{"id":376,"date":"2023-07-04T05:10:26","date_gmt":"2023-07-04T05:10:26","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d0%b1%d0%be%d0%ba%d0%be%d0%b2%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\/"},"modified":"2023-07-04T05:10:26","modified_gmt":"2023-07-04T05:10:26","slug":"%d0%b1%d0%be%d0%ba%d0%be%d0%b2%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d0%b1%d0%be%d0%ba%d0%be%d0%b2%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\/","title":{"rendered":"\u0411\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b"},"content":{"rendered":"<p>\u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0431\u043e\u043a\u043e\u0432\u043e\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 (\u0441 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u043c\u0438). \u041c\u044b \u0442\u0430\u043a\u0436\u0435 \u043d\u0430\u0443\u0447\u0438\u043c \u0432\u0430\u0441 \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0442\u044c \u043b\u0435\u0432\u044b\u0439 \u0438 \u043f\u0440\u0430\u0432\u044b\u0439 \u0431\u043e\u043a\u043e\u0432\u043e\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043a\u0430\u043a \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u0438, \u0442\u0430\u043a \u0438 \u0447\u0438\u0441\u043b\u0435\u043d\u043d\u043e. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u0442\u0440\u0435\u043d\u0438\u0440\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u0441 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f\u043c\u0438, \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u043e \u0440\u0435\u0448\u0430\u044e\u0449\u0438\u043c\u0438 \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0438\u044f. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-los-limites-laterales\"><\/span> \u041a\u0430\u043a\u043e\u0432\u044b \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u0411\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0438<\/strong> \u0432 \u0442\u043e\u0447\u043a\u0435 \u0438\u0437\u0443\u0447\u0430\u044e\u0442 \u043f\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432\u043e\u043a\u0440\u0443\u0433 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0438. \u0421\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043b\u0435\u0432\u044b\u0439 \u0431\u043e\u043a\u043e\u0432\u043e\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u0438 \u043f\u0440\u0430\u0432\u044b\u0439 \u0431\u043e\u043a\u043e\u0432\u043e\u0439 \u043f\u0440\u0435\u0434\u0435\u043b, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0430\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u0443\u0435\u0442 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u043b\u0435\u0432\u0430 \u0438 \u0441\u043f\u0440\u0430\u0432\u0430 \u043e\u0442 \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u0435\u043c\u043e\u0439 \u0442\u043e\u0447\u043a\u0438 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"limites-laterales-por-la-izquierda-y-por-la-derecha\"><\/span> \u0411\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0441\u043b\u0435\u0432\u0430 \u0438 \u0441\u043f\u0440\u0430\u0432\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041a\u0430\u043a \u043c\u044b \u0432\u0438\u0434\u0435\u043b\u0438 \u0432 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0438 \u0431\u043e\u043a\u043e\u0432\u044b\u0445 \u0433\u0440\u0430\u043d\u0438\u0446, \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0434\u0432\u0430 \u0442\u0438\u043f\u0430: \u043b\u0435\u0432\u044b\u0435 \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u0433\u0440\u0430\u043d\u0438\u0446\u044b \u0438 \u043f\u0440\u0430\u0432\u044b\u0435 \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u0433\u0440\u0430\u043d\u0438\u0446\u044b.<\/p>\n<p> \u041b\u0435\u0432\u044b\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442\u0441\u044f \u0437\u043d\u0430\u043a\u043e\u043c \u043c\u0438\u043d\u0443\u0441 \u0432 \u0442\u043e\u0447\u043a\u0435 \u0430\u043d\u0430\u043b\u0438\u0437\u0430 \u043f\u0440\u0435\u0434\u0435\u043b\u0430, \u0430 \u043f\u0440\u0430\u0432\u044b\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442\u0441\u044f \u0437\u043d\u0430\u043a\u043e\u043c \u043f\u043b\u044e\u0441. <\/p>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-129\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-center\"> <strong><u style=\"text-decoration-color:#FF9B28;\">\u0411\u043e\u043a\u043e\u0432\u0430\u044f \u0433\u0440\u0430\u043d\u0438\u0446\u0430 \u0441\u043b\u0435\u0432\u0430<\/u><\/strong> <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3224554094b2418a485786bfbe4db5f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to a^{\\color{orange}\\bm{-}\\color{black}}}f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"141\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-center\"> <strong><u style=\"text-decoration-color:#FF9B28;\">\u0411\u043e\u043a\u043e\u0432\u0430\u044f \u0433\u0440\u0430\u043d\u0438\u0446\u0430 \u0441\u043f\u0440\u0430\u0432\u0430<\/u><\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9e2e49ad15a0b5fd2db93797689ea1b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to a^{\\color{orange}\\bm{+}\\color{black}}}f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"141\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p> \u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u0442\u0435 \u043d\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u043f\u0440\u0438\u043c\u0435\u0440, \u0447\u0442\u043e\u0431\u044b \u043b\u0443\u0447\u0448\u0435 \u043f\u043e\u043d\u044f\u0442\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0431\u043e\u043a\u043e\u0432\u044b\u0445 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0438\u0439: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/limites-laterales.webp\" alt=\"\u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b\" class=\"wp-image-823\" width=\"299\" height=\"314\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> \u041a\u0430\u043a \u0432\u0438\u0434\u043d\u043e \u0438\u0437 \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u044d\u0442\u043e\u0439 \u043a\u0443\u0441\u043e\u0447\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0437\u0430\u0432\u0438\u0441\u044f\u0442 \u043e\u0442 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u043d\u0430 \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u043e\u043d\u0438 \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u044e\u0442\u0441\u044f.<\/p>\n<p> \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0435\u0442\u0441\u044f \u043a 3, \u043a\u043e\u0433\u0434\u0430 x \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0435\u0442\u0441\u044f \u043a 2 \u0441\u043b\u0435\u0432\u0430, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u0440\u0438\u043d\u0438\u043c\u0430\u0435\u0442 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0431\u043b\u0438\u0436\u0435 \u043a 3, \u043a\u043e\u0433\u0434\u0430 <em>x<\/em> \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0435\u0442\u0441\u044f \u043a x=2 \u0441\u043b\u0435\u0432\u0430.<\/p>\n<p> \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0431\u043e\u043a\u043e\u0432\u043e\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0438 x=2 \u043f\u043e \u043b\u0438\u043d\u0438\u0438 \u0441\u0442\u043e\u0438\u0442 6. \u041f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e \u0435\u0441\u043b\u0438 \u043c\u044b \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0435\u043c\u0441\u044f \u043a \u0442\u043e\u0447\u043a\u0435 x=2 \u043f\u043e \u0435\u0435 \u043b\u0438\u043d\u0438\u0438, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u0440\u0438\u043d\u0438\u043c\u0430\u0435\u0442 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0432\u0441\u0435 \u0431\u043b\u0438\u0436\u0435 \u0438 \u0431\u043b\u0438\u0436\u0435 \u043a f(x)= 6.<\/p>\n<p> \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0441\u043b\u0435\u0434\u0443\u0435\u0442 \u0437\u043d\u0430\u0442\u044c, \u0447\u0442\u043e \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u043e\u0431\u043b\u0430\u0434\u0430\u044e\u0442 \u0442\u0435\u043c\u0438 \u0436\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430\u043c\u0438, \u0447\u0442\u043e \u0438 \u043e\u0431\u044b\u0447\u043d\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b. \u041f\u043e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0441\u0441\u044b\u043b\u043a\u0435 \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c, \u043a\u0430\u043a\u043e\u0432\u044b \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u0433\u0440\u0430\u043d\u0438\u0446:<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0421\u043c.:<\/strong> <span style=\"text-decoration: underline;\"> \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u0433\u0440\u0430\u043d\u0438\u0446. <\/span><\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"limites-laterales-iguales\"><\/span>\u0440\u0430\u0432\u043d\u044b\u0435 \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041c\u044b \u0442\u043e\u043b\u044c\u043a\u043e \u0447\u0442\u043e \u0432\u0438\u0434\u0435\u043b\u0438 \u043f\u0440\u0438\u043c\u0435\u0440, \u0433\u0434\u0435 \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b, \u043d\u043e&#8230; \u0447\u0442\u043e \u043f\u0440\u043e\u0438\u0437\u043e\u0439\u0434\u0435\u0442, \u0435\u0441\u043b\u0438 \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u044b?<\/p>\n<p> <strong>\u0415\u0441\u043b\u0438 \u043e\u0431\u0430 \u0431\u043e\u043a\u043e\u0432\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0442\u043e\u0447\u043a\u0435 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442 \u0438 \u0440\u0430\u0432\u043d\u044b<\/strong> , \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435, \u0438 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u043e\u043c \u043f\u0440\u0435\u0434\u0435\u043b\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0431\u043e\u043a\u043e\u0432\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432.