{"id":1233,"date":"2023-08-19T11:36:37","date_gmt":"2023-08-19T08:36:37","guid":{"rendered":"https:\/\/bagrut-ru.com\/?p=1233"},"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%93","status":"publish","type":"post","link":"https:\/\/bagrut-ru.com\/?p=1233","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\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=\"744\" data-id=\"1234\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/127-1024x744.png\" alt=\"\" class=\"wp-image-1234\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/127-1024x744.png 1024w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/127-300x218.png 300w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/127-768x558.png 768w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/127.png 1288w\" 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=\"717\" data-id=\"1235\" src=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/128-1024x717.png\" alt=\"\" class=\"wp-image-1235\" srcset=\"https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/128-1024x717.png 1024w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/128-300x210.png 300w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/128-768x538.png 768w, https:\/\/bagrut-ru.com\/wp-content\/uploads\/2023\/08\/128.png 1380w\" 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\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">(1)<\/mark><\/strong> \u0418\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u041d\u044c\u044e\u0442\u043e\u043d\u0430 &#8212; \u041b\u0435\u0439\u0431\u043d\u0438\u0446\u0430 \u0437\u0430\u043f\u0438\u0448\u0435\u043c:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(g(t)=\\int _{-2}^t f(x) dx=F(t)-F(-2)\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0417\u0434\u0435\u0441\u044c \\(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)\\), \u0430 \u044d\u0442\u043e \u0437\u043d\u0430\u0447\u0438\u0442, \u0447\u0442\u043e <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">\\(F'(x)=f(x)\\)<\/mark>. \u041e\u0442\u0441\u044e\u0434\u0430 <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(g'(t)=F'(t)-F'(-2)=f(t)\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u043e \u0433\u0440\u0430\u0444\u0438\u043a\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(f(x)\\)  \u043c\u044b \u0432\u0438\u0434\u0438\u043c, \u0447\u0442\u043e \\(f(x)&lt;0\\) \u043d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435 \\(-2&lt;x&lt;0\\), \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \\(g'(x)&lt;0\\) \u043d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435 \\(-2&lt;x&lt;0\\). \u0415\u0441\u043b\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u0443\u0435\u043c\u043e\u0439 \u043d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435 \\(a&lt;x&lt;b\\) \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u0430 \u043d\u0430 \u044d\u0442\u043e\u043c \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435, \u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0443\u0431\u044b\u0432\u0430\u0435\u0442 \u043d\u0430 \u044d\u0442\u043e\u043c \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \\(g(t)\\)  \u0443\u0431\u044b\u0432\u0430\u0435\u0442 \u043d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435 \\(-2&lt;t&lt;0\\). <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>\u041e\u0442\u0432\u0435\u0442:<\/em> \\(-2&lt;t&lt;0\\)<\/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> \u0422\u0430\u043a \u043a\u0430\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u044f \\(f(x)\\) &#8212; \u043d\u0435\u0447\u0435\u0442\u043d\u0430\u044f, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0435\u0435 \u0433\u0440\u0430\u0444\u0438\u043a \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.  \\(f(-x)=-f(x)\\). \u041d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435 \\(-2&lt;t&lt;0\\) \u0444\u0443\u043d\u043a\u0446\u0438\u044f \\(F(t)\\) \u0443\u0431\u044b\u0432\u0430\u0435\u0442, \u0430 \u043d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435 \\(0&lt;t&lt;2\\) \u043e\u043d\u0430 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u044b\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430\u0435\u0442, \u0442\u0430\u043a \u043a\u0430\u043a \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438  \\(F(t)\\) \u0440\u0430\u0432\u043d\u044b \u043f\u043e \u043c\u043e\u0434\u0443\u043b\u044e \u0438 \u043f\u0440\u043e\u0442\u0438\u0432\u043e\u043f\u043e\u043b\u043e\u0436\u043d\u044b \u043f\u043e \u0437\u043d\u0430\u043a\u0443. \u0422\u043e \u0435\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u044f \\(F(t)\\) &#8212; \u0447\u0435\u0442\u043d\u0430\u044f, \u0438 \u0435\u0435 \u0433\u0440\u0430\u0444\u0438\u043a \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 Y. \u041e\u0442\u0441\u044e\u0434\u0430 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c, \u0447\u0442\u043e \\(F(t)\\) \u043f\u0440\u0438\u043d\u0438\u043c\u0430\u0435\u0442 \u043d\u0430\u0438\u0431\u043e\u043b\u044c\u0448\u0435\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435 \\(-2&lt;t&lt;2\\) \u0432 \u0442\u043e\u0447\u043a\u0430\u0445 \\(t=-2\\) \u0438 \\(t=2\\). \u042d\u0442\u043e \u0437\u043d\u0430\u0447\u0438\u0442, \u0447\u0442\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(F(t)\\) \u0432 \u0442\u043e\u0447\u043a\u0430\u0445 \\(t=-2\\) \u0438 \\(t=2\\) \u0431\u043e\u043b\u044c\u0448\u0435, \u0447\u0435\u043c \u0432\u043e \u0432\u0441\u0435\u0445 \u043e\u0441\u0442\u0430\u043b\u044c\u043d\u044b\u0445 \u0442\u043e\u0447\u043a\u0430\u0445 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0430 \\(-2&lt;t&lt;2\\). \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \\(g(t)=F(t)-F(-2)&lt;0\\) \u0434\u043b\u044f \u043b\u044e\u0431\u043e\u0433\u043e \\(-2&lt;t&lt;2\\). \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u0438  \\(-2&lt;t&lt;2\\) \u043d\u0435\u0442 \u0442\u043e\u0447\u0435\u043a, \u0432 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \\(g(t)&gt;0\\). <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>\u041e\u0442\u0432\u0435\u0442: <\/em>\u0442\u0430\u043a\u0438\u0445 \u0442\u043e\u0447\u0435\u043a \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\">(3)<\/mark><\/strong> \u0422\u043e\u0447\u043a\u0438 \u043f\u0435\u0440\u0435\u0433\u0438\u0431\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 &#8212; \u044d\u0442\u043e \u0442\u0430\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438 \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 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0440\u0430\u0432\u043d\u0430 \u043d\u0443\u043b\u044e \u0438 \u043c\u0435\u043d\u044f\u0435\u0442 \u0437\u043d\u0430\u043a. \u0412\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f &#8212; \u044d\u0442\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043e\u0442 \u043f\u0435\u0440\u0432\u043e\u0439 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439. \u041f\u0435\u0440\u0435\u0434 \u043d\u0430\u043c\u0438 \u0433\u0440\u0430\u0444\u0438\u043a \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(g(t)=F(t)-F(-2)\\): \\(g'(t)=F'(t)-F'(-2)=f(t)\\). \u0422\u043e\u0433\u0434\u0430 \\({g&#8217;}'(t)=f'(t)\\).  \u0417\u043d\u0430\u0447\u0438\u0442, \u043f\u043e \u0433\u0440\u0430\u0444\u0438\u043a\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \\(f(x)\\) \u043d\u0430\u043c \u043d\u0430\u0434\u043e \u043d\u0430\u0439\u0442\u0438 \u0435\u0435 \u0442\u043e\u0447\u043a\u0438 \u044d\u043a\u0441\u0442\u0440\u0435\u043c\u0443\u043c\u0430 &#8212; \u044d\u0442\u043e \u0442\u043e\u0447\u043a\u0438, \u0432 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \\(f'(t)\\) \u0440\u0430\u0432\u043d\u0430 \u043d\u0443\u043b\u044e \u0438 \u043c\u0435\u043d\u044f\u0435\u0442 \u0437\u043d\u0430\u043a. \u0422\u0430\u043a\u0438\u0445 \u0442\u043e\u0447\u0435\u043a 2: \u0442\u043e\u0447\u043a\u0430 \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u0430 \u043d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435 \\(-2&lt;t&lt;0\\) \u0438 \u0442\u043e\u0447\u043a\u0430 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u0430 \u043d\u0430 \u043f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0435 \\(0&lt;t&lt;2\\). <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>\u041e\u0442\u0432\u0435\u0442:<\/em> 2 \u0442\u043e\u0447\u043a\u0438.<\/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":[8,9],"tags":[],"class_list":["post-1233","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\/1233","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=1233"}],"version-history":[{"count":9,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts\/1233\/revisions"}],"predecessor-version":[{"id":1323,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts\/1233\/revisions\/1323"}],"wp:attachment":[{"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1233"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1233"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1233"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}