{"id":26,"date":"2023-09-17T11:07:18","date_gmt":"2023-09-17T11:07:18","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d1%82%d0%b8%d0%bf%d1%8b-%d1%80%d0%b0%d0%b7%d1%80%d1%8b%d0%b2%d0%be%d0%b2\/"},"modified":"2023-09-17T11:07:18","modified_gmt":"2023-09-17T11:07:18","slug":"%d1%82%d0%b8%d0%bf%d1%8b-%d1%80%d0%b0%d0%b7%d1%80%d1%8b%d0%b2%d0%be%d0%b2","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d1%82%d0%b8%d0%bf%d1%8b-%d1%80%d0%b0%d0%b7%d1%80%d1%8b%d0%b2%d0%be%d0%b2\/","title":{"rendered":"\u0422\u0438\u043f\u044b \u0440\u0430\u0437\u0440\u044b\u0432\u043e\u0432"},"content":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u043a\u0430\u043a\u0438\u0435 \u0432\u0438\u0434\u044b \u0440\u0430\u0437\u0440\u044b\u0432\u043e\u0432 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0432\u0441\u0435\u0445 \u0442\u0438\u043f\u043e\u0432 \u0440\u0430\u0437\u0440\u044b\u0432\u043e\u0432 \u0438 \u043f\u043e\u0442\u0440\u0435\u043d\u0438\u0440\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u043d\u0430 \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0445 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f\u0445 \u043d\u0430 \u0442\u0438\u043f\u044b \u0440\u0430\u0437\u0440\u044b\u0432\u043e\u0432 \u0444\u0443\u043d\u043a\u0446\u0438\u0439. <\/p>\n<p><strong><\/strong><\/p>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-104\"><strong> <\/strong><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcuales-son-todos-los-tipos-de-discontinuidades\"><\/span> \u041a\u0430\u043a\u043e\u0432\u044b \u0432\u0441\u0435 \u0432\u0438\u0434\u044b \u0440\u0430\u0437\u0440\u044b\u0432\u043e\u0432?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0420\u0430\u0437\u043b\u0438\u0447\u0430\u044e\u0442 \u0442\u0440\u0438 \u0442\u0438\u043f\u0430 \u0440\u0430\u0437\u0440\u044b\u0432\u043e\u0432, \u0430 \u0438\u043c\u0435\u043d\u043d\u043e:<\/p>\n<ul>\n<li> <strong>\u041f\u0440\u0435\u043e\u0434\u043e\u043b\u0438\u043c\u044b\u0439 \u0440\u0430\u0437\u0440\u044b\u0432<\/strong> : \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 \u043d\u0435 \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u044e\u0442 \u0441\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/li>\n<li> <strong>\u041d\u0435\u0438\u0437\u0431\u0435\u0436\u043d\u044b\u0439 \u0440\u0430\u0437\u0440\u044b\u0432 \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0433\u043e \u0441\u043a\u0430\u0447\u043a\u0430<\/strong> : \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 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b.<\/li>\n<li> <strong>\u041d\u0435\u0438\u0437\u0431\u0435\u0436\u043d\u044b\u0439 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0439 \u0441\u043a\u0430\u0447\u043e\u043a \u0440\u0430\u0437\u0440\u044b\u0432\u0430<\/strong> : \u043e\u0434\u0438\u043d \u0438\u0437 \u0431\u043e\u043a\u043e\u0432\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0434\u0430\u0435\u0442 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u044c \u0438\u043b\u0438 \u043d\u0435 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442.<\/li>\n<\/ul>\n<p> \u0427\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\u0439, \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c \u043a\u0430\u0436\u0434\u044b\u0439 \u0442\u0438\u043f \u0440\u0430\u0437\u0440\u044b\u0432\u0430 \u0431\u043e\u043b\u0435\u0435 \u043f\u043e\u0434\u0440\u043e\u0431\u043d\u043e \u0438 \u0443\u0432\u0438\u0434\u0438\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0441 \u0442\u0440\u0435\u043c\u044f \u0442\u0438\u043f\u0430\u043c\u0438 \u0440\u0430\u0437\u0440\u044b\u0432\u043e\u0432.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"discontinuidad-evitable\"><\/span> \u041f\u0440\u0435\u043e\u0434\u043e\u043b\u0438\u043c\u044b\u0435 \u0440\u0430\u0437\u0440\u044b\u0432\u044b <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><strong> <\/strong><\/div>\n<\/div>\n<p><strong>\u0423\u0441\u0442\u0440\u0430\u043d\u0438\u043c\u044b\u0439 \u0440\u0430\u0437\u0440\u044b\u0432<\/strong> \u2014 \u044d\u0442\u043e \u0442\u0438\u043f \u0440\u0430\u0437\u0440\u044b\u0432\u0430, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0438\u043c\u0435\u0435\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0432 \u0442\u043e\u0447\u043a\u0435, \u0435\u0441\u043b\u0438 \u0433\u0440\u0430\u043d\u0438\u0446\u0430 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435, \u043d\u043e \u043d\u0435 \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u0435\u0442 \u0441\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0438\u043b\u0438 \u043d\u0435 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043e\u0431\u0440\u0430\u0437\u0430 \u0444\u0443\u043d\u043a\u0446\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-c26b9be97568ba85e1f8f22b568a2354_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\exists \\lim_{x \\to a} f(x) \\neq f(a) \\qquad | \\qquad \\displaystyle \\exists\\lim_{x \\to a} f(x) \\text{ y } \\ \\cancel{\\exists} \\ f(a)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"367\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-columns are-vertically-aligned-top is-layout-flex wp-container-99\">\n<div class=\"wp-block-column is-vertically-aligned-top is-layout-flow\">\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\/discontinuite-evitable-d-une-fonction.webp\" alt=\"\u043f\u0440\u0435\u0434\u043e\u0442\u0432\u0440\u0430\u0442\u0438\u043c\u044b\u0439 \u0440\u0430\u0437\u0440\u044b\u0432 \u0444\u0443\u043d\u043a\u0446\u0438\u0438\" class=\"wp-image-1400\" width=\"276\" height=\"259\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p> \u0411\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u044d\u0442\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0440\u0430\u0432\u043d\u044b \u043c\u0435\u0436\u0434\u0443 \u0441\u043e\u0431\u043e\u0439, \u043d\u043e \u043e\u0442\u043b\u0438\u0447\u0430\u044e\u0442\u0441\u044f \u043e\u0442 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \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<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ac5bdc61d377477ddcc788b7230bcfbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left. \\begin{array}{l}\\displaystyle \\lim_{x \\to a^-} f(x) =b \\\\[3ex] \\displaystyle \\lim_{x \\to a^+} f(x)=b \\end{array} \\right\\} \\ \\bm{\\longrightarrow} \\ \\lim_{x \\to a} f(x)=b\" title=\"Rendered by QuickLaTeX.com\" height=\"76\" width=\"276\" style=\"vertical-align: 0px;\"><\/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-9f61efde161e83828572db200f128ced_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to a} f(x)=b \\qquad f(a)=c\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"198\" style=\"vertical-align: -12px;\"><\/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-de211758fe99134c01f6eec8ea7c6348_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\exists \\lim_{x \\to a} f(x) \\neq f(a)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"135\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-top is-layout-flow\">\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\/discontinuite-evitable-d-une-fonction-sans-image.webp\" alt=\"\u043f\u0440\u0435\u0434\u043e\u0442\u0432\u0440\u0430\u0442\u0438\u043c\u044b\u0439 \u0440\u0430\u0437\u0440\u044b\u0432 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0431\u0435\u0437 \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u044f\" class=\"wp-image-1401\" width=\"276\" height=\"259\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p class=\"has-text-align-left\"> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u0432 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \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, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u043f\u0440\u0438 x=a \u0438\u043c\u0435\u044e\u0442 \u043e\u0434\u043d\u043e \u0438 \u0442\u043e \u0436\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435, \u043d\u043e \u043e\u0431\u0440\u0430\u0437 \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-ac5bdc61d377477ddcc788b7230bcfbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left. \\begin{array}{l}\\displaystyle \\lim_{x \\to a^-} f(x) =b \\\\[3ex] \\displaystyle \\lim_{x \\to a^+} f(x)=b \\end{array} \\right\\} \\ \\bm{\\longrightarrow} \\ \\lim_{x \\to a} f(x)=b\" title=\"Rendered by QuickLaTeX.com\" height=\"76\" width=\"276\" style=\"vertical-align: 0px;\"><\/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-87531b3fbfb53b42e79af5a7305ffc37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to a} f(x)=b \\qquad \\cancel{\\exists} \\ f(a)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"181\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0421\u043c.:<\/strong> <span style=\"text-decoration: underline;\"> \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0438. <\/span> <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"discontinuidad-inevitable-de-salto-finito\"><\/span> \u041d\u0435\u0438\u0437\u0431\u0435\u0436\u043d\u044b\u0439 \u0440\u0430\u0437\u0440\u044b\u0432 \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0433\u043e \u0441\u043a\u0430\u0447\u043a\u0430 <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><strong> <\/strong><\/div>\n<p><strong><br \/><\/strong><\/p>\n<\/div>\n<p><strong>\u041d\u0435\u0438\u0437\u0431\u0435\u0436\u043d\u044b\u0439 \u0440\u0430\u0437\u0440\u044b\u0432 \u0441 \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u043c \u0441\u043a\u0430\u0447\u043a\u043e\u043c<\/strong> \u2014 \u044d\u0442\u043e \u0442\u0438\u043f \u0440\u0430\u0437\u0440\u044b\u0432\u0430, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0432 \u0442\u043e\u0447\u043a\u0435, \u043a\u043e\u0433\u0434\u0430 \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u043d\u0435 \u0440\u0430\u0432\u043d\u044b.<\/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-66fd7a55b2fad1a91622d738925d3304_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to a^-} f(x) \\neq \\lim_{x \\to a^+} f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"175\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \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\u0435 \u0438\u0437\u043c\u0435\u043d\u0435\u043d\u0438\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u043c\u0435\u0435\u0442 \u043d\u0435\u0438\u0437\u0431\u0435\u0436\u043d\u044b\u0439 \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0439 \u0441\u043a\u0430\u0447\u043e\u043a \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\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\/saut-fini-inevitable-discontinuite.webp\" alt=\"\u043d\u0435\u0438\u0437\u0431\u0435\u0436\u043d\u044b\u0439 \u0440\u0430\u0437\u0440\u044b\u0432 \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0433\u043e \u0441\u043a\u0430\u0447\u043a\u0430\" class=\"wp-image-1406\" width=\"275\" height=\"258\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4f7173f197ec50976b07e8ab608ec4aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to a^-} f(x)=b \\qquad  \\lim_{x \\to a^+} f(x)=c\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"254\" 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-66fd7a55b2fad1a91622d738925d3304_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to a^-} f(x) \\neq \\lim_{x \\to a^+} f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"175\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> \u042d\u0442\u043e\u0442 \u0442\u0438\u043f \u0440\u0430\u0437\u0440\u044b\u0432\u0430 \u043e\u0431\u044b\u0447\u043d\u043e \u0432\u043e\u0437\u043d\u0438\u043a\u0430\u0435\u0442 \u0432 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u0445, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u044b\u0445 \u043a\u0443\u0441\u043e\u0447\u043d\u043e (\u0438\u043b\u0438 \u043a\u0443\u0441\u043e\u0447\u043d\u043e).