<\/p>\n<p> \u0414\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u0447\u0442\u043e\u0431\u044b \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u043e\u0432\u0430\u043b \u0432 \u0442\u043e\u0447\u043a\u0435, \u0434\u043e\u043b\u0436\u043d\u043e \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0442\u044c\u0441\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435 \u0443\u0441\u043b\u043e\u0432\u0438\u0435:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1d596fffab33786b9af4466210642acf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to a^-}f(x)=\\lim_{x\\to a^+}f(x)=L \\ \\iff \\ \\lim_{x\\to a}f(x)=L\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"378\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0435\u0441\u043b\u0438 \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u043a\u0430\u043a\u043e\u0439-\u0442\u043e \u0442\u043e\u0447\u043a\u0435 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b, \u0442\u043e \u043f\u0440\u0435\u0434\u0435\u043b\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u043d\u0435 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442.<\/p>\n<p> \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u043e\u0432\u0430\u043d\u0438\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0442\u043e\u0447\u043a\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u043c \u0443\u0441\u043b\u043e\u0432\u0438\u0435\u043c \u0442\u043e\u0433\u043e, \u0447\u0442\u043e\u0431\u044b \u043e\u043d\u0430 \u0431\u044b\u043b\u0430 <span style=\"text-decoration: underline;\"> \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439 \u0432 \u0442\u043e\u0447\u043a\u0435 <\/span> .<\/p>\n<p> \u0414\u0430\u0432\u0430\u0439\u0442\u0435 \u0440\u0435\u0448\u0438\u043c \u043f\u0440\u0438\u043c\u0435\u0440, \u0447\u0442\u043e\u0431\u044b \u0437\u0430\u0432\u0435\u0440\u0448\u0438\u0442\u044c \u043f\u043e\u043d\u0438\u043c\u0430\u043d\u0438\u0435 \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0438\u0438 \u0431\u043e\u043a\u043e\u0432\u044b\u0445 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0438\u0439: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/continuite-dune-fonction-definie-par-morceaux.webp\" alt=\"\" class=\"wp-image-201\" width=\"429\" height=\"299\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> \u0411\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0432 \u0442\u043e\u0447\u043a\u0435 \u0445=-2 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u043d\u043e\u0439 \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u0438, \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u044e\u0442, \u0442\u0430\u043a \u043a\u0430\u043a \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u0442\u0440\u0435\u043c\u0438\u0442\u0441\u044f \u043a 3 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e \u043e\u0442 \u0442\u043e\u0433\u043e, \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0435\u043c\u0441\u044f \u043b\u0438 \u043c\u044b \u043a \u0445=-2 \u0441\u043b\u0435\u0432\u0430 \u0438\u043b\u0438 \u0441\u043f\u0440\u0430\u0432\u0430. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0438 x=-2 \u0440\u0430\u0432\u0435\u043d 3.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b7e7a7ee82b827ba469558c38fc81a45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to -2^-}f(x)=\\lim_{x\\to -2^+}f(x)=3 \\ \\longrightarrow \\ \\lim_{x\\to -2}f(x)=3\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"389\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0432 \u0442\u043e\u0447\u043a\u0435 x=4 \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0434\u0440\u0443\u0433\u0438\u0435, \u0442\u0430\u043a \u043a\u0430\u043a \u0441\u043b\u0435\u0432\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0435\u0442\u0441\u044f \u043a f(x)=3, \u0430 \u0441\u043f\u0440\u0430\u0432\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0435\u0442\u0441\u044f \u043a f(x)=2. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043f\u0440\u0435\u0434\u0435\u043b\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u043d\u0435 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442. <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a3a52e97ba4cff3c4cd84977fb27db89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 4^-}f(x)=3 \\neq \\lim_{x\\to 4^+}f(x)=2 \\ \\longrightarrow \\ \\cancel{\\exists} \\ \\lim_{x\\to 4}f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"374\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calculo-de-limites-laterales\"><\/span> \u0420\u0430\u0441\u0447\u0435\u0442 \u0431\u043e\u043a\u043e\u0432\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0423\u0447\u0438\u0442\u044b\u0432\u0430\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0431\u043e\u043a\u043e\u0432\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432, \u043c\u044b \u0443\u0432\u0438\u0434\u0438\u043c, \u043a\u0430\u043a \u043e\u043d\u0438 \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u044e\u0442\u0441\u044f \u0447\u0438\u0441\u043b\u0435\u043d\u043d\u043e, \u0440\u0435\u0448\u0438\u0432 