{"id":1383,"date":"2023-09-08T19:18:45","date_gmt":"2023-09-08T16:18:45","guid":{"rendered":"https:\/\/bagrut-ru.com\/?p=1383"},"modified":"2025-09-04T17:43:41","modified_gmt":"2025-09-04T14:43:41","slug":"%d0%b1%d0%b0%d0%b3%d1%80%d1%83%d1%82-5-%d0%b7%d0%b8%d0%bc%d0%b0-2023-%d0%b2%d0%b0%d1%80%d0%b8%d0%b0%d0%bd%d1%82-35571-%d0%b7%d0%b0%d0%b4%d0%b0%d0%bd%d0%b8%d0%b5-7","status":"publish","type":"post","link":"https:\/\/bagrut-ru.com\/?p=1383","title":{"rendered":"\u0411\u0410\u0413\u0420\u0423\u0422 (5). \u0417\u0418\u041c\u0410 2023, \u0412\u0410\u0420\u0418\u0410\u041d\u0422 35571, \u0417\u0410\u0414\u0410\u041d\u0418\u0415 7"},"content":{"rendered":"\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-1 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"484\" data-id=\"1385\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/147-1024x484.png\" alt=\"\" class=\"wp-image-1385\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/147-1024x484.png 1024w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/147-300x142.png 300w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/147-768x363.png 768w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/147.png 1114w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/figure>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-2 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"507\" data-id=\"1387\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/146-1-1024x507.png\" alt=\"\" class=\"wp-image-1387\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/146-1-1024x507.png 1024w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/146-1-300x148.png 300w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/146-1-768x380.png 768w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/146-1-1536x760.png 1536w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/146-1.png 1702w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><div class=\"spoiler-wrap\">\n\t\t\t\t<div class=\"spoiler-head folded\">\u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/div>\n\t\t\t\t<div class=\"spoiler-body\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">(\u05d0)<\/mark><\/strong>  (1) \u041d\u0430\u0439\u0434\u0435\u043c \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(f(x)=\\frac{2\\sin x}{\\cos ^2 x-1}\\), \u0437\u0430\u0434\u0430\u043d\u043d\u043e\u0439 \u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \\(-2\\pi\\le x \\le 2\\pi\\). <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(f(x)=\\frac{2\\sin x}{\\cos ^2 x-1}=\\frac{2\\sin x}{-\\sin^2 x}=-\\frac{2}{\\sin x}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0424\u0443\u043d\u043a\u0446\u0438\u0438 \\(\\sin x\\) \u0438 \\(\\cos x\\) \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u044b \u043f\u0440\u0438 \u0432\u0441\u0435\u0445 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u0445 \\(x\\). \u0414\u0440\u043e\u0431\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0430 \u043f\u0440\u0438 \u0432\u0441\u0435\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u0445 \\(x\\), \u043f\u0440\u0438 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u043d\u0435 \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\u044e. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\sin x\\ne 0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435  \\(-2\\pi\\le x \\le 2\\pi\\) \u043f\u043e\u043b\u0443\u0447\u0438\u043c \\(x\\ne -2\\pi,\\  \\ x\\ne-\\pi, \\ \\ x\\ne0, \\ \\ x\\ne \\pi,\\  \\ x\\ne2\\pi\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041e\u0442\u0432\u0435\u0442: \\(x\\ne -2\\pi,\\  \\ x\\ne-\\pi, \\ \\ x\\ne0, \\ \\ x\\ne \\pi,\\  \\ x\\ne2\\pi\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(2) \u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u043e\u0439 \u043e\u0441\u0438 \u0425 \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434 \\(x=x_0\\), \u0433\u0434\u0435  \\(x_0\\) &#8212; \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \\(x\\), \u043f\u0440\u0438 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\u044e. \u0412 \u043d\u0430\u0448\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0435, \u0443\u0447\u0438\u0442\u044b\u0432\u0430\u044f \u043f. 