<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0421\u043c.:<\/strong> <span style=\"text-decoration: underline;\"> \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c \u043a\u0443\u0441\u043e\u0447\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. <\/span> <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"discontinuidad-inevitable-de-salto-infinito\"><\/span> \u0411\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0439 \u043f\u0440\u044b\u0436\u043e\u043a, \u043d\u0435\u0438\u0437\u0431\u0435\u0436\u043d\u044b\u0439 \u0440\u0430\u0437\u0440\u044b\u0432 <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-107\"><strong> <\/strong><\/div>\n<\/div>\n<p><strong>\u041d\u0435\u0438\u0437\u0431\u0435\u0436\u043d\u044b\u0439 \u0440\u0430\u0437\u0440\u044b\u0432 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0433\u043e \u0441\u043a\u0430\u0447\u043a\u0430<\/strong> \u2014 \u044d\u0442\u043e \u0442\u0438\u043f \u0440\u0430\u0437\u0440\u044b\u0432\u0430, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0438\u043d\u043e\u0433\u0434\u0430 \u0438\u043c\u0435\u0435\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u0435\u0441\u043b\u0438 \u043e\u0434\u0438\u043d \u0438\u0437 \u0431\u043e\u043a\u043e\u0432\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432 \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u0435\u043d \u0438\u043b\u0438 \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-a67f3a84bbd7cc965e932b0cb681912a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to a^-} f(x) = \\pm \\infty \\qquad \\lim_{x \\to a^+} f(x)= \\pm \\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"301\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-102\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p> \u041b\u0435\u0432\u044b\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0434\u0430\u0435\u0442 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e, \u0430 \u043f\u0440\u0430\u0432\u044b\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u0434\u0430\u0435\u0442 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u044c. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u043d\u0435\u0438\u0437\u0431\u0435\u0436\u043d\u044b\u0439 \u0440\u0430\u0437\u0440\u044b\u0432 \u0432 \u0432\u0438\u0434\u0435 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0433\u043e \u0441\u043a\u0430\u0447\u043a\u0430. <\/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\/saut-infini-discontinuite.webp\" alt=\"\u0440\u0430\u0437\u0440\u044b\u0432 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0433\u043e \u043f\u0440\u044b\u0436\u043a\u0430\" class=\"wp-image-1411\" width=\"276\" height=\"259\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9e12509ad0839664b52f4224f0fc2e56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to a^-} f(x)=b \\qquad \\lim_{x \\to a^+} f(x)=+\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"277\" 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-left\"> \u041d\u0438\u0436\u0435 \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u0433\u0440\u0430\u0444\u0438\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0434\u0432\u0430 \u0431\u043e\u043a\u043e\u0432\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u0430 \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0434\u0430\u044e\u0442 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u044c \u0438, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u043c\u0435\u0435\u0442 \u043d\u0435\u0438\u0437\u0431\u0435\u0436\u043d\u044b\u0439 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0439 \u0441\u043a\u0430\u0447\u043e\u043a. <\/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\/discontinuite-infinie.webp\" alt=\"\u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0439 \u0440\u0430\u0437\u0440\u044b\u0432\" class=\"wp-image-1412\" width=\"276\" height=\"259\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-99099617bca8a79ef975169f06f5c14e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to a^-} f(x)=-\\infty \\qquad \\lim_{x \\to a^+} f(x)=+\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"301\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p> \u042d\u0442\u043e\u0442 \u0442\u0438\u043f \u0440\u0430\u0437\u0440\u044b\u0432\u0430 \u043e\u0431\u044b\u0447\u043d\u043e \u0432\u043e\u0437\u043d\u0438\u043a\u0430\u0435\u0442 \u0432 <span style=\"text-decoration: underline;\"> \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 (\u0438\u043b\u0438 \u0434\u0440\u043e\u0431\u043d\u044b\u0445) \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u0445 <\/span> . <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-tipos-de-discontinuidades\"><\/span> \u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u043f\u043e \u0442\u0438\u043f\u0430\u043c \u0440\u0430\u0437\u0440\u044b\u0432\u043e\u0432<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><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-108\"><strong> <\/strong><\/div>\n<p><strong><br \/><\/strong><\/p>\n<\/div>\n<p>\u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u043c \u0442\u0438\u043f \u0440\u0430\u0437\u0440\u044b\u0432\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u043a\u0443\u0441\u043e\u0447\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0442\u043e\u0447\u043a\u0435 x=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-8185827ad36ab3921bb96eb5a6da21a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)= \\left\\{ \\begin{array}{lcl} -2x+1 &amp;  \\text{si} &amp;  x\\leq 3 \\\\[2ex] 4x - 5 &amp; \\text{si} &amp; x > 3 \\end{array} \\right.