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u043f\u0440\u0438\u043c\u0435\u0440:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-42104fdcfcbc6e35486c13774c7288ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 2}\\frac{3}{x-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"74\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u0415\u0441\u043b\u0438 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043f\u0440\u0435\u0434\u0435\u043b \u043a\u0430\u043a \u043e\u0431\u044b\u0447\u043d\u043e, \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0441\u0442\u044c \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0433\u043e \u0447\u0438\u0441\u043b\u0430, \u0440\u0430\u0437\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0433\u043e \u043d\u0430 0:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d98b33a08f3017676e2271bdb0b325d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 2}\\frac{3}{x-2}=\\frac{3}{2-2}=\\frac{3}{0}=\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"220\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u041e\u0434\u043d\u0430\u043a\u043e \u043f\u0440\u0438 \u0440\u0430\u0441\u0447\u0435\u0442\u0435 \u0431\u043e\u043a\u043e\u0432\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432 \u043c\u044b \u043d\u0435 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u043d\u0438\u043a\u0430\u043a\u043e\u0439 \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0441\u0442\u0438.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-df0f7477f84abd22a805c7cf70300f16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 2^-}\\frac{3}{x-2}=\\ \\color{red}\\bm{?}\\color{black} \\qquad \\lim_{x\\to 2^+}\\frac{3}{x-2}=\\ \\color{red}\\bm{?}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"378\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> \u0427\u0442\u043e\u0431\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0431\u043e\u043a\u043e\u0432\u043e\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u043b\u0435\u0432\u0430 \u043f\u0440\u0438 x=2, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0432\u0437\u044f\u0442\u044c \u0447\u0438\u0441\u043b\u043e \u043c\u0435\u043d\u044c\u0448\u0435 x=2, \u043d\u043e \u043e\u0447\u0435\u043d\u044c \u0431\u043b\u0438\u0437\u043a\u043e\u0435 \u043a \u043d\u0435\u043c\u0443, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440 x=1,999.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e3cc43d40eb552932818635f1abcd310_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 2^-}\\frac{3}{x-2}=\\frac{3}{\\color{red}\\bm{1,999}\\color{black}-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"252\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u0431\u0443\u0434\u0435\u0442 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u043c \u0447\u0438\u0441\u043b\u043e\u043c \u0441 \u043e\u0447\u0435\u043d\u044c \u043c\u0430\u043b\u0435\u043d\u044c\u043a\u0438\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435\u043c, \u043d\u043e \u0434\u0430\u0436\u0435 \u043d\u0435 \u043d\u0443\u043b\u0435\u0432\u044b\u043c, \u0438 \u043e\u0431\u044b\u0447\u043d\u043e \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442\u0441\u044f \u043d\u0443\u043b\u0435\u043c \u0438 \u0437\u043d\u0430\u043a\u043e\u043c \u043c\u0438\u043d\u0443\u0441 \u043f\u0435\u0440\u0435\u0434 \u043d\u0438\u043c:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-32da1df64469d97474fd1b9e25efcd31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 2^-}\\frac{3}{x-2}=\\frac{3}{1,999-2}=\\frac{3}{\\color{red}\\bm{-0}\\color{black}}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"302\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442 \u0431\u043e\u043a\u043e\u0432\u043e\u0433\u043e \u043f\u0440\u0435\u0434\u0435\u043b\u0430 \u0440\u0430\u0432\u0435\u043d \u043c\u0438\u043d\u0443\u0441 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043b\u044e\u0431\u043e\u0435 \u0447\u0438\u0441\u043b\u043e, \u0440\u0430\u0437\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0435 \u043d\u0430 0, \u0434\u0430\u0435\u0442 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u044c, \u0430 \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0435, \u0440\u0430\u0437\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0435 \u043d\u0430 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0435, \u0434\u0430\u0435\u0442 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0435:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-44072ab37d2d34b0a1cf8655d4b576c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 2^-}\\frac{3}{x-2}=\\frac{3}{1,999-2}=\\frac{3}{-0}=\\color{red}\\bm{-\\infty}\\color{black}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"358\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> \u041c\u044b \u043c\u043e\u0436\u0435\u043c \u0443\u0431\u0435\u0434\u0438\u0442\u044c\u0441\u044f, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0435\u0442\u0441\u044f \u043a \u043c\u0438\u043d\u0443\u0441 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438, \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u044f \u0441\u043b\u0435\u0432\u0430 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u043c\u0438 \u0431\u043b\u0438\u0436\u0435 \u043a x=2.