1, \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c: <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041e\u0442\u0432\u0435\u0442: \\(x= -2\\pi,\\ \\ x=-\\pi, \\ \\ x=0, \\ \\ x= \\pi,\\ \\ x=2\\pi\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(3) \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0447\u0435\u0442\u043d\u043e\u0439, \u0435\u0441\u043b\u0438 \u0434\u043b\u044f \u043b\u044e\u0431\u043e\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \\(x\\) \u0438\u0437 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442\u0441\u044f \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e: <\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(f(-x)=f(x)\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0424\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043d\u0435\u0447\u0435\u0442\u043d\u043e\u0439, \u0435\u0441\u043b\u0438 \u0434\u043b\u044f \u043b\u044e\u0431\u043e\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \\(x\\) \u0438\u0437 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442\u0441\u044f \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e: <\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(f(-x)=-f(x)\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u0440\u043e\u0432\u0435\u0440\u0438\u043c. \\(\\sin(- x)=-\\sin( x)\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(f(-x)=-\\frac{2}{\\sin(-x)}=\\frac{2\\sin( x)}{\\sin x}=-f(x)\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \\(f(x)\\) &#8212; \u043d\u0435\u0447\u0435\u0442\u043d\u0430\u044f.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>\u041e\u0442\u0432\u0435\u0442:<\/em> \u043d\u0435\u0447\u0435\u0442\u043d\u0430\u044f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">(\u05d1)<\/mark><\/strong> <strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">(1)<\/mark><\/strong> \u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u044e \\(f(x)=-\\frac{2}{\\sin x}\\)  \u043d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435 \\(0\\le x \\le 2\\pi\\). \u041d\u0430\u0439\u0434\u0435\u043c \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0442\u043e\u0447\u0435\u043a \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f  \u0441 \u043e\u0441\u044f\u043c\u0438 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0412\u0441\u0435 \u0442\u043e\u0447\u043a\u0438, \u043b\u0435\u0436\u0430\u0449\u0438\u0435 \u043d\u0430 \u043e\u0441\u0438 \u0425 \u0438\u043c\u0435\u044e\u0442 y- \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0443, \u0440\u0430\u0432\u043d\u0443\u044e \u043d\u0443\u043b\u044e. \u041d\u0430\u0439\u0434\u0435\u043c x- \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u044d\u0442\u0438\u0445 \u0442\u043e\u0447\u0435\u043a. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0440\u0435\u0448\u0438\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \\(-\\frac{2}{\\sin x}=0\\) \u043d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435 \\(0\\le x \\le 2\\pi\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0414\u0440\u043e\u0431\u044c \u0440\u0430\u0432\u043d\u0430 \u043d\u0443\u043b\u044e, \u043a\u043e\u0433\u0434\u0430 \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044c \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\u044e, \u0430 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u043d\u0435 \u0440\u0430\u0432\u0435\u043d.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0427\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044c \u0434\u0440\u043e\u0431\u0438 \u043d\u0443\u043b\u044e \u043d\u0435 \u0440\u0430\u0432\u0435\u043d, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0435 \u0438\u043c\u0435\u0435\u0442 \u0442\u043e\u0447\u0435\u043a \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u0441 \u043e\u0441\u044c\u044e \u0425.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0412\u0441\u0435 \u0442\u043e\u0447\u043a\u0438, \u043b\u0435\u0436\u0430\u0449\u0438\u0435 \u043d\u0430 \u043e\u0441\u0438 Y \u0438\u043c\u0435\u044e\u0442 x- \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0443, \u0440\u0430\u0432\u043d\u0443\u044e \u043d\u0443\u043b\u044e. \u0415\u0441\u043b\u0438 \\(x=0\\), \\(\\sin x=0\\).  \u042d\u0442\u043e \u043d\u0435\u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0442\u043e\u0447\u0435\u043a \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u0441 \u043e\u0441\u044c\u044e Y \u043d\u0435\u0442. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041e\u0442\u0432\u0435\u0442:  \u0442\u043e\u0447\u0435\u043a \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u0441 \u043e\u0441\u044c\u044e X \u0438 \u0441 \u043e\u0441\u044c\u044e Y \u043d\u0435\u0442.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">(2)<\/mark><\/strong> \u041d\u0430\u0439\u0434\u0435\u043c \u0442\u043e\u0447\u043a\u0438 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(f(x)=-\\frac{2}{\\sin x}\\)  \u043d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435 \\(0\\le x \\le 2\\pi\\). <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041d\u0430\u0439\u0434\u0435\u043c \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0434\u0440\u043e\u0431\u0438 \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435: <\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">\\((\\frac{U}{V})&#8217;=\\frac{U&#8217;V-V&#8217;U}{V^2}\\)<\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(U=2,\\ U&#8217;=0\\),  \\(V= \\sin x,\\ V&#8217;=\\cos x\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u043e\u0433\u0434\u0430 \\(f'(x)=-\\frac{0\\cdot(\\sin x)-(2)\\cos x )}{(\\sin x)^2}=\\frac{2\\cos x}{(\\sin x)^2}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041d\u0430\u0439\u0434\u0435\u043c \u043d\u0443\u043b\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439. \u0414\u0440\u043e\u0431\u044c \u0440\u0430\u0432\u043d\u0430 \u043d\u0443\u043b\u044e, \u043a\u043e\u0433\u0434\u0430 \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044c \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\u044e, \u0430 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u043d\u0435 \u0440\u0430\u0432\u0435\u043d. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\( \\Bigg \\{ \\begin {matrix} {2\\cos x=0}\\\\{(\\sin x)^2\\ne 0}\\end {matrix}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435 \\(0\\le x \\le 2\\pi\\) \u043f\u043e\u043b\u0443\u0447\u0438\u043c \\(x=\\frac{\\pi}{2},\\ x=\\frac{3\\pi}{2}\\) &#8212; \u044d\u0442\u043e \u0442\u043e\u0447\u043a\u0438, \u0432 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0440\u0430\u0432\u043d\u0430 \u043d\u0443\u043b\u044e. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0418\u0441\u0441\u043b\u0435\u0434\u0443\u0435\u043c \u0437\u043d\u0430\u043a\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \\(f'(x)=\\frac{2\\cos x}{(\\sin x)^2}\\) \u0438 \u043d\u0430\u0439\u0434\u0435\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438  \\(f(x)=-\\frac{2}{\\sin x}\\) \u0432 \u0442\u043e\u0447\u043a\u0430\u0445 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u0430.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(f'(\\frac{\\pi}{4})=\\frac{2\\cos (\\frac{\\pi}{4})}{(\\sin (\\frac{\\pi}{4}))^2}&gt;0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(f'(\\frac{3\\pi}{4})=\\frac{2\\cos (\\frac{3\\pi}{4})}{(\\sin (\\frac{3\\pi}{4}))^2}&lt;0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(f'(\\frac{5\\pi}{4})=\\frac{2\\cos (\\frac{5\\pi}{4})}{(\\sin (\\frac{5\\pi}{4}))^2}&lt;0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(f'(\\frac{7\\pi}{4})=\\frac{2\\cos (\\frac{7\\pi}{4})}{(\\sin (\\frac{7\\pi}{4}))^2}>0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(f(\\frac{\\pi}{2})=-\\frac{2}{\\sin (\\frac{\\pi}{2})}=-\\frac{2}{1}=-2\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(f(\\frac{3\\pi}{2})=-\\frac{2}{\\sin (\\frac{3\\pi}{2})}==-\\frac{2}{-1}=2\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041d\u0430\u0440\u0438\u0441\u0443\u0435\u043c \u0442\u0430\u0431\u043b\u0438\u0446\u0443:<\/p>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-3 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"245\" data-id=\"1438\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/09\/149-1024x245.png\" alt=\"\" class=\"wp-image-1438\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/09\/149-1024x245.png 1024w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/09\/149-300x72.png 