&#187; title=&#187;Rendered by QuickLaTeX.com&#187; height=&#187;65&#8243; width=&#187;232&#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>\u041f\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\"> \u041e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043f\u0435\u0440\u0432\u043e\u0433\u043e \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u0430 \u0444\u0443\u043d\u043a\u0446\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-490b7f67d1b8735fc34485932796cef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-2x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"61\" style=\"vertical-align: -2px;\"><\/p>\n<p> , \u043a\u0430\u043a \u0438 \u0432\u043e \u0432\u0442\u043e\u0440\u043e\u0439 \u0447\u0430\u0441\u0442\u0438,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-82dafeb4abb94d9f10e1603d00cc3d59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4x-5\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"49\" style=\"vertical-align: 0px;\"><\/p>\n<p> , \u0432\u0441\u0435 \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u043c\u0438 \u0447\u0438\u0441\u043b\u0430\u043c\u0438, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043e\u043d\u0438 \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u044b\u043c\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u043c\u0438.<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u0442\u043e\u0447\u043a\u0430, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u0440\u0430\u0437\u0440\u044b\u0432\u043d\u043e\u0439, \u2014 \u044d\u0442\u043e \u0442\u043e\u0447\u043a\u0430 \u043e\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0438 \u043a\u0443\u0441\u043e\u0447\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043d\u0430 \u044d\u0442\u043e\u043c \u044d\u0442\u0430\u043f\u0435 \u043c\u044b \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0435\u043c \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b: <\/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-e5aa03a9198a249e6cb09793b67754f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to 3^-} f(x)=\\lim_{x \\to 3} (-2x+1) = -2\\cdot 3+1=-5\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"349\" 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-c8e29ea20c018b8936dca674ada7590a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to 3^+} f(x)=\\lim_{x \\to 3}(4x-5)=4\\cdot 3-5=7\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"308\" 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-ffa1cc3d456b55bfef8f4a5999e072e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 3^-} f(x) \\neq \\lim_{x \\to 3^+} f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"174\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0414\u0432\u0430 \u0431\u043e\u043a\u043e\u0432\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u0430 \u043f\u0440\u0438 x=3 \u0434\u0430\u044e\u0442 \u0440\u0430\u0437\u043d\u044b\u0435 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u044b. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0442\u043e\u0447\u043a\u0430 x=3 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043d\u0435\u0438\u0437\u0431\u0435\u0436\u043d\u044b\u043c \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u043c \u0441\u043a\u0430\u0447\u043a\u043e\u043e\u0431\u0440\u0430\u0437\u043d\u044b\u043c \u0440\u0430\u0437\u0440\u044b\u0432\u043e\u043c.<\/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> \u041d\u0430\u0439\u0434\u0438\u0442\u0435, \u043a\u0430\u043a\u043e\u0439 \u0442\u0438\u043f \u0440\u0430\u0437\u0440\u044b\u0432\u0430 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0430\u044f \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432 \u0442\u043e\u0447\u043a\u0430\u0445, \u043d\u0435 \u043f\u0440\u0438\u043d\u0430\u0434\u043b\u0435\u0436\u0430\u0449\u0438\u0445 \u0435\u0435 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f: <\/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-44d5d873cde7d3365fc55943c61e78f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)= \\cfrac{x^2-4}{x+2}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"109\" style=\"vertical-align: -14px;\"><\/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>\u041f\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\"> \u041b\u043e\u0433\u0438\u0447\u043d\u043e, \u0447\u0442\u043e \u0434\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u044d\u0442\u043e\u0433\u043e \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u043d\u0430\u0439\u0442\u0438 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0418\u0442\u0430\u043a, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u044d\u0442\u043e \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u043f\u0440\u0438\u043c\u0435\u043c \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u0440\u0430\u0432\u043d\u044b\u043c 0 \u0438 \u0440\u0435\u0448\u0438\u043c \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\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-24e301fa7ea2e8d9f0041192d9a84927_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x+2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"73\" style=\"vertical-align: -2px;\"><\/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-01f282abd343bbe6b83c45e54b86c6ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=-2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\"><\/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-fbd5fe607cd89a42b4db6e52bc047c56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\{-2\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"152\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0431\u0443\u0434\u0435\u0442 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0439 \u0432\u043e \u0432\u0441\u0435\u0445 \u0442\u043e\u0447\u043a\u0430\u0445, \u043a\u0440\u043e\u043c\u0435 x=-2, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0434\u0430\u0432\u0430\u0439\u0442\u0435 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a\u0438\u043c \u0442\u0438\u043f\u043e\u043c \u0440\u0430\u0437\u0440\u044b\u0432\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0442\u043e\u0447\u043a\u0430 x=-2. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043c \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0442\u043e\u0447\u043a\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-bf6f3ceb66dcd630224097f54365ef24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -2} \\cfrac{x^2-4}{x+2} = \\cfrac{ (-2)^2-4}{-2+2}= \\cfrac{0}{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"227\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041d\u043e \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u043d\u0443\u043b\u0435\u0432\u0443\u044e \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0441\u0442\u044c \u043c\u0435\u0436\u0434\u0443 \u043d\u0443\u043b\u0435\u043c, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0443\u0435\u043c \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u044b \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044f \u0438 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044f \u0438 \u0443\u043f\u0440\u043e\u0449\u0430\u0435\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-e939f4fee6ac399b046fa809daab31c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -2} \\cfrac{x^2-4}{x+2}=\\lim_{x \\to -2} \\cfrac{ (x-2)\\cancel{(x+2)}}{\\cancel{x+2}}  =\\lim_{x \\to -2} (x-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"385\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0435\u043f\u0435\u0440\u044c \u0440\u0435\u0448\u0430\u0435\u043c \u043f\u0440\u0435\u0434\u0435\u043b:<\/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-5e05e20f45a4d8b2fbe26bb0d3ae5091_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -2} (x-2) =-2-2=-4\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"217\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \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 \u0432 \u0442\u043e\u0447\u043a\u0435 x=-2 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0438 \u0434\u0430\u0435\u0442 -4. \u0422\u0435\u043f\u0435\u0440\u044c \u043f\u0440\u043e\u0432\u0435\u0440\u0438\u043c, \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043b\u0438 \u043e\u043d <\/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-80b84d482e50cebc375313e005736c97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-2):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"56\" style=\"vertical-align: -5px;\"><\/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-c58a37ec90f203b24b790c7cfacaf2c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-2)=\\cfrac{(-2)^2-4}{-2+2}= \\cfrac{4-4}{0} = \\cfrac{0}{0} \\quad \\bm{\\longrightarrow} \\quad \\cancel{\\exists} \\ f(2)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"359\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041f\u0440\u0438 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0438 \u043e\u0431\u0440\u0430\u0437\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0441\u0442\u044c 0\/0 \u043d\u0435 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u0443\u043f\u0440\u043e\u0449\u0435\u043d\u0430 \u0438 \u043d\u0435 \u0438\u043c\u0435\u0435\u0442 \u0440\u0435\u0448\u0435\u043d\u0438\u044f. \u0422\u0410\u041a<\/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-7ee53c0d0a8e84c09c63d946334cd34b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"47\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u043d\u0435 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442.<\/p>\n<p class=\"has-text-align-left\"> \u0412 \u0437\u0430\u043a\u043b\u044e\u0447\u0435\u043d\u0438\u0435 \u043e\u0442\u043c\u0435\u0442\u0438\u043c, \u0447\u0442\u043e \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0438 x=-2 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442, \u043d\u043e<\/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-7ee53c0d0a8e84c09c63d946334cd34b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"47\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u041d\u0435\u0442. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, x=-2 \u2014 \u044d\u0442\u043e \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><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-110\"><strong> <\/strong><\/div>\n<p><strong><br \/><\/strong><\/p>\n<\/div>\n<p>\u041f\u0440\u043e\u0430\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u0443\u0439\u0442\u0435 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c \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: <\/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-59ee18262fd6f3427ebab6ceabb22868_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)= \\frac{2}{x-5}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"101\" 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>\u041f\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 \u0443\u0431\u0435\u0434\u0438\u0442\u044c\u0441\u044f, \u0447\u0442\u043e \u044d\u0442\u043e \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0435\u0435 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u043f\u0440\u0438\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u0435\u043c \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043a \u043d\u0443\u043b\u044e, \u0447\u0442\u043e\u0431\u044b \u0443\u0432\u0438\u0434\u0435\u0442\u044c, \u043a\u0430\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438 \u043d\u0435 \u043f\u0440\u0438\u043d\u0430\u0434\u043b\u0435\u0436\u0430\u0442 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f: <\/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-845b4cbd750afedb8e09b0ed6a9809c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x-5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"73\" style=\"vertical-align: 0px;\"><\/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-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=5\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\"><\/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-96a28ea816d10d62e90dd13ad1aa79c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\{5\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0431\u0443\u0434\u0435\u0442 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0439 \u0432\u043e \u0432\u0441\u0435\u0445 \u0442\u043e\u0447\u043a\u0430\u0445, \u043a\u0440\u043e\u043c\u0435 x=5. \u0418\u0442\u0430\u043a, \u0434\u0430\u0432\u0430\u0439\u0442\u0435 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a\u043e\u0439 \u0442\u0438\u043f \u0440\u0430\u0437\u0440\u044b\u0432\u0430 x = 5, \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0432 \u043f\u0440\u0435\u0434\u0435\u043b \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\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-976747f92d549df73e0cf24ee4ff2953_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 5} \\frac{2}{x-5} = \\frac{2}{5-5} = \\frac{2}{0} = \\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"220\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041c\u044b \u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u043c\u0441\u044f \u0441 \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0441\u0442\u044c\u044e \u0447\u0438\u0441\u043b\u0430, \u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0433\u043e \u043d\u0430 0. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0438 x=5: <\/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-98edca328c2637f8b7ae59dde1789f44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 5^{-}} \\frac{2}{x-5}=\\frac{2}{4,999-5}=\\frac{2}{-0}= \\bm{-\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"292\" style=\"vertical-align: -16px;\"><\/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-378f3bdf00d4375069e68f4fc8547ca0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 5^{+}} \\frac{2}{x-5}=\\frac{2}{5,001-5}=\\frac{2}{+0}=\\bm{+\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"292\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041b\u0435\u0432\u044b\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0438 x=5 \u0434\u0430\u0435\u0442 \u043c\u0438\u043d\u0443\u0441 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u044c, \u0430 \u043f\u0440\u0430\u0432\u044b\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u0434\u0430\u0435\u0442 \u043f\u043b\u044e\u0441 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u044c. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u043c\u0435\u0435\u0442 \u043d\u0435\u0438\u0437\u0431\u0435\u0436\u043d\u044b\u0439 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0439 \u0441\u043a\u0430\u0447\u043e\u043a \u043f\u0440\u0438 x = 5, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0445\u043e\u0442\u044f \u0431\u044b \u043e\u0434\u0438\u043d \u0431\u043e\u043a\u043e\u0432\u043e\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u0441\u0442\u0440\u0435\u043c\u0438\u0442\u0441\u044f \u043a \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> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435 \u0432\u0441\u0435 \u0440\u0430\u0437\u0440\u044b\u0432\u044b \u043a\u0443\u0441\u043e\u0447\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043f\u043e\u043a\u0430\u0437\u0430\u043d\u043d\u043e\u0439 \u043d\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u043c \u0433\u0440\u0430\u0444\u0438\u043a\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\/exercice-resolu-discontinuites-de-fonctions.webp\" alt=\"\u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u0440\u0430\u0437\u0440\u0435\u0448\u0438\u043b\u0438 \u0440\u0430\u0437\u0440\u044b\u0432\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0439\" class=\"wp-image-1433\" width=\"400\" height=\"344\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/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>\u041f\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 \u043d\u0430\u0440\u0438\u0441\u043e\u0432\u0430\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u044e, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043f\u043e\u0434\u043d\u044f\u0442\u044c \u043a\u0430\u0440\u0430\u043d\u0434\u0430\u0448 \u0432 \u0442\u043e\u0447\u043a\u0430\u0445 x=-2, x=1 \u0438 x=4. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0440\u0430\u0437\u0440\u044b\u0432\u043d\u0430 \u0432 \u044d\u0442\u0438\u0445 \u0442\u0440\u0435\u0445 \u0442\u043e\u0447\u043a\u0430\u0445.<\/p>\n<p class=\"has-text-align-left\"> \u041f\u0440\u0438 x=-2 \u043b\u0435\u0432\u044b\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u0440\u0430\u0432\u0435\u043d +\u221e, \u0430 \u043f\u0440\u0430\u0432\u044b\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u0440\u0430\u0432\u0435\u043d 3. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043e\u0434\u0438\u043d \u0438\u0437 \u0431\u043e\u043a\u043e\u0432\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u0435\u043d, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u043c\u0435\u0435\u0442 \u043d\u0435\u0438\u0437\u0431\u0435\u0436\u043d\u044b\u0439 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0439 \u0441\u043a\u0430\u0447\u043e\u043a \u043f\u0440\u0438 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-eff79ace33659ceb8203e6e27f38fe35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -2^-} f(x) = +\\infty \\ \\neq \\ \\lim_{x \\to -2^+} f(x) = 3\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"296\" 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=1 \u0440\u0430\u0432\u0435\u043d 0, \u0438, \u0441 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0438 x=1 \u0440\u0430\u0432\u043d\u043e 2. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \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 \u043f\u0440\u0438 x=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-3a616cc5210984ffeed3525a219dd53a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 1^-} f(x) =   \\lim_{x \\to 1^+} f(x) = 0 \\ \\bm{\\longrightarrow} \\ \\lim_{x \\to 1} f(x) = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"350\" 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-9a3aea29db1a67d08d91d510033ffd1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 1} f(x) =  0 \\neq  f(1) = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"187\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041f\u0440\u0438 x = 4 \u043b\u0435\u0432\u044b\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u0440\u0430\u0432\u0435\u043d -3, \u0430 \u043f\u0440\u0430\u0432\u044b\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u0440\u0430\u0432\u0435\u043d 1. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \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 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b \u0438 \u043d\u0438 \u043e\u0434\u0438\u043d \u0438\u0437 \u043d\u0438\u0445 \u043d\u0435 \u0434\u0430\u0435\u0442 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0435\u0438\u0437\u0431\u0435\u0436\u043d\u043e \u0438\u043c\u0435\u0435\u0442 \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0439 \u0441\u043a\u0430\u0447\u043e\u043a \u043f\u0440\u0438 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-b758745a987f927350b2d885009c3a87_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) = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"265\" 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 5<\/h3>\n<p> \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u0432\u0441\u0435 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b \u0438 \u0440\u0430\u0437\u0440\u044b\u0432\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u043d\u043e\u0439 \u043d\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u043c \u0433\u0440\u0430\u0444\u0438\u043a\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\/exercice-resolu-types-de-discontinuites-d-une-fonction.webp\" alt=\"\u0440\u0435\u0448\u0430\u0435\u043c\u043e\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 \u043d\u0430 \u0442\u0438\u043f\u044b \u0440\u0430\u0437\u0440\u044b\u0432\u043e\u0432 \u0444\u0443\u043d\u043a\u0446\u0438\u0438\" class=\"wp-image-1435\" width=\"537\" height=\"453\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/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>\u041f\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\"> <strong><span style=\"text-decoration: underline;\">\u0410\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u044b<\/span><\/strong><\/p>\n<p class=\"has-text-align-left\"> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u043e\u0447\u0435\u043d\u044c \u0431\u043b\u0438\u0437\u043a\u043e \u043a \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u043e\u0439 \u043b\u0438\u043d\u0438\u0438 x=3, \u043d\u043e \u043d\u0438\u043a\u043e\u0433\u0434\u0430 \u043d\u0435 \u043a\u0430\u0441\u0430\u0435\u0442\u0441\u044f \u0435\u0435. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u043b\u0435\u0432\u044b\u0439 \u0431\u043e\u043a\u043e\u0432\u043e\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u043f\u0440\u0438 x=3 \u0440\u0430\u0432\u0435\u043d +\u221e, \u0430 \u043f\u0440\u0430\u0432\u044b\u0439 \u0431\u043e\u043a\u043e\u0432\u043e\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u0440\u0430\u0432\u0435\u043d -\u221e. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, x=3 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u044c\u043d\u043e\u0439 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u043e\u0439.