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-97d799f09c2e0890cf3a856bf9c711a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\begin{array}{l}f(1,9)=\\cfrac{3}{1,9-2}=-30\\\\[2ex]f(1,99)=\\cfrac{3}{1,99-2}=-300\\\\[2ex]f(1,999)=\\cfrac{3}{1,999-2}=-3000\\\\[2ex]f(1,9999)=\\cfrac{3}{1,9999-2}=-30000\\\\[2ex]f(1,99999)=\\cfrac{3}{1,99999-2}=-300000\\end{array}\\\\[16ex]\\vdots\\\\[1.5ex] f(2^-)=-\\infty\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"317\" width=\"294\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0410\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e, \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0442\u043e\u0447\u043a\u0435 x=2 \u0441\u043f\u0440\u0430\u0432\u0430, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u0442\u0435 \u0436\u0435 \u0440\u0430\u0441\u0441\u0443\u0436\u0434\u0435\u043d\u0438\u044f: \u043c\u044b \u0431\u0435\u0440\u0435\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0431\u043e\u043b\u044c\u0448\u0435 2, \u043d\u043e \u043e\u0447\u0435\u043d\u044c \u0431\u043b\u0438\u0437\u043a\u043e\u0435, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440 2001.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-21cbd07eef353c53bdfa09eaceb6bd25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 2^+}\\frac{3}{x-2}=\\frac{3}{2,001-2}=\\frac{3}{+0}=+\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"292\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> \u0422\u043e\u0447\u043d\u043e \u0442\u0430\u043a \u0436\u0435 \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0443\u0431\u0435\u0434\u0438\u0442\u044c\u0441\u044f \u0432 \u0441\u0442\u0440\u0435\u043c\u043b\u0435\u043d\u0438\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043a \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438, \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u044f \u0441\u043f\u0440\u0430\u0432\u0430 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u043c\u0438 \u0432\u0441\u0435 \u0431\u043b\u0438\u0436\u0435 \u0438 \u0431\u043b\u0438\u0436\u0435 \u043a x=2.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e6d448cdad3ac6ba82e749b30d2bcc11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\begin{array}{l}f(2,1)=\\cfrac{3}{2,1-2}=30\\\\[2ex]f(2,01)=\\cfrac{3}{2,01-2}=300\\\\[2ex]f(2,001)=\\cfrac{3}{2,001-2}=3000\\\\[2ex]f(2,0001)=\\cfrac{3}{2,0001-2}=30000\\\\[2ex]f(2,00001)=\\cfrac{3}{2,00001-2}=300000\\end{array}\\\\[16ex]\\vdots\\\\[1.5ex] f(2^+)=+\\infty\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"317\" width=\"280\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u041d\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u043c \u0433\u0440\u0430\u0444\u0438\u043a\u0435 \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u0430\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u0443\u0435\u043c\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e. \u041a\u0430\u043a \u0432\u0438\u0434\u0438\u0442\u0435, \u0431\u043e\u043a\u043e\u0432\u043e\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0442\u043e\u0447\u043a\u0435 x=2 \u0441\u043b\u0435\u0432\u0430 \u0440\u0430\u0432\u0435\u043d \u043c\u0438\u043d\u0443\u0441 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438, \u0430 \u0431\u043e\u043a\u043e\u0432\u043e\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0442\u043e\u0447\u043a\u0435 x=2 \u0441\u043f\u0440\u0430\u0432\u0430 \u0440\u0430\u0432\u0435\u043d \u043f\u043b\u044e\u0441 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438. <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/representation-graphique-dune-fonction-de-proportionnalite-inverse.webp\" alt=\"\" class=\"wp-image-166\" width=\"508\" height=\"514\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-limites-laterales\"><\/span> \u0418\u0441\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u044b \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u0441 \u0431\u043e\u043a\u043e\u0432\u044b\u043c\u0438 \u0433\u0440\u0430\u043d\u0438\u0446\u0430\u043c\u0438<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> \u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 1<\/h3>\n<p> \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u043a\u0443\u0441\u043e\u0447\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0442\u043e\u0447\u043a\u0430\u0445 \u0438\u0437\u043c\u0435\u043d\u0435\u043d\u0438\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f (x=-2 \u0438 x=4). <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercices-resolus-de-fonctions-definies-par-parties.webp\" alt=\"\" class=\"wp-image-209\" width=\"395\" height=\"307\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0411\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u043d\u0435 \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u044e\u0442 \u0432 \u0442\u043e\u0447\u043a\u0435 