{"id":163,"date":"2023-06-24T15:51:43","date_gmt":"2023-06-24T12:51:43","guid":{"rendered":"https:\/\/bagrut-ru.com\/?p=163"},"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%b5-1%d7%93","status":"publish","type":"post","link":"https:\/\/bagrut-ru.com\/?p=163","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 1\u05d3"},"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=\"547\" data-id=\"164\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/06\/\u0431\u0430\u0433\u0440\u0443\u0442-\u043b\u0435\u0442\u043e-2023-9-1024x547.png\" alt=\"\" class=\"wp-image-164\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/06\/\u0431\u0430\u0433\u0440\u0443\u0442-\u043b\u0435\u0442\u043e-2023-9-1024x547.png 1024w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/06\/\u0431\u0430\u0433\u0440\u0443\u0442-\u043b\u0435\u0442\u043e-2023-9-300x160.png 300w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/06\/\u0431\u0430\u0433\u0440\u0443\u0442-\u043b\u0435\u0442\u043e-2023-9-768x410.png 768w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/06\/\u0431\u0430\u0433\u0440\u0443\u0442-\u043b\u0435\u0442\u043e-2023-9.png 1360w\" 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=\"656\" data-id=\"165\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/06\/\u0431\u0430\u0433\u0440\u0443\u0442-\u043b\u0435\u0442\u043e-2023-10-1024x656.png\" alt=\"\" class=\"wp-image-165\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/06\/\u0431\u0430\u0433\u0440\u0443\u0442-\u043b\u0435\u0442\u043e-2023-10-1024x656.png 1024w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/06\/\u0431\u0430\u0433\u0440\u0443\u0442-\u043b\u0435\u0442\u043e-2023-10-300x192.png 300w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/06\/\u0431\u0430\u0433\u0440\u0443\u0442-\u043b\u0435\u0442\u043e-2023-10-768x492.png 768w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/06\/\u0431\u0430\u0433\u0440\u0443\u0442-\u043b\u0435\u0442\u043e-2023-10.png 1252w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/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<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\">(1) \u041d\u0430\u0440\u0438\u0441\u0443\u0435\u043c \u044d\u0441\u043a\u0438\u0437 \u0433\u0440\u0430\u0444\u0438\u043a\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438\\( \\frac {1}{f(x)} \\), \u043e\u043f\u0438\u0440\u0430\u044f\u0441\u044c \u043d\u0430 \u0433\u0440\u0430\u0444\u0438\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u0438  \\(f(x) \\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0417\u0430\u043c\u0435\u0442\u0438\u043c, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \\(f(x) \\) &#8212; \u0447\u0435\u0442\u043d\u0430\u044f, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \\( \\frac {1}{f(x)} \\) \u0442\u0430\u043a\u0436\u0435 \u0447\u0435\u0442\u043d\u0430\u044f, \u0438 \u0433\u0440\u0430\u0444\u0438\u043a \u044d\u0442\u043e\u0439 \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 \u043e\u0441\u0438  \\(OY \\). <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0415\u0441\u043b\u0438 \u043f\u0440\u0438 \\(x\\rightarrow \\infty \\) \u0444\u0443\u043d\u043a\u0446\u0438\u044f  \\(f(x) \\rightarrow k\\), \u043f\u0440\u0438\u0447\u0435\u043c \\(f(x) &gt; k\\), \u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f  \\(\\frac {1}{f(x)} \\rightarrow \\frac {1}{k} \\), \u043f\u0440\u0438\u0447\u0435\u043c \\( \\frac {1}{f(x)} &lt; \\frac {1}{k} \\). \u041f\u043e \u0443\u0441\u043b\u043e\u0432\u0438\u044e  \\(k&gt;1\\), \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \\(\\frac{1} {k}&lt;1\\). <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u043e \u0435\u0441\u0442\u044c \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0442\u0430\u043a\u0443\u044e \u043a\u0430\u0440\u0442\u0438\u043d\u043a\u0443: \u043a\u0440\u0430\u0441\u043d\u0430\u044f \u043f\u0443\u043d\u043a\u0442\u0438\u0440\u043d\u0430\u044f \u043b\u0438\u043d\u0438\u044f &#8212; \u044d\u0442\u043e \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0430\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430 \u0433\u0440\u0430\u0444\u0438\u043a\u0430  \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\( \\frac {1}{f(x)}  \\), \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \\( y=  \\frac {1}{k} \\). \u0424\u0440\u0430\u0433\u043c\u0435\u043d\u0442\u044b \u043a\u0440\u0430\u0441\u043d\u043e\u0439 \u043a\u0440\u0438\u0432\u043e\u0439 &#8212;  \u044d\u0441\u043a\u0438\u0437 \u0433\u0440\u0430\u0444\u0438\u043a\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\( \\frac {1}{f(x)}  \\) \u043d\u0430 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438. <\/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=\"798\" height=\"646\" data-id=\"176\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/06\/\u0431\u0430\u0433\u0440\u0443\u0442-\u043b\u0435\u0442\u043e-2023-11.png\" alt=\"\" class=\"wp-image-176\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/06\/\u0431\u0430\u0433\u0440\u0443\u0442-\u043b\u0435\u0442\u043e-2023-11.png 798w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/06\/\u0431\u0430\u0433\u0440\u0443\u0442-\u043b\u0435\u0442\u043e-2023-11-300x243.png 300w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/06\/\u0431\u0430\u0433\u0440\u0443\u0442-\u043b\u0435\u0442\u043e-2023-11-768x622.png 768w\" sizes=\"auto, (max-width: 798px) 100vw, 798px\" \/><\/figure>\n<\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u0414\u0430\u043b\u0435\u0435: \u043f\u0440\u0438  \\( x \\rightarrow 1 \\) \u0441\u043f\u0440\u0430\u0432\u0430, \u0444\u0443\u043d\u043a\u0446\u0438\u044f  \\( {f(x)} \\rightarrow \\infty \\), \u0442\u043e\u0433\u0434\u0430 \u043f\u0440\u0438 \\(x \\rightarrow 1 \\) \u0441\u043f\u0440\u0430\u0432\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044f  \\(\\frac{1}{f(x)} \\rightarrow 0\\) &#171;\u0441\u0432\u0435\u0440\u0445\u0443&#187;.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u0440\u0438  \\( x \\rightarrow 1 \\) \u0441\u043b\u0435\u0432\u0430, \u0444\u0443\u043d\u043a\u0446\u0438\u044f  \\( {f(x)} \\rightarrow -\\infty \\), \u0442\u043e\u0433\u0434\u0430 \u043f\u0440\u0438 \\(x \\rightarrow 1 \\) \u0441\u043f\u0440\u0430\u0432\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044f  \\(\\frac{1}{f(x)} \\rightarrow 0\\) &#171;\u0441\u043d\u0438\u0437\u0443&#187;.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u0440\u0438 \\(x=0\\) \\(f(0)=-a,\\ a&gt;0\\), \u0442\u043e\u0433\u0434\u0430 \\(\\frac{1}{f(0)}=-\\frac{1}{a},\\ a&gt;0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0421 \u0443\u0447\u0435\u0442\u043e\u043c \u0447\u0435\u0442\u043d\u043e\u0441\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\( \\frac {1}{f(x)}  \\) \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u044d\u0441\u043a\u0438\u0437 \u0433\u0440\u0430\u0444\u0438\u043a\u0430: <\/p>\n\n\n\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=\"798\" data-id=\"182\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/06\/\u0431\u0430\u0433\u0440\u0443\u0442-\u043b\u0435\u0442\u043e-2023-12-1024x798.png\" alt=\"\" class=\"wp-image-182\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/06\/\u0431\u0430\u0433\u0440\u0443\u0442-\u043b\u0435\u0442\u043e-2023-12-1024x798.png 1024w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/06\/\u0431\u0430\u0433\u0440\u0443\u0442-\u043b\u0435\u0442\u043e-2023-12-300x234.png 300w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/06\/\u0431\u0430\u0433\u0440\u0443\u0442-\u043b\u0435\u0442\u043e-2023-12-768x599.png 768w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/06\/\u0431\u0430\u0433\u0440\u0443\u0442-\u043b\u0435\u0442\u043e-2023-12.png 1052w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u0430\u043a \u043a\u0430\u043a \\(k&gt;1\\) \u043f\u0440\u044f\u043c\u0430\u044f \\(y=k\\) \u0440\u0430\u0441\u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0430 \u0432\u044b\u0448\u0435 \u043f\u0440\u044f\u043c\u043e\u0439 \\(y=\\frac{1}{k}\\). \u0413\u0440\u0430\u0444\u0438\u043a\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \\(f(x) \\) \u0438 \\( \\frac {1}{f(x)}  \\) \u0438\u043c\u0435\u044e\u0442 \u0434\u0432\u0435 \u0442\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u043f\u0440\u0438 \u0442\u0430\u043a\u043e\u043c \u0440\u0430\u0441\u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u0438 \u0433\u0440\u0430\u0444\u0438\u043a\u043e\u0432: <\/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<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-5 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=\"792\" data-id=\"186\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/06\/\u0431\u0430\u0433\u0440\u0443\u0442-\u043b\u0435\u0442\u043e-2023-13-2-1024x792.png\" alt=\"\" class=\"wp-image-186\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/06\/\u0431\u0430\u0433\u0440\u0443\u0442-\u043b\u0435\u0442\u043e-2023-13-2-1024x792.png 1024w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/06\/\u0431\u0430\u0433\u0440\u0443\u0442-\u043b\u0435\u0442\u043e-2023-13-2-300x232.png 300w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/06\/\u0431\u0430\u0433\u0440\u0443\u0442-\u043b\u0435\u0442\u043e-2023-13-2-768x594.png 768w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/06\/\u0431\u0430\u0433\u0440\u0443\u0442-\u043b\u0435\u0442\u043e-2023-13-2.png 1040w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u042d\u0442\u043e \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e \u043f\u0440\u0438 \u0443\u0441\u043b\u043e\u0432\u0438\u0438 \\(-a&gt;-\\frac{1}{a}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0420\u0435\u0448\u0438\u043c \u044d\u0442\u043e \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(a&lt;\\frac{1}{a}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(a-\\frac{1}{a}&lt;0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\frac{a^2-1}{a}&lt;0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\frac{(a-1)(a+1)}{a}&lt;0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0423\u0447\u0438\u0442\u044b\u0432\u0430\u044f, \u0447\u0442\u043e \\(a&gt;0\\), \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c, \u0447\u0442\u043e \\(0&lt;a&lt;1\\)<\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">\u041e\u0442\u0432\u0435\u0442: \\(0&lt;a&lt;1\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(2) \u0418\u0437 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0433\u043e \u0432 \u043f.(1) \u0440\u0430\u0441\u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u0433\u0440\u0430\u0444\u0438\u043a\u043e\u0432 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \\(f(x) \\) \u0438 \\( \\frac {1}{f(x)}  \\) \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c, \u0447\u0442\u043e \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u043c\u0438 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430\u043c\u0438 \u0440\u0430\u0432\u043d\u043e \\(k-\\frac{1}{k}\\). \u041d\u0430\u0439\u0434\u0435\u043c, \u043f\u0440\u0438 \u043a\u0430\u043a\u043e\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0438 \\(k\\) \u043e\u043d\u043e \u0440\u0430\u0432\u043d\u043e \\(1.5\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0420\u0435\u0448\u0438\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435:  \\( k-\\frac{1}{k}=1.5\\) <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u0435\u0440\u0435\u043d\u0435\u0441\u0435\u043c \u0432\u0441\u0435 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u044b\u0435 \u0432\u043b\u0435\u0432\u043e \u0438 \u043f\u0440\u0438\u0432\u0435\u0434\u0435\u043c \u043a \u043e\u0431\u0449\u0435\u043c\u0443 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044e. \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\">\\(\\frac{k^2-1.5k-1}{k}=0\\) <\/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\u0443\u043b\u044e \u043d\u0435 \u0440\u0430\u0432\u0435\u043d. \u041f\u0440\u0438\u0440\u0430\u0432\u043d\u044f\u0435\u043c \u043a \u043d\u0443\u043b\u044e \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044c \u0438  \u043d\u0430\u0439\u0434\u0435\u043c \u043a\u043e\u0440\u043d\u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f: \\(k^2-1.5k-1=0\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u043e\u043b\u0443\u0447\u0438\u043c \\(k_1=2, \\ k_2=-0,5\\). \u0423\u0447\u0438\u0442\u044b\u0432\u0430\u044f, \u0447\u0442\u043e \\(k&gt;1\\), \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u043e\u0442\u0432\u0435\u0442 \\(k=2\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041e\u0442\u0432\u0435\u0442: \\(k=2\\)<\/p>\n\n\n\n<p 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