u043e\u043b\u044c\u043a\u043e \u043a \u0432\u0435\u0440\u0445\u043d\u0435\u0439 \u0447\u0430\u0441\u0442\u0438 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438, \u0430 \u043d\u0435 \u043a \u043f\u043e\u043b\u043d\u043e\u0439 \u0444\u0438\u0433\u0443\u0440\u0435.<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-AxSf-9lgnuE\/YNVbSJpd-rI\/AAAAAAAAFOg\/0APXEMWIFpAm8DX9651iD6wcq5bTJwFoQCLcBGAsYHQ\/s0\/circulounitario%2B2.PNG\" alt=\"\u0415\u0434\u0438\u043d\u0438\u0447\u043d\u0430\u044f \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u044c \u0438 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0438 \u0433\u0440\u0430\u0444\u0438\u043a\" class=\" aligncenter lazyload\" width=\"401\" height=\"361\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-AxSf-9lgnuE\/YNVbSJpd-rI\/AAAAAAAAFOg\/0APXEMWIFpAm8DX9651iD6wcq5bTJwFoQCLcBGAsYHQ\/s0\/circulounitario%2B2.PNG\" alt=\"\u0415\u0434\u0438\u043d\u0438\u0447\u043d\u0430\u044f \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u044c \u0438 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0438 \u0433\u0440\u0430\u0444\u0438\u043a\" class=\" aligncenter lazyload\" width=\"401\" height=\"361\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u0418\u0437 \u044d\u0442\u043e\u0433\u043e \u0440\u0438\u0441\u0443\u043d\u043a\u0430 \u044f\u0441\u043d\u043e, \u0447\u0442\u043e:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">Dom(f) = \\{x\\in\\mathbb{R}\\;|\\; |x|\\leq 1\\} = [-1,1]<\/span>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">Rec(f) = \\{y\\in\\mathbb{\u0420}\\;|\\; 0\\leq y\\leq 1\\} = [0,1]<\/span>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">Graf(f) = \\{(x,y)\\in \\mathbb{\u0420}\\times \\mathbb{\u0420}\\;|\\; x\\in [-1,1] \\wedge y=\\sqrt{1-x^2}\\}<\/span>\n<p style=\"text-align: justify;\">\u0425\u043e\u0442\u044f \u044f \u043f\u0440\u043e\u0432\u0435\u043b \u044d\u0442\u043e\u0442 \u0430\u043d\u0430\u043b\u0438\u0437 \u0441 \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0442\u043e\u0447\u043a\u0438 \u0437\u0440\u0435\u043d\u0438\u044f, \u0435\u0433\u043e \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u043f\u043e\u043b\u043d\u0438\u0442\u044c \u0441 \u0431\u043e\u043b\u0435\u0435 \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0442\u043e\u0447\u043a\u0438 \u0437\u0440\u0435\u043d\u0438\u044f, \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u0432 \u0443\u0447\u0430\u0441\u0442\u0432\u0443\u044e\u0449\u0438\u0435 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438.<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\color{red}{\\sqrt{{1-x^2}}}<\/span>\n<p style=\"text-align: justify;\">\u0427\u0430\u0441\u0442\u044c <span class=\"katex-eq\" data-katex-display=\"false\">1-x^2<\/span> \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0430 \u0434\u043b\u044f \u0432\u0441\u0435\u0445 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b.<\/p>\n<p style=\"text-align: justify;\">\u041e\u0434\u043d\u0430\u043a\u043e \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0439 \u043a\u043e\u0440\u0435\u043d\u044c \u043f\u0440\u0438\u043d\u0438\u043c\u0430\u0435\u0442 \u0442\u043e\u043b\u044c\u043a\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f, \u0431\u043e\u043b\u044c\u0448\u0438\u0435 \u0438\u043b\u0438 \u0440\u0430\u0432\u043d\u044b\u0435 \u043d\u0443\u043b\u044e.<\/p>\n<p style=\"text-align: justify;\">\u0418\u0437 \u044d\u0442\u043e\u0433\u043e \u0441\u043b\u0435\u0434\u0443\u0435\u0442:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rlrl}\n\nx\\in Dom(f) &amp; \\leftrightarrow &amp; 0 &amp;\\leq 1-x^2 \\\\\n\n{} &amp; \\leftrightarrow &amp; x^2 &amp;\\leq 1 \\\\\n\n&amp; \\leftrightarrow &amp; |x| &amp;\\leq 1 \\\\\n\n&amp; \\leftrightarrow &amp; -1 &amp;\\leq x \\leq 1 \\\\\n\n\\end{array}\n\n<\/span>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e:\\; Dom(f) = \\{x\\in \\mathbb{\u0420}\\;|x| \\leq 1\\} = [-1,1]\n<\/span>\n<p style=\"text-align: justify;\">\u0410\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043c\u0435\u0442\u043e\u0434\u044b \u0434\u043b\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439, \u043a\u0430\u043a \u043f\u0440\u0430\u0432\u0438\u043b\u043e, \u043d\u0430\u043c\u043d\u043e\u0433\u043e \u0441\u043b\u043e\u0436\u043d\u0435\u0435; \u0431\u043e\u043b\u0435\u0435 \u043f\u0440\u043e\u0441\u0442\u044b\u0435 \u0441\u043b\u0443\u0447\u0430\u0438 \u0440\u0435\u0448\u0430\u044e\u0442\u0441\u044f \u043f\u0443\u0442\u0435\u043c \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043d\u043e \u043f\u0440\u0435\u0436\u0434\u0435 \u0447\u0435\u043c \u043f\u043e\u0434\u0440\u043e\u0431\u043d\u043e \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u0442\u044c \u044d\u0442\u0443 \u0442\u0435\u043c\u0443, \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u043b\u0443\u0447\u0448\u0435 \u0438\u0437\u0443\u0447\u0438\u0442\u044c \u043a\u043e\u043c\u043f\u043e\u0437\u0438\u0446\u0438\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0438 \u0434\u0440\u0443\u0433\u0438\u0435 \u0431\u043e\u043b\u0435\u0435 \u043f\u0440\u043e\u0441\u0442\u044b\u0435 \u0441\u043b\u0443\u0447\u0430\u0438, \u0447\u0442\u043e\u0431\u044b \u0438\u043c\u0435\u0442\u044c \u0442\u0432\u0435\u0440\u0434\u0443\u044e \u043e\u0441\u043d\u043e\u0432\u0443. \u041c\u0435\u0436\u0434\u0443 \u0442\u0435\u043c, \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043c\u0435\u0442\u043e\u0434\u044b, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043c\u044b \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0432 \u0431\u043b\u0438\u0436\u0430\u0439\u0448\u0435\u0435 \u0432\u0440\u0435\u043c\u044f, \u043e\u0445\u0432\u0430\u0442\u044f\u0442 \u0431\u043e\u043b\u044c\u0448\u0438\u043d\u0441\u0442\u0432\u043e \u0441\u043b\u043e\u0436\u043d\u043e\u0441\u0442\u0435\u0439, \u0441\u0432\u044f\u0437\u0430\u043d\u043d\u044b\u0445 \u0441 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435\u043c \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439.<\/p>\n<h3>\u0410\u043d\u0430\u043b\u0438\u0437 \u0434\u043b\u044f: <span class=\"katex-eq\" data-katex-display=\"false\">g(x) =\\displaystyle \\frac{x^2 - 1}{x^2 + 1}<\/span><\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=zhb8GKlcdA8&amp;t=1049s\" target=\"_blank\" rel=\"noopener\"><strong>\u041e\u0434\u0438\u043d \u0438\u0437 \u0441\u043f\u043e\u0441\u043e\u0431\u043e\u0432 \u0431\u044b\u0441\u0442\u0440\u043e<\/strong><\/a> \u043d\u0430\u0439\u0442\u0438 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u2014 \u044d\u0442\u043e \u0437\u0430\u0434\u0430\u0442\u044c \u0432\u043e\u043f\u0440\u043e\u0441 \u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u0445 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span>, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u00ab\u0438\u0441\u043f\u043e\u0440\u0442\u044f\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u044e\u00bb. \u041e\u0447\u0435\u0432\u0438\u0434\u043d\u043e, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u043e\u0440\u0442\u0438\u0442\u0441\u044f \u0442\u043e\u043b\u044c\u043a\u043e \u0442\u043e\u0433\u0434\u0430, \u043a\u043e\u0433\u0434\u0430 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u043e\u0431\u0440\u0430\u0449\u0430\u0435\u0442\u0441\u044f \u0432 \u043d\u043e\u043b\u044c. \u0422\u043e \u0435\u0441\u0442\u044c:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n&amp; x^2 + 1 = 0 \\\\\n\n\\equiv &amp; x^2 = -1 \\\\\n\n\\end{array}<\/span>\n<p style=\"text-align: justify;\">\u0422\u0430\u043a \u043a\u0430\u043a \u043d\u0438 \u043e\u0434\u043d\u043e \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e \u043d\u0435 \u043c\u043e\u0436\u0435\u0442 \u0443\u0434\u043e\u0432\u043b\u0435\u0442\u0432\u043e\u0440\u0438\u0442\u044c \u044d\u0442\u043e\u043c\u0443 \u0443\u0441\u043b\u043e\u0432\u0438\u044e, \u0442\u043e \u044f\u0441\u043d\u043e, \u0447\u0442\u043e<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\color{blue}{Dom(g) = \\mathbb{\u0420}}<\/span>\n<p style=\"text-align: justify;\">\u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0433\u0440\u0430\u0444\u0438\u043a\u0430 \u043e\u0431\u044b\u0447\u043d\u043e \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u0430\u043c\u044b\u043c \u0431\u044b\u0441\u0442\u0440\u044b\u043c \u0441\u043f\u043e\u0441\u043e\u0431\u043e\u043c \u043d\u0430\u0439\u0442\u0438 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438; \u0438 \u0434\u043b\u044f \u044d\u0442\u043e\u0433\u043e <a href=\"https:\/\/toposuranos.com\/algebra-de-polinomios-de-numeros-reais\/\" rel=\"noopener\" target=\"_blank\">\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432<\/a> \u0431\u0443\u0434\u0435\u0442 \u0445\u043e\u0440\u043e\u0448\u0438\u043c \u0438\u043d\u0441\u0442\u0440\u0443\u043c\u0435\u043d\u0442\u043e\u043c.