x=-2, \u0441\u043b\u0435\u0432\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0441\u0442\u0440\u0435\u043c\u0438\u0442\u0441\u044f \u043a f(x)=5, \u0430 \u0441 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b \u0441\u043f\u0440\u0430\u0432\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u0430 \u0438 \u0438\u043c\u0435\u0435\u0442 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 3. <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-36fbddc8f36db5a92d77dd9e9b3b81ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to -2^-}f(x)=5\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"118\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8e153627ce1a29511f502c30bd599a6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to -2^+}f(x)=3\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"119\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0411\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0442\u0430\u043a\u0436\u0435 \u0440\u0430\u0437\u043b\u0438\u0447\u0430\u044e\u0442\u0441\u044f \u043f\u043e \u043c\u0435\u0440\u0435 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a x \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0435\u0442\u0441\u044f \u043a 4. \u041a\u0443\u0441\u043e\u0447\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0435\u0442\u0441\u044f \u043a 3 \u0441\u043b\u0435\u0432\u0430, \u043d\u043e \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u0435\u0442\u0441\u044f \u043a -2 \u0441\u043f\u0440\u0430\u0432\u0430. <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c590b4da48c82d7a43ef65e89b3e9977_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 4^-}f(x)=3\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"109\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a4d4c175b4f2e5ecfe44fb41fe420820_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 4^+}f(x)=-2\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"121\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 2<\/h3>\n<p> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435, \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043b\u0438 \u043f\u0440\u0435\u0434\u0435\u043b \u043f\u0440\u0438 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0438 x \u043a 3 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u043a\u0443\u0441\u043e\u0447\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0438 \u0435\u0441\u043b\u0438 \u0434\u0430, \u0442\u043e \u043a\u0430\u043a\u043e\u0432\u043e \u0435\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435. <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/limites-laterales-dune-fonction-par-morceaux.webp\" alt=\"\u0411\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u043a\u0443\u0441\u043e\u0447\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438\" class=\"wp-image-866\" width=\"337\" height=\"303\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0412 \u044d\u0442\u043e\u0439 \u0437\u0430\u0434\u0430\u0447\u0435 \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0432 \u0442\u043e\u0447\u043a\u0435 x=3 \u0441\u043b\u0435\u0432\u0430 \u0438 \u0441\u043f\u0440\u0430\u0432\u0430 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u044b, \u0442\u0430\u043a \u043a\u0430\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0441\u0442\u0440\u0435\u043c\u0438\u0442\u0441\u044f \u043a \u043e\u0434\u043d\u043e\u043c\u0443 \u0438 \u0442\u043e\u043c\u0443 \u0436\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044e (f(x)=3) \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e \u043e\u0442 \u0442\u043e\u0433\u043e, \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0430\u044e\u0442\u0441\u044f \u043b\u0438 \u043a \u043d\u0435\u0439 \u0441\u043b\u0435\u0432\u0430 \u0438\u043b\u0438 \u0441\u043f\u0440\u0430\u0432\u0430. . \u0435\u0433\u043e \u043f\u0440\u0430\u0432\u0430\u044f \u0441\u0442\u043e\u0440\u043e\u043d\u0430: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d8f2aea7db3ddf52e74f09960dd15629_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 3^-}f(x)=3\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"109\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6ee9606c4d6e820e4ac3bb5fa5aa3575_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 3^+}f(x)=3\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"108\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0441\u043e\u0433\u043b\u0430\u0441\u043d\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u043c\u0443 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044e \u043f\u0440\u0435\u0434\u0435\u043b\u0430, \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0438 \u0441\u0442\u0440\u0435\u043c\u043b\u0435\u043d\u0438\u0438 \u0445 \u043a 3 \u0440\u0430\u0432\u0435\u043d 3, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0434\u0432\u0430 \u0431\u043e\u043a\u043e\u0432\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u0430 \u0432 \u044d\u0442\u043e\u0439 \u0436\u0435 \u0442\u043e\u0447\u043a\u0435 \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u044e\u0442 \u043f\u0440\u0438 \u044d\u0442\u043e\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0438:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f82de582de8671680e14cfbf92001010_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 3^-}f(x)=\\lim_{x\\to 3^+}f(x)=3 \\ \\longrightarrow \\ \\lim_{x\\to 3}f(x)=3\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"357\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0425\u043e\u0442\u044f \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0438 x=3 \u0440\u0430\u0432\u0435\u043d 3, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0443\u0447\u0438\u0442\u044b\u0432\u0430\u0442\u044c, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u0440\u0430\u0432\u043d\u0430 \u043d\u0435 3, \u0430 f(3)=7. \u041a\u0430\u043a \u043c\u044b \u0443\u0432\u0438\u0434\u0438\u043c \u043f\u043e\u0437\u0436\u0435, \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0439 \u043f\u0440\u0438 x=3, \u0430 \u0438\u043c\u0435\u0435\u0442 \u0440\u0430\u0437\u0440\u044b\u0432, \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u043c\u043e\u0436\u043d\u043e \u0438\u0437\u0431\u0435\u0436\u0430\u0442\u044c.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> \u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 3<\/h3>\n<p> \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0442\u043e\u0447\u043a\u0435 x=4. <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b5eff7e2ff1b4df8ee2ec49b7db80a18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{-2x+3}{x-4}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"132\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0427\u0442\u043e\u0431\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043f\u0440\u0435\u0434\u0435\u043b, \u043a\u043e\u0433\u0434\u0430 x \u0441\u0442\u0440\u0435\u043c\u0438\u0442\u0441\u044f \u043a 4 \u0441\u043b\u0435\u0432\u0430, \u043c\u044b \u0431\u0435\u0440\u0435\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043c\u0435\u043d\u044c\u0448\u0435 4, \u043d\u043e \u043e\u0447\u0435\u043d\u044c \u0431\u043b\u0438\u0437\u043a\u043e\u0435 \u043a \u043d\u0435\u043c\u0443, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440 3999:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-845fc23ff2883308a9b535c84cd69d83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 4^-}\\frac{-2x+3}{x-4}=\\frac{-2\\cdot 3,999+3}{3,999-4}=\\frac{-4,998}{-0}=+\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"385\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0431\u043e\u043a\u043e\u0432\u043e\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u043f\u0440\u0438 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0438 x \u043a 4 \u0441\u043b\u0435\u0432\u0430 \u0440\u0430\u0432\u0435\u043d \u043f\u043b\u044e\u0441 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438.<\/p>\n<p class=\"has-text-align-left\"> \u0418 \u0447\u0442\u043e\u0431\u044b \u0440\u0435\u0448\u0438\u0442\u044c \u043f\u0440\u0435\u0434\u0435\u043b, \u043a\u043e\u0433\u0434\u0430 x \u0441\u0442\u0440\u0435\u043c\u0438\u0442\u0441\u044f \u043a 4 \u0441\u043f\u0440\u0430\u0432\u0430, \u043c\u044b \u043e\u0446\u0435\u043d\u0438\u0432\u0430\u0435\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u043f\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044e \u0431\u043e\u043b\u044c\u0448\u0435 4, \u043d\u043e \u043e\u0447\u0435\u043d\u044c \u0431\u043b\u0438\u0437\u043a\u043e\u043c\u0443 \u043a \u043d\u0435\u043c\u0443, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440 4001:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ef680d721aae4b9b993bbc65542d5d2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 4^+}\\frac{-2x+3}{x-4}=\\frac{-2\\cdot 4,001+3}{4,001-4}=\\frac{-5,002}{+0}=-\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"385\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0431\u043e\u043a\u043e\u0432\u043e\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u043f\u0440\u0438 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0438 x \u043a 4 \u0441\u043f\u0440\u0430\u0432\u0430 \u0440\u0430\u0432\u0435\u043d \u043c\u0438\u043d\u0443\u0441 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> \u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 4<\/h3>\n<p> \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043f\u0440\u0435\u0434\u0435\u043b, \u0435\u0441\u043b\u0438 \u043e\u043d \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442, \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u043a\u0443\u0441\u043e\u0447\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u0432 \u0442\u043e\u0447\u043a\u0435 x=2: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-40d5632016e70b9d9ab8e46e76e0102b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)= \\left\\{ \\begin{array}{lcl} x^2-3 &amp; \\text{si} &amp;  x \\leq 2 \\\\[2ex]\\displaystyle \\frac{-3x+5}{x-3} &amp; \\text{si} &amp; x>2 \\end{array} \\right.