{"id":547,"date":"2023-07-02T15:49:45","date_gmt":"2023-07-02T12:49:45","guid":{"rendered":"https:\/\/bagrut-ru.com\/?p=547"},"modified":"2025-09-04T17:44:34","modified_gmt":"2025-09-04T14:44:34","slug":"%d0%b1%d0%b0%d0%b3%d1%80%d1%83%d1%82-5-%d0%bb%d0%b5%d1%82%d0%be-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=547","title":{"rendered":"\u0411\u0410\u0413\u0420\u0423\u0422 (5). \u041b\u0415\u0422\u041e 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=\"1004\" height=\"816\" data-id=\"548\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/39.png\" alt=\"\" class=\"wp-image-548\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/39.png 1004w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/39-300x244.png 300w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/39-768x624.png 768w\" sizes=\"auto, (max-width: 1004px) 100vw, 1004px\" \/><\/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=\"716\" height=\"698\" data-id=\"549\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/40.png\" alt=\"\" class=\"wp-image-549\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/40.png 716w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/40-300x292.png 300w\" sizes=\"auto, (max-width: 716px) 100vw, 716px\" \/><\/figure>\n<\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/meyda.education.gov.il\/sheeloney_bagrut\/2023\/1\/RUS\/35571.pdf\" data-type=\"link\" data-id=\"https:\/\/meyda.education.gov.il\/sheeloney_bagrut\/2023\/1\/RUS\/35571.pdf\">\u0438\u0441\u0442\u043e\u0447\u043d\u0438\u043a<\/a><\/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\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">(\u05d0)<\/mark><\/strong> (1) \u0413\u0440\u0430\u0444\u0438\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \\(f'(x)\\) \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d \u043d\u0430 \u0440\u0438\u0441.1. \u041d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435  \\(x&lt;0\\) \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(f(x)\\) \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u0430, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \\(f(x)\\) \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u0435\u0442 \u043f\u0440\u0438 \\(x&lt;0\\).  <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435  \\(0&lt;x&lt;a\\) \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(f(x)\\) \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u0430, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \\(f(x)\\) \u0443\u0431\u044b\u0432\u0430\u0435\u0442 \u043f\u0440\u0438 \\(0&lt;x&lt; a\\). <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>\u041e\u0442\u0432\u0435\u0442:<\/em> \u0444\u0443\u043d\u043a\u0446\u0438\u044f \\(f(x)\\)  \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u0435\u0442 \u043f\u0440\u0438 \\(x&lt;0\\)  \u0438 \u0443\u0431\u044b\u0432\u0430\u0435\u0442 \u043f\u0440\u0438 \\(0&lt;x&lt; a\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(2) \u0412 \u0442\u043e\u0447\u043a\u0435 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0432\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(f(x)\\), \u0442\u043e \u0435\u0441\u0442\u044c \u043f\u0435\u0440\u0432\u0430\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(f'(x)\\), \u0440\u0430\u0432\u043d\u0430 \u043d\u0443\u043b\u044e \u0438 \u043c\u0435\u043d\u044f\u0435\u0442 \u0437\u043d\u0430\u043a. \u041c\u044b \u0432\u0438\u0434\u0438\u043c \u043d\u0430 \u0433\u0440\u0430\u0444\u0438\u043a\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \\(f'(x)\\) \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u043d\u043e\u043c \u043d\u0430 \u0440\u0438\u0441.1, \u0447\u0442\u043e \u043d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435   \\(0&lt;x&lt; a\\) \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \\(f'(x)\\) \u0438\u043c\u0435\u0435\u0442 \u043e\u0434\u043d\u0443 \u0442\u043e\u0447\u043a\u0443 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u0430, \u0442\u043e \u0435\u0441\u0442\u044c \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435  \u0432\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \\({{f}&#8217;}'(x)\\) \u0440\u0430\u0432\u043d\u0430 \u043d\u0443\u043b\u044e \u0438 \u043c\u0435\u043d\u044f\u0435\u0442 \u0437\u043d\u0430\u043a \u0441 \u043f\u043b\u044e\u0441\u0430 \u043d\u0430 \u043c\u0438\u043d\u0443\u0441. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u044d\u0442\u043e \u0442\u043e\u0447\u043a\u0430 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(f(x)\\). \u041f\u0440\u0438\u0447\u0435\u043c \u0441\u043b\u0435\u0432\u0430 \u043e\u0442 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \\(f(x)\\) \u0432\u044b\u043f\u0443\u043a\u043b\u0430 \u0432\u0432\u0435\u0440\u0445  \\((\\cup)\\), \u0430 \u0441\u043f\u0440\u0430\u0432\u0430 \u043e\u0442 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0438 \u0432\u044b\u043f\u0443\u043a\u043b\u0430 \u0432\u043d\u0438\u0437  \\((\\cap)\\). <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>\u041e\u0442\u0432\u0435\u0442:<\/em> 1 \u0442\u043e\u0447\u043a\u0430 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430.