{"id":1220,"date":"2023-08-16T21:44:01","date_gmt":"2023-08-16T18:44:01","guid":{"rendered":"https:\/\/bagrut-ru.com\/?p=1220"},"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%b5-1%d7%92","status":"publish","type":"post","link":"https:\/\/bagrut-ru.com\/?p=1220","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 1\u05d2"},"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=\"251\" data-id=\"1221\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/125-1024x251.png\" alt=\"\" class=\"wp-image-1221\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/125-1024x251.png 1024w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/125-300x74.png 300w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/125-768x188.png 768w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/125.png 1248w\" 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=\"313\" data-id=\"1222\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/126-1024x313.png\" alt=\"\" class=\"wp-image-1222\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/126-1024x313.png 1024w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/126-300x92.png 300w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/126-768x234.png 768w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/126.png 1376w\" 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\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\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">(1)<\/mark> \u041d\u0430\u0439\u0434\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442, \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0445 \u043e\u0441\u044f\u043c \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442 (\u0435\u0441\u043b\u0438 \u0442\u0430\u043a\u043e\u0432\u044b\u0435 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0410\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b, \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u0435 \u043e\u0441\u044f\u043c \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442 &#8212; \u044d\u0442\u043e  \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0412\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u0430\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430 \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434 \\(x=x_0\\). \u0415\u0441\u043b\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u0434\u0440\u043e\u0431\u044c , \u0442\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \\(x_0\\) &#8212; \u0442\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \\(x\\), \u043f\u0440\u0438 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u0434\u0440\u043e\u0431\u0438 \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\u044e. \u0412 \u0441\u043b\u0443\u0447\u0430\u0435 \u0434\u0430\u043d\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(f(x)=\\frac{\\sqrt{4x^2+1}}{x}\\) \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\u044e \u043f\u0440\u0438 \\(x=0\\), \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e,  \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u043e\u0439 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b \\(x=0\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0413\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0430\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430 \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434 \\(y=y_0\\),  \u0433\u0434\u0435 \\(y_0\\) &#8212; \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435, \u043a \u043a\u043e\u0442\u043e\u0440\u043e\u043c\u0443 \u0441\u0442\u0440\u0435\u043c\u0438\u0442\u0441\u044f  \\(y=f(x)\\) \u0435\u0441\u043b\u0438 \\(x\\) \u0441\u0442\u0440\u0435\u043c\u0438\u0442\u0441\u044f \u043a \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438. \u0413\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0430\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442, \u0435\u0441\u043b\u0438 \u0432 \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u0435 \u0434\u0440\u043e\u0431\u0438 \u0441\u0442\u043e\u044f\u0442 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u044b \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438. \u0422\u0430\u043a \u043a\u0430\u043a \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(f(x)=\\frac{\\sqrt{4x^2+1}}{x}\\) \u0440\u0430\u0432\u043d\u0430 1,  \u0438 \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044f \u0440\u0430\u0432\u043d\u0430 1, \u0442\u043e \u0435\u0441\u0442\u044c \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044f \u0440\u0430\u0432\u043d\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044f,  \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0434\u0430\u043d\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f  \u0438\u043c\u0435\u0435\u0442 \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041d\u0430\u0439\u0434\u0435\u043c \u0438\u0445. \u0412 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432\u044b\u043d\u0435\u0441\u0435\u043c \u0438\u0437 \u043f\u043e\u0434 \u043a\u043e\u0440\u043d\u044f \\(x\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\frac{\\sqrt{4x^2+1}}{x}=\\frac{\\sqrt{x^2(4+\\frac{1}{x^2})}}{x}=\\frac{|x|\\sqrt{4+\\frac{1}{x^2}}}{x}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u0440\u0438 \\(x\\rightarrow-\\infty\\)  \\(|x|=-x\\), \\(f(x)=\\frac{(-x)\\sqrt{4+\\frac{1}{x^2}}}{x}=-\\sqrt{4+\\frac{1}{x^2}}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043f\u0440\u0438 \\(x\\rightarrow-\\infty\\)  \\(\\frac{1}{x^2}\\rightarrow0\\) \u0438 \\(f(x)=-(\\sqrt{4+\\frac{1}{x^2}})\\rightarrow-2\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u043e \u0435\u0441\u0442\u044c \u043f\u0440\u0438 \\(x\\rightarrow-\\infty\\) \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0430\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430 \\(y=-2\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u0440\u0438 \\(x\\rightarrow\\infty\\)  \\(|x|=x\\), \\(f(x)=\\frac{x\\sqrt{4+\\frac{1}{x^2}}}{x}=\\sqrt{4+\\frac{1}{x^2}}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043f\u0440\u0438 \\(x\\rightarrow\\infty\\)  \\(\\frac{1}{x^2}\\rightarrow0\\) \u0438 \\(f(x)=(\\sqrt{4+\\frac{1}{x^2}})\\rightarrow2\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u043e \u0435\u0441\u0442\u044c \u043f\u0440\u0438 \\(x\\rightarrow-\\infty\\) \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0430\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430 \\(y=2\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041e\u0442\u0432\u0435\u0442: \u043f\u0440\u0438 \\(x\\rightarrow-\\infty\\) \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0430\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430 \\(y=-2\\), \u043f\u0440\u0438 \\(x\\rightarrow\\infty\\) \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u0430\u044f \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430 \\(y=2\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">(2)<\/mark> \u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u044e \\(g(x)=k\\cdot f(x+3)\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0413\u0440\u0430\u0444\u0438\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(g(x)\\) \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u0442\u0441\u044f \u0438\u0437 \u0433\u0440\u0430\u0444\u0438\u043a\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(f(x)\\) \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0441\u0434\u0432\u0438\u0433\u0430 \u043d\u0430 3 \u0435\u0434\u0438\u043d\u0438\u0446\u044b \u0432\u043b\u0435\u0432\u043e \u0432\u0434\u043e\u043b\u044c \u043e\u0441\u0438 \u0425 \u0438 \u0440\u0430\u0441\u0442\u044f\u0436\u0435\u043d\u0438\u0435\u043c \u0432 \\(k\\) \u0440\u0430\u0437 \u0432\u0434\u043e\u043b\u044c \u043e\u0441\u0438 Y. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0420\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430\u043c\u0438 \u0433\u0440\u0430\u0444\u0438\u043a\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438  \\(f(x)\\) \u0440\u0430\u0432\u043d\u043e 4. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0421\u0434\u0432\u0438\u0433 \u043d\u0430 3 \u0435\u0434\u0438\u043d\u0438\u0446\u044b \u0432\u043b\u0435\u0432\u043e \u0432\u0434\u043e\u043b\u044c \u043e\u0441\u0438 \u0425 \u043d\u0430 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430\u043c\u0438 \u043d\u0430 \u0432\u043b\u0438\u044f\u0435\u0442.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u0440\u0438 \u0440\u0430\u0441\u0442\u044f\u0436\u0435\u043d\u0438\u0438 \u0432 \\(k\\) \u0440\u0430\u0437 \u0432\u0434\u043e\u043b\u044c \u043e\u0441\u0438 Y \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430\u043c\u0438 \u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0441\u044f \u0440\u0430\u0432\u043d\u044b\u043c  \\(4\\cdot k\\). \u041f\u043e \u0443\u0441\u043b\u043e\u0432\u0438\u044e \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u0430\u043c\u0438 \u0433\u0440\u0430\u0444\u0438\u043a\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(g(x)\\) \u0440\u0430\u0432\u043d\u043e 10. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(4\\cdot k=10\\), \\( k=2,5\\). <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>\u041e\u0442\u0432\u0435\u0442<\/em>: \\( k=2,5\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/div>\n\t\t\t<\/div><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0438\u0441\u0442\u043e\u0447\u043d\u0438\u043a<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9],"tags":[],"class_list":["post-1220","post","type-post","status-publish","format-standard","hentry","category-9"],"_links":{"self":[{"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts\/1220","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=1220"}],"version-history":[{"count":10,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts\/1220\/revisions"}],"predecessor-version":[{"id":1322,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts\/1220\/revisions\/1322"}],"wp:attachment":[{"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1220"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1220"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1220"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}