<\/p>\n<p style=\"text-align: justify;\">\u0420\u0430\u0437\u0434\u0435\u043b\u0438\u0432 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d, \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">y= \\displaystyle\\frac{x^2-1}{x^2+1} =<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">1<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">-\\displaystyle\\frac{2}{x^2 + 1}<\/span>\n<p style=\"text-align: justify;\">\u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043c\u044b \u0440\u0430\u0437\u0434\u0435\u043b\u0438\u043b\u0438 \u0438\u0441\u0445\u043e\u0434\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u043d\u0430 \u0434\u0432\u0435 \u0431\u043e\u043b\u0435\u0435 \u043f\u0440\u043e\u0441\u0442\u044b\u0435 \u0447\u0430\u0441\u0442\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u043c \u00ab\u0446\u0435\u043b\u043e\u0439 \u0447\u0430\u0441\u0442\u044c\u044e\u00bb \u0438 \u00ab\u0434\u0440\u043e\u0431\u043d\u043e\u0439 \u0447\u0430\u0441\u0442\u044c\u044e\u00bb. \u041f\u043e\u0441\u0442\u0440\u043e\u0435\u043d\u0438\u0435 \u0433\u0440\u0430\u0444\u0438\u043a\u043e\u0432 \u043a\u0430\u0436\u0434\u043e\u0439 \u0438\u0437 \u044d\u0442\u0438\u0445 \u0447\u0430\u0441\u0442\u0435\u0439 \u043f\u043e \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u043e\u0441\u0442\u0438 \u0433\u043e\u0440\u0430\u0437\u0434\u043e \u043f\u0440\u043e\u0449\u0435, \u0447\u0435\u043c \u043f\u043e\u0441\u0442\u0440\u043e\u0435\u043d\u0438\u0435 \u0433\u0440\u0430\u0444\u0438\u043a\u0430 \u0432\u0441\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u0440\u0430\u0437\u0443.<\/p>\n<h3>\u0410\u043d\u0430\u043b\u0438\u0437 \u0434\u043b\u044f: <span class=\"katex-eq\" data-katex-display=\"false\">h(x) =\\displaystyle \\frac{x - 1}{\\sqrt{x+1}}<\/span><\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=zhb8GKlcdA8&amp;t=1580s\" target=\"_blank\" rel=\"noopener\"><strong>\u0410\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0430\u043d\u0430\u043b\u0438\u0437<\/strong><\/a> \u043f\u043e\u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0441\u0442\u0440\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u044d\u0442\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0414\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e \u0437\u0430\u043c\u0435\u0442\u0438\u0442\u044c, \u0447\u0442\u043e \u043e\u043d\u0430 \u0431\u0443\u0434\u0435\u0442 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0430, \u043a\u043e\u0433\u0434\u0430:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rrl}\n\n&amp; 0 &amp; \\lt x + 1 \\\\\n\n\\equiv &amp; -1 &amp; \\lt x \\\\\n\n\\end{array}\n\n<\/span>\n<p style=\"text-align: justify;\">\u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u044f\u0441\u043d\u043e, \u0447\u0442\u043e <span class=\"katex-eq\" data-katex-display=\"false\">Dom(h)=]-1,+\\infty[.<\/span>\n<p style=\"text-align: justify;\">\u0427\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439, \u043f\u043e\u043b\u0435\u0437\u043d\u043e \u043f\u043e\u0441\u0442\u0440\u043e\u0438\u0442\u044c \u0433\u0440\u0430\u0444\u0438\u043a, \u0438 \u0434\u043b\u044f \u0442\u043e\u0433\u043e, \u0447\u0442\u043e\u0431\u044b \u0441\u0434\u0435\u043b\u0430\u0442\u044c \u044d\u0442\u043e \u043f\u0440\u043e\u0441\u0442\u043e, \u043c\u044b \u0431\u0443\u0434\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c <strong>\u0442\u0430\u0431\u043b\u0438\u0446\u0443 \u0437\u043d\u0430\u043a\u043e\u0432.<\/strong> \u0424\u0443\u043d\u043a\u0446\u0438\u044f <span class=\"katex-eq\" data-katex-display=\"false\">h(x)<\/span> \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0438\u0437 \u0434\u0432\u0443\u0445 \u0447\u0430\u0441\u0442\u0435\u0439:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">h(x)=\\displaystyle\\frac{\\color{green}{x-1}}{\\color{red}{\\sqrt{x+1}}}<\/span>\n<p style=\"text-align: justify;\">\u0412\u0435\u0440\u0445\u043d\u044f\u044f \u0447\u0430\u0441\u0442\u044c \u043e\u0431\u0440\u0430\u0449\u0430\u0435\u0442\u0441\u044f \u0432 \u043d\u043e\u043b\u044c \u043f\u0440\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">x=1<\/span>; \u043d\u0438\u0436\u043d\u044f\u044f \u0447\u0430\u0441\u0442\u044c \u043e\u0431\u0440\u0430\u0449\u0430\u0435\u0442\u0441\u044f \u0432 \u043d\u043e\u043b\u044c \u043f\u0440\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">x=-1<\/span> \u0438 \u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0441\u044f \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u043f\u0440\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">x\\lt-1<\/span>. \u041d\u0430 \u043e\u0441\u043d\u043e\u0432\u0435 \u044d\u0442\u043e\u0439 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u0438 \u0441\u0442\u0440\u043e\u0438\u0442\u0441\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0430\u044f \u0442\u0430\u0431\u043b\u0438\u0446\u0430 \u0437\u043d\u0430\u043a\u043e\u0432:<\/p>\n<table>\n<tbody>\n<tr>\n<th style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/th>\n<th style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">-\\infty<\/span><\/th>\n<th style=\"text-align: center;\"><\/th>\n<th style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">-1<\/span><\/th>\n<th style=\"text-align: center;\"><\/th>\n<th style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">+1<\/span><\/th>\n<th style=\"text-align: center;\"><\/th>\n<th style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">+\\infty<\/span><\/th>\n<\/tr>\n<tr>\n<th style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">x-1<\/span><\/th>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">-\\infty <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> - <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">{} - <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> - <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> 0 <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> + <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">{} +\\infty <\/span><\/td>\n<\/tr>\n<tr>\n<th style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{x+1}<\/span><\/th>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> \u041d\u0435\\,\u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442  <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> \u041d\u0435\\,\u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> 0 <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> + <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">{} + <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> + <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">{} + <\/span><\/td>\n<\/tr>\n<tr>\n<th style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\frac{x-1}{\\sqrt{x+1}}<\/span><\/th>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> \u041d\u0435\\,\u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">{}\u041d\u0435\\,\u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> -\\infty <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">{} - <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> 0 <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> + <\/span><\/td>\n<td style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">{} +\\infty <\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u0418\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u044e, \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u043d\u0443\u044e \u0432 \u044d\u0442\u043e\u0439 \u0442\u0430\u0431\u043b\u0438\u0446\u0435, \u0442\u0435\u043f\u0435\u0440\u044c \u043e\u0447\u0435\u043d\u044c \u043f\u0440\u043e\u0441\u0442\u043e \u043f\u043e\u0441\u0442\u0440\u043e\u0438\u0442\u044c \u0433\u0440\u0430\u0444\u0438\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-mWc6Hza3Wl0\/YNWMYho7pPI\/AAAAAAAAFO4\/0D8zrIeKcc8HY7hlWuvJOWDnYE6Zw--cQCLcBGAsYHQ\/s0\/grafico%2B2.PNG\" alt=\"\u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0438 \u0433\u0440\u0430\u0444\u0438\u043a \u0441 \u0442\u0430\u0431\u043b\u0438\u0446\u0435\u0439 \u0437\u043d\u0430\u043a\u043e\u0432\" class=\" aligncenter lazyload\" width=\"498\" height=\"310\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-mWc6Hza3Wl0\/YNWMYho7pPI\/AAAAAAAAFO4\/0D8zrIeKcc8HY7hlWuvJOWDnYE6Zw--cQCLcBGAsYHQ\/s0\/grafico%2B2.PNG\" alt=\"\u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0438 \u0433\u0440\u0430\u0444\u0438\u043a \u0441 \u0442\u0430\u0431\u043b\u0438\u0446\u0435\u0439 \u0437\u043d\u0430\u043a\u043e\u0432\" class=\" aligncenter lazyload\" width=\"498\" height=\"310\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">\u0421 \u044d\u0442\u0438\u043c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0438 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0441\u044f \u0442\u0440\u0438\u0432\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0437\u0430\u0434\u0430\u0447\u0435\u0439:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">Dom(h)=]-1,+\\infty[<\/span>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">Rec(h)=\\mathbb{\u0420}<\/span>\n<h3>\u041f\u0440\u0435\u0434\u043b\u0430\u0433\u0430\u0435\u043c\u043e\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435<\/h3>\n<p style=\"text-align: justify;\">\u0418\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0438\u043d\u0441\u0442\u0440\u0443\u043c\u0435\u043d\u0442\u044b, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043c\u044b \u0442\u043e\u043b\u044c\u043a\u043e \u0447\u0442\u043e \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u043b\u0438, \u043d\u0430\u0439\u0434\u0438\u0442\u0435 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0438 \u0433\u0440\u0430\u0444\u0438\u043a \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">F(x) = \\displaystyle\\frac{4x^3 + 6x^2 -2x + 1}{x^2-4}<\/span>\n","protected":false},"excerpt":{"rendered":"<p>\u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0438 \u0433\u0440\u0430\u0444\u0438\u043a \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0420\u0435\u0437\u044e\u043c\u0435: \u042d\u0442\u043e\u0442 \u0443\u0440\u043e\u043a \u0432\u0432\u043e\u0434\u0438\u0442 \u043f\u043e\u043d\u044f\u0442\u0438\u044f \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0438 \u0433\u0440\u0430\u0444\u0438\u043a\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u044f \u0438\u0445 \u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435 \u0434\u043b\u044f \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439. \u0420\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u044e\u0442\u0441\u044f \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0438 \u0430\u043d\u0430\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043c\u0435\u0442\u043e\u0434\u044b \u0434\u043b\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u044d\u0442\u0438\u0445 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u043e\u0432. \u0423\u0447\u0435\u0431\u043d\u044b\u0435 \u0446\u0435\u043b\u0438: \u041a \u043a\u043e\u043d\u0446\u0443 \u044d\u0442\u043e\u0433\u043e \u0443\u0440\u043e\u043a\u0430 \u0443\u0447\u0430\u0449\u0438\u0435\u0441\u044f \u0441\u043c\u043e\u0433\u0443\u0442: \u041f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0438 \u0433\u0440\u0430\u0444\u0438\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u041f\u0440\u0438\u043c\u0435\u043d\u044f\u0442\u044c [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":29058,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":8,"footnotes":""},"categories":[589,573],"tags":[],"class_list":["post-29067","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-589","category-573"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0438 \u0433\u0440\u0430\u0444\u0438\u043a \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 - toposuranos.com\/material<\/title>\n<meta name=\"description\" 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\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0438 \u0433\u0440\u0430\u0444\u0438\u043a \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439\" \/>\n<meta property=\"og:description\" content=\"\u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0438 \u0433\u0440\u0430\u0444\u0438\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u2014 \u044d\u0442\u043e \u0444\u0443\u043d\u0434\u0430\u043c\u0435\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u043f\u043e\u043d\u044f\u0442\u0438\u044f \u0432 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435. \u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0434\u043e\u043f\u0443\u0441\u0442\u0438\u043c\u044b\u0435 \u0432\u0445\u043e\u0434\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f, \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u2014 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u0435 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u044b, \u0430 \u0433\u0440\u0430\u0444\u0438\u043a \u0432\u0438\u0437\u0443\u0430\u043b\u0438\u0437\u0438\u0440\u0443\u0435\u0442 \u0432\u0437\u0430\u0438\u043c\u043e\u0441\u0432\u044f\u0437\u044c \u043c\u0435\u0436\u0434\u0443 \u043d\u0438\u043c\u0438.\" \/>\n<meta property=\"og:url\" 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