300w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/09\/149-768x184.png 768w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/09\/149-1536x367.png 1536w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/09\/149.png 1598w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u041e\u0442\u0432\u0435\u0442: (1) \u0442\u043e\u0447\u043a\u0430 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u0430 \\((\\frac{\\pi}{2},-2)\\), \u0442\u043e\u0447\u043a\u0430 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u0430 \\((\\frac{3\\pi}{2},2)\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">(\u05d2)<\/mark><\/strong> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \\(f(x)=-\\frac{2}{\\sin x}\\) &#8212; \u043d\u0435\u0447\u0435\u0442\u043d\u0430\u044f, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0433\u0440\u0430\u0444\u0438\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \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. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u043e\u0447\u043a\u0438, \u0432 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u0434\u0440\u043e\u0431\u0438 \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\u044e, \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u043c\u0438 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430\u043c\u0438. \u0422\u043e \u0435\u0441\u0442\u044c \u043f\u0440\u044f\u043c\u044b\u0435 \\(x=0,\\ x=\\pi,\\ x=2\\pi\\) \u0438, \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u044b\u0435 \u0438\u043c \\(\\ x=-\\pi,\\ x=-2\\pi\\) \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u044b\u043c\u0438 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430\u043c\u0438. <\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u0423\u0447\u0438\u0442\u044b\u0432\u0430\u044f \u0434\u0430\u043d\u043d\u044b\u0435 \u0442\u0430\u0431\u043b\u0438\u0446\u044b,  \u0438\u0437\u043e\u0431\u0440\u0430\u0437\u0438\u043c \u0433\u0440\u0430\u0444\u0438\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(f(x)=-\\frac{2}{\\sin x}\\) \u043d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435 \\(0\\le x \\le 2\\pi\\) \u0438 \u043e\u0442\u043e\u0431\u0440\u0430\u0437\u0438\u0432 \u0435\u0433\u043e \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u043e \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, \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u0433\u0440\u0430\u0444\u0438\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(f(x)=-\\frac{2}{\\sin x}\\) \u043d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435 \\(-2\\pi\\le x \\le 2\\pi\\): <\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-4 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"815\" data-id=\"1443\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/09\/150-1024x815.png\" alt=\"\" class=\"wp-image-1443\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/09\/150-1024x815.png 1024w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/09\/150-300x239.png 300w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/09\/150-768x611.png 768w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/09\/150.png 1164w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/figure>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">(\u05d3)<\/mark><\/strong> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u043c\u0435\u0435\u0442 \u043f\u0435\u0440\u0435\u0433\u0438\u0431 \u0432 \u0442\u0435\u0445 \u0442\u043e\u0447\u043a\u0430\u0445, \u0432 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0432\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0440\u0430\u0432\u043d\u0430 \u043d\u0443\u043b\u044e \u0438 \u043c\u0435\u043d\u044f\u0435\u0442 \u0437\u043d\u0430\u043a. \u041d\u0430\u0439\u0434\u0435\u043c \u0432\u0442\u043e\u0440\u0443\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u0438  \\(f(x)=-\\frac{2}{\\sin x}\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\({f&#8217;}'(x)=(f'(x))&#8217;=(\\frac{2\\cos x}{(\\sin x)^2})&#8217;=\\frac{(2\\cos x)&#8217;\\cdot (\\sin x)^2-((\\sin x)^2)&#8217;\\cdot(2\\cos x)}{(\\sin x)^4}=\\frac{-2\\sin x\\cdot (\\sin x)^2-2\\sin x\\cdot\\cos x\\cdot2\\cos x}{(\\sin x)^4}=\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(=\\frac{-2\\sin ^3 x-4\\sin x\\cdot \\cos ^2 x}{(\\sin x)^4}=\\frac{-2\\sin x(\\sin ^2 x+2\\cos ^2 x)}{(\\sin x)^4}=\\frac{-2(\\sin ^2 x+2\\cos ^2 x)}{(\\sin x)^3}\\). <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u0440\u0438\u0440\u0430\u0432\u043d\u044f\u0435\u043c \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044c \u0434\u0440\u043e\u0431\u0438 \u043a \u043d\u0443\u043b\u044e:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(-2(\\sin ^2 x+2\\cos ^2 x)=0\\) \u0420\u0430\u0437\u0434\u0435\u043b\u0438\u043c \u043e\u0431\u0435 \u0447\u0430\u0441\u0442\u0438 \u043d\u0430 -2. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\sin ^2 x+\\cos ^2 x+\\cos ^2 x=0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(1+\\cos ^2 x=0\\) &#8212; \u044d\u0442\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043d\u0435 \u0438\u043c\u0435\u0435\u0442 \u0440\u0435\u0448\u0435\u043d\u0438\u0439, \u0442\u0430\u043a \u043a\u0430\u043a \\(1+\\cos ^2 x>0\\) \u043f\u0440\u0438 \u043b\u044e\u0431\u043e\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0438 \\(x\\). \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0432\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043d\u0435 \u0440\u0430\u0432\u043d\u0430 \u043d\u0443\u043b\u044e \u043d\u0438 \u043f\u0440\u0438 \u043a\u0430\u043a\u0438\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u0445 \\(x\\)  \u0438, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \\(f(x)=-\\frac{2}{\\sin x}\\) \u043d\u0435 \u0438\u043c\u0435\u0435\u0442 \u0442\u043e\u0447\u0435\u043a \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">(\u05d4)<\/mark><\/strong> \u041d\u0430\u0439\u0434\u0435\u043c \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0444\u0438\u0433\u0443\u0440\u044b, \u0437\u0430\u043a\u043b\u044e\u0447\u0435\u043d\u043d\u043e\u0439 \u043c\u0435\u0436\u0434\u0443 \u0433\u0440\u0430\u0444\u0438\u043a\u043e\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \\(f'(x)\\) \u0438 \u043e\u0441\u044c\u044e \\(x\\) \u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \\(1.7\\le x\\le 2\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435 \u041d\u044c\u044e\u0442\u043e\u043d\u0430-\u041b\u0435\u0439\u0431\u043d\u0438\u0446\u0430 \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0444\u0438\u0433\u0443\u0440\u044b, \u0437\u0430\u043a\u043b\u044e\u0447\u0435\u043d\u043d\u043e\u0439 \u043c\u0435\u0436\u0434\u0443 \u0433\u0440\u0430\u0444\u0438\u043a\u043e\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(f(x)\\) \u0438 \u043e\u0441\u044c\u044e \\(x\\) \u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \\(a\\le x\\le b\\), \u0440\u0430\u0432\u043d\u0430 \\(S=\\int_a^b f(x) dx=F(b)-F(a)\\), \u0433\u0434\u0435 \\(F(x)\\) &#8212; \u043f\u0435\u0440\u0432\u043e\u043e\u0431\u0440\u0430\u0437\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(f(x)\\), \u0442\u043e \u0435\u0441\u0442\u044c \\(F'(x)=f(x)\\) <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"> \u0412 \u043d\u0430\u0448\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \\(S=\\int_{1.7}^2 f'(x) dx=f(2)-f(1.7)=-\\frac{2}{\\sin 2}-(-\\frac{2}{\\sin 1.7})=\\frac{2}{\\sin 1.7}-\\frac{2}{\\sin 2}\\approx 10.11\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041e\u0442\u0432\u0435\u0442: \\(\\approx 10.11\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/div>\n\t\t\t<\/div><\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8,9],"tags":[],"class_list":["post-1383","post","type-post","status-publish","format-standard","hentry","category-8","category-9"],"_links":{"self":[{"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts\/1383","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1383"}],"version-history":[{"count":67,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts\/1383\/revisions"}],"predecessor-version":[{"id":1529,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts\/1383\/revisions\/1529"}],"wp:attachment":[{"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1383"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1383"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1383"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}