<\/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-3 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"358\" height=\"418\" data-id=\"552\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/41.png\" alt=\"\" class=\"wp-image-552\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/41.png 358w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/41-257x300.png 257w\" sizes=\"auto, (max-width: 358px) 100vw, 358px\" \/><figcaption class=\"wp-element-caption\">\u0440\u0438\u0441.1<\/figcaption><\/figure>\n<\/figure>\n<\/div>\n<\/div>\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\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">(\u05d1)<\/mark><\/strong> \u0418\u0442\u0430\u043a: \u0444\u0443\u043d\u043a\u0446\u0438\u044f \\(f(x)\\) \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0430  \u043d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0430\u0445 \\(x&lt;0\\), \\(0&lt;x\\le a\\),  <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u0438\u043c\u0435\u0435\u0442 \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0443\u044e \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0443 \\(y=0\\), <\/li>\n\n\n\n<li>\u0438\u043c\u0435\u0435\u0442 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0443\u044e \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0443  \\(x=0\\),<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u0435\u0442 \u043d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435 \\(x&lt;0\\), <\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u0443\u0431\u044b\u0432\u0430\u0435\u0442 \u043d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435 \\(0&lt;x&lt;a\\), <\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u0438\u043c\u0435\u0435\u0442 \u0442\u043e\u0447\u043a\u0443 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u043d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435 \\(0&lt;x&lt;a\\), \u043f\u0440\u0438\u0447\u0435\u043c \u0441\u043b\u0435\u0432\u0430 \u043e\u0442 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \\(f(x)\\)  \u0432\u043e\u0433\u043d\u0443\u0442\u0430 \u0432\u0432\u0435\u0440\u0445 \\((\\cup)\\), \u0430 \u0441\u043f\u0440\u0430\u0432\u0430 \u043e\u0442 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0438 \u0432\u043e\u0433\u043d\u0443\u0442\u0430 \u0432\u043d\u0438\u0437 \\((\\cap)\\), <\/li>\n\n\n\n<li>\\(f(a)=0\\), <\/li>\n\n\n\n<li>\u0415\u0441\u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \\(f(x)\\) \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u0435\u0442 \u043d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435 \\(x&lt;0\\) \u0438 \u0438\u043c\u0435\u0435\u0442 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0443\u044e \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0443 \\(x=0\\), \u0438 \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0443\u044e \\(y=0\\), \u0442\u043e \\(f(x)&gt;0\\) \u043d\u0430 \u044d\u0442\u043e\u043c \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435.<\/li>\n\n\n\n<li>\u0415\u0441\u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \\(f(x)\\) \u0443\u0431\u044b\u0432\u0430\u0435\u0442 \u043d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435 \\(0&lt;x&lt;a\\),   \u0438\u043c\u0435\u0435\u0442 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0443\u044e \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0443 \\(x=0\\) \u0438 \\(f(a)=0\\), \u0442\u043e \\(f(x)&gt;0\\) \u043d\u0430 \u044d\u0442\u043e\u043c \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0433\u0440\u0430\u0444\u0438\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(f(x)\\) \u0432\u044b\u0433\u043b\u044f\u0434\u0438\u0442 \u043f\u0440\u0438\u043c\u0435\u0440\u043d\u043e \u043a\u0430\u043a \u043d\u0430 \u0440\u0438\u0441. 2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/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=\"694\" height=\"566\" data-id=\"559\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/42.png\" alt=\"\" class=\"wp-image-559\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/42.png 694w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/07\/42-300x245.png 300w\" sizes=\"auto, (max-width: 694px) 100vw, 694px\" \/><figcaption class=\"wp-element-caption\">\u0440\u0438\u0441.2<\/figcaption><\/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\">(\u05d2)<\/mark><\/strong> \u0412\u044b\u0431\u0435\u0440\u0435\u043c, \u043a\u0430\u043a\u043e\u0435 \u0438\u0437 \u043f\u0440\u0438\u0432\u0435\u0434\u0435\u043d\u043d\u044b\u0445 \u043d\u0438\u0436\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0439 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u0438  \\(f(x)\\):<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\frac{\\sqrt{x-a}}{x}\\) <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">(IV)<\/mark> \\(\\frac{\\sqrt{a-x}}{x}\\) <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">(III)<\/mark> \\(\\frac{\\sqrt{x-a}}{x^2}\\) <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">(II)<\/mark> \\(\\frac{\\sqrt{a-x}}{x^2}\\) <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">(I)<\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"> \u0412\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">(IV)<\/mark> \u0438 <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">(II)<\/mark> \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u043c, \u0443 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \\(x\\ge a\\), \\(x\\ne0\\) &#8212; \u044d\u0442\u043e \u043d\u0435 \u043d\u0430\u0448 \u0441\u043b\u0443\u0447\u0430\u0439. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0412\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">(III)<\/mark> \u0438  <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">(I)<\/mark> \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u043c, \u0443 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \\(x\\le a\\), \\(x\\ne0\\). \u041d\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">(III)<\/mark> \u043c\u0435\u043d\u044f\u0435\u0442 \u0437\u043d\u0430\u043a \u0432 \u0442\u043e\u0447\u043a\u0435 \\(x=0\\) \u0438 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u0440\u0438 \\(x&lt;0\\), \u0430 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">(I)<\/mark> \u043f\u0440\u0438\u043d\u0438\u043c\u0430\u0435\u0442 \u0442\u043e\u043b\u044c\u043a\u043e \u043d\u0435\u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f, \u0442\u0430\u043a \u043a\u0430\u043a \u0432 \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u0435 \u0434\u0440\u043e\u0431\u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0439 \u043a\u043e\u0440\u0435\u043d\u044c, \u0430 \u0432 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u0435 \\(x^2\\). \u041d\u0430\u0448\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u0440\u0438\u043d\u0438\u043c\u0430\u0435\u0442 \u0442\u043e\u043b\u044c\u043a\u043e \u043d\u0435\u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0435  \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0444\u0443\u043d\u043a\u0446\u0438\u0438  \\(f(x)\\) \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">(I)<\/mark>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>\u041e\u0442\u0432\u0435\u0442:<\/em>  I<\/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\">(\u05d3)<\/mark><\/strong> \u041d\u0430\u0439\u0434\u0435\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \\(a\\) \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(\\frac{\\sqrt{a-x}}{x^2}\\), \u0435\u0441\u043b\u0438 \u0443\u0433\u043b\u043e\u0432\u043e\u0439 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442 \u043a\u0430\u0441\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0439 \u043a \u0433\u0440\u0430\u0444\u0438\u043a\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(y=\\frac{\\sqrt{a-x}}{x^2}\\), \u043f\u0440\u043e\u0432\u0435\u0434\u0435\u043d\u043d\u043e\u0439 \u0432 \u0442\u043e\u0447\u043a\u0435 \\(x=-2\\) \u0440\u0430\u0432\u0435\u043d \\(\\frac{7}{16}\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0423\u0433\u043b\u043e\u0432\u043e\u0439 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442 \u043a\u0430\u0441\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0439, \u043f\u0440\u043e\u0432\u0435\u0434\u0435\u043d\u043d\u043e\u0439 \u043a \u0433\u0440\u0430\u0444\u0438\u043a\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(y=f(x)\\) \u0432 \u0442\u043e\u0447\u043a\u0435 \\(x_0\\) \u0440\u0430\u0432\u0435\u043d \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0442\u043e\u0447\u043a\u0435 \\(x_0\\). <\/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 \\(\\frac{\\sqrt{a-x}}{x^2}\\):<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\((\\frac{\\sqrt{a-x}}{x^2})&#8217;=\\frac{(\\sqrt{a-x})&#8217;\\cdot x^2-(x^2)&#8217;\\cdot \\sqrt{a-x} }{(x^2)^2}=\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(=\\frac{-\\frac{1}{2\\sqrt{a-x}}\\cdot x^2-2x\\cdot \\sqrt{a-x} }{x^4}=\\) (\u043f\u0440\u0438\u0432\u0435\u0434\u0435\u043c \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044c \u043a \u043e\u0431\u0449\u0435\u043c\u0443 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044e)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(=\\frac{-x^2-4x(a-x) }{2 \\sqrt{a-x}\\cdot x^4}=\\frac{3x^2-4ax}{2 \\sqrt{a-x}\\cdot x^4}=\\) (\u0440\u0430\u0437\u0434\u0435\u043b\u0438\u043c \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044c \u0438 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u043d\u0430 \\(x\\))<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(=\\frac{3x-4a}{2 \\sqrt{a-x}\\cdot x^3}\\) <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u043e\u0434\u0441\u0442\u0430\u0432\u0438\u043c  \\(x=-2\\) \u0438 \u043f\u0440\u0438\u0440\u0430\u0432\u043d\u044f\u0435\u043c \u043a \\(\\frac{7}{16}\\):<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\frac{3\\cdot (-2)-4a}{2 \\sqrt{a-(-2)}\\cdot (-2)^3}=\\frac{7}{16}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\frac{-6-4a}{2 \\sqrt{a+2}\\cdot (-8)}=\\frac{7}{16}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\frac{3+2a}{ \\sqrt{a+2}\\cdot (8)}=\\frac{7}{16}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\frac{3+2a}{ \\sqrt{a+2}}=\\frac{7}{2}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(2(3+2a)=7\\sqrt{a+2}\\)  \u0412\u043e\u0437\u0432\u0435\u0434\u0435\u043c \u043e\u0431\u0435 \u0447\u0430\u0441\u0442\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u0438 \u0443\u043f\u0440\u043e\u0441\u0442\u0438\u043c. \u041f\u043e\u043b\u0443\u0447\u0438\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(16a^2-a-62=0\\), \\(D=3969, \\ \\sqrt{3969}=63\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(a_1=2, \\ a_2=-\\frac{31}{32}\\) <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u0430\u043a \u043a\u0430\u043a \u043f\u043e \u0443\u0441\u043b\u043e\u0432\u0438\u044e \\(a&gt;0, \\ a=2\\) <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041e\u0442\u0432\u0435\u0442: \\(a=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\">(\u05d4)<\/mark><\/strong> \\((f(x))^2=(\\frac{\\sqrt{a-x}}{x^2})^2=\\frac{2-x}{x^4}\\)<\/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\">\u0424\u0443\u043d\u043a\u0446\u0438\u044f \\(f(x)\\) \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0430 \u043f\u0440\u0438 \\(x\\le 2\\), \\(x\\ne 0\\). \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \\((f(x))^2\\) \u0438\u043c\u0435\u0435\u0442 \u0442\u0430\u043a\u0443\u044e \u0436\u0435 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f. \u041a\u0440\u0438\u0432\u043e\u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u0442\u0440\u0430\u043f\u0435\u0446\u0438\u044e, \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u0443\u044e \u0433\u0440\u0430\u0444\u0438\u043a\u043e\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\((f(x))^2\\),  \u043e\u0441\u044c\u044e \\(X\\) \u0438 \u043f\u0440\u044f\u043c\u043e\u0439 \\(x=1\\), \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0442\u043e\u043b\u044c\u043a\u043e \u043d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435 \\(1\\le x \\le 2\\). \u041d\u0430\u0439\u0434\u0435\u043c \u0435\u0435 \u043f\u043b\u043e\u0449\u0430\u0434\u044c. <\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">\\( S= \\int_1^2 \\frac{2-x}{x^4}dx=\\int_1^2(\\frac{2}{x^4}-\\frac{1}{x^3})dx= \\int_1^2(2x^{-4}-x^{-3})dx =\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\((\\frac{2x^{-3}}{-3}-\\frac{x^{-2}}{-2})\\bigg |_1^2=(\\frac{1}{2x^2}-\\frac{2}{3x^3})\\bigg |_1^2=\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(=(\\frac{1}{8}-\\frac{2}{24})-(\\frac{1}{2}-\\frac{2}{3})=\\frac{1}{24}+\\frac{1}{6}=\\frac{5}{24}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>\u041e\u0442\u0432\u0435\u0442:<\/em> \\(\\frac{5}{24}\\)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0438\u0441\u0442\u043e\u0447\u043d\u0438\u043a (\u05d0) (1) \u0413\u0440\u0430\u0444\u0438\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \\(f'(x)\\) \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d \u043d\u0430 \u0440\u0438\u0441.1. \u041d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435 \\(x&lt;0\\) \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(f(x)\\) \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u0430, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \\(f(x)\\) \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u0435\u0442 \u043f\u0440\u0438 \\(x&lt;0\\). \u041d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435 \\(0&lt;x&lt;a\\) \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(f(x)\\) \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u0430, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \\(f(x)\\) \u0443\u0431\u044b\u0432\u0430\u0435\u0442 \u043f\u0440\u0438 \\(0&lt;x&lt; a\\). \u041e\u0442\u0432\u0435\u0442: \u0444\u0443\u043d\u043a\u0446\u0438\u044f \\(f(x)\\) \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u0435\u0442 \u043f\u0440\u0438 \\(x&lt;0\\) \u0438 \u0443\u0431\u044b\u0432\u0430\u0435\u0442 \u043f\u0440\u0438 \\(0&lt;x&lt; a\\) (2) \u0412 \u0442\u043e\u0447\u043a\u0435 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0432\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438<br \/><a class=\"moretag\" href=\"https:\/\/bagrut-ru.com\/?p=547\">+ Read More<\/a><\/p>\n","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-547","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\/547","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=547"}],"version-history":[{"count":52,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts\/547\/revisions"}],"predecessor-version":[{"id":1304,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts\/547\/revisions\/1304"}],"wp:attachment":[{"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=547"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=547"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=547"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}