&#187; title=&#187;Rendered by QuickLaTeX.com&#187; height=&#187;75&#8243; width=&#187;235&#8243; style=&#187;vertical-align: 0px;&#187;><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0443\u0441\u043b\u043e\u0432\u0438\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043f\u0440\u043e\u0441\u0438\u0442 \u043d\u0430\u0441 \u043d\u0430\u0439\u0442\u0438 \u043f\u0440\u0435\u0434\u0435\u043b, \u043f\u0440\u0438 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u043a\u0443\u0441\u043e\u0447\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043c\u0435\u043d\u044f\u0435\u0442 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u043d\u0430\u0439\u0442\u0438 \u043f\u0440\u0435\u0434\u0435\u043b \u0432 \u043b\u0435\u0432\u043e\u0439 \u0447\u0430\u0441\u0442\u0438, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u043f\u0435\u0440\u0432\u043e\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435, \u0438 \u043f\u0440\u0435\u0434\u0435\u043b \u0432 \u043f\u0440\u0430\u0432\u043e\u0439 \u0447\u0430\u0441\u0442\u0438, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0432\u0442\u043e\u0440\u043e\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435. <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-312aa6dc645115b9d1a680ef3cc5fb9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 2^-}f(x)=\\lim_{x\\to 2^-}(x^2-3)=2^2-3=1\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"303\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cad9d8ff045408344a1435ec6441aa73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 2^+}f(x)=\\lim_{x\\to 2^+}\\frac{-3x+5}{x-3}=\\frac{-3\\cdot 2+5}{2-3}=\\frac{-1}{-1}=1\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"392\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0438 x=2 \u0441\u043b\u0435\u0432\u0430 \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u0435\u0442 \u0441 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u043f\u0440\u0430\u0432\u0430, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0438 \u0440\u0430\u0432\u0435\u043d 1: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fe286d19fdb8b3f5859e8073869660ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x\\to 2^-}f(x)=\\lim_{x\\to 2^+}f(x)=1 \\ \\longrightarrow \\ \\lim_{x\\to 2}f(x)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"356\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0431\u043e\u043a\u043e\u0432\u043e\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 (\u0441 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u043c\u0438). \u041c\u044b \u0442\u0430\u043a\u0436\u0435 \u043d\u0430\u0443\u0447\u0438\u043c \u0432\u0430\u0441 \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0442\u044c \u043b\u0435\u0432\u044b\u0439 \u0438 \u043f\u0440\u0430\u0432\u044b\u0439 \u0431\u043e\u043a\u043e\u0432\u043e\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043a\u0430\u043a \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u0438, \u0442\u0430\u043a \u0438 \u0447\u0438\u0441\u043b\u0435\u043d\u043d\u043e. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u0442\u0440\u0435\u043d\u0438\u0440\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u0441 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f\u043c\u0438, \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u043e \u0440\u0435\u0448\u0430\u044e\u0449\u0438\u043c\u0438 \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0438\u044f. \u041a\u0430\u043a\u043e\u0432\u044b \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b? \u0411\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0442\u043e\u0447\u043a\u0435 \u0438\u0437\u0443\u0447\u0430\u044e\u0442 \u043f\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432\u043e\u043a\u0440\u0443\u0433 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0438. \u0421\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043b\u0435\u0432\u044b\u0439 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ru\/%d0%b1%d0%be%d0%ba%d0%be%d0%b2%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\/\"> <span class=\"screen-reader-text\">\u0411\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b<\/span> \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[11],"tags":[],"class_list":["post-376","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"<!-- This site is optimized 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&hellip; \u0411\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/ru\/\u0431\u043e\u043a\u043e\u0432\u044b\u0435-\u043f\u0440\u0435\u0434\u0435\u043b\u044b\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-04T05:10:26+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3224554094b2418a485786bfbe4db5f1_l3.png\" \/>\n<meta name=\"author\" content=\"Mathority \u041a\u043e\u043c\u0430\u043d\u0434\u0430\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u041d\u0430\u043f\u0438\u0441\u0430\u043d\u043e \u0430\u0432\u0442\u043e\u0440\u043e\u043c\" \/>\n\t<meta name=\"twitter:data1\" content=\"Mathority \u041a\u043e\u043c\u0430\u043d\u0434\u0430\" \/>\n<script 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