<\/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-89bdb1598b6153cec4e9efce7b0927b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 3^-} f(x)=+\\infty \\qquad \\lim_{x \\to 3^+} f(x)=-\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"300\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u043e \u0436\u0435 \u0441\u0430\u043c\u043e\u0435 \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0434\u0438\u0442 \u0438 \u0441 \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u043e\u0439 \u043b\u0438\u043d\u0438\u0435\u0439 y=-1: \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043e\u0447\u0435\u043d\u044c \u0431\u043b\u0438\u0437\u043a\u043e \u043f\u043e\u0434\u0445\u043e\u0434\u0438\u0442 \u043a y=-1, \u043d\u043e \u043d\u0438\u043a\u043e\u0433\u0434\u0430 \u0435\u0435 \u043d\u0435 \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u0435\u0442. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u043f\u0440\u0435\u0434\u0435\u043b \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u0440\u0438 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0438 x \u043a +\u221e \u0438 -\u221e \u0440\u0430\u0432\u0435\u043d -1. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, y=-1 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u044c\u043d\u043e\u0439 \u0430\u0441\u0438\u043c\u043f\u0442\u043e\u0442\u043e\u0439.<\/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-d0f0ee09aaa4a3bfa4fcb77ecc84640a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} f(x)=-1 \\qquad \\lim_{x \\to -\\infty} f(x)=-1\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"297\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong><span style=\"text-decoration: underline;\">\u0440\u0430\u0437\u0440\u044b\u0432\u044b<\/span><\/strong><\/p>\n<p class=\"has-text-align-left\"> \u041f\u0440\u0438 x=6 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u0440\u0435\u0440\u044b\u0432\u0430\u0435\u0442\u0441\u044f, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0438\u043c\u0435\u0435\u0442\u0441\u044f \u043e\u0442\u043a\u0440\u044b\u0442\u0430\u044f \u0442\u043e\u0447\u043a\u0430. \u041f\u0440\u0435\u0434\u0435\u043b \u043f\u0440\u0438 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0438 x \u043a 6 \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 -1,4, \u043d\u043e f(6)=1. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \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 \u043f\u0440\u0438 x=6, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u0430 \u043d\u0435 \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u0435\u0442 \u0441\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435\u043c \u0444\u0443\u043d\u043a\u0446\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-33612be383c71fea04c8c886710f7f10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left. \\begin{array}{l} \\displaystyle \\lim_{x \\to 6^-} f(x)=-1,4\\\\[3ex] \\displaystyle \\lim_{x \\to 6^+} f(x)=-1,4 \\end{array} \\right\\} \\bm{\\longrightarrow} \\lim_{x \\to 6} f(x)=-1,4\" title=\"Rendered by QuickLaTeX.com\" height=\"76\" width=\"326\" style=\"vertical-align: 0px;\"><\/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-647b9aea6cc8b605d7e8bc7d5e83ee64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 6} f(x)=-1,4 \\neq f(6)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"217\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041f\u0440\u0438 x=-3 \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u043d\u0435 \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u044e\u0442 \u0438 \u043d\u0438 \u043e\u0434\u0438\u043d \u0438\u0437 \u043d\u0438\u0445 \u043d\u0435 \u0434\u0430\u0435\u0442 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u043c\u0435\u0435\u0442 \u043d\u0435\u0438\u0437\u0431\u0435\u0436\u043d\u044b\u0439 \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0439 \u0441\u043a\u0430\u0447\u043e\u043a \u043f\u0440\u0438 x=-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-3f7d2a2c7abbc525adfcc7576b449f1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -3^-} f(x)=-2 \\neq \\lim_{x \\to -3^+} f(x)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"275\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u043c\u0435\u0435\u0442 \u043d\u0435\u0438\u0437\u0431\u0435\u0436\u043d\u044b\u0439 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0439 \u0441\u043a\u0430\u0447\u043e\u043a \u043f\u0440\u0438 x = 3, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0445\u043e\u0442\u044f \u0431\u044b \u043e\u0434\u0438\u043d \u0431\u043e\u043a\u043e\u0432\u043e\u0439 \u043f\u0440\u0435\u0434\u0435\u043b \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u043f\u0440\u0438\u0432\u043e\u0434\u0438\u0442 \u043a \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\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-89bdb1598b6153cec4e9efce7b0927b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 3^-} f(x)=+\\infty \\qquad \\lim_{x \\to 3^+} f(x)=-\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"300\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-109\"><strong> <\/strong><\/div>\n<p><strong><br \/><\/strong><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u0417\u0434\u0435\u0441\u044c \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u043a\u0430\u043a\u0438\u0435 \u0432\u0438\u0434\u044b \u0440\u0430\u0437\u0440\u044b\u0432\u043e\u0432 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0432\u0441\u0435\u0445 \u0442\u0438\u043f\u043e\u0432 \u0440\u0430\u0437\u0440\u044b\u0432\u043e\u0432 \u0438 \u043f\u043e\u0442\u0440\u0435\u043d\u0438\u0440\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u043d\u0430 \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0445 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f\u0445 \u043d\u0430 \u0442\u0438\u043f\u044b \u0440\u0430\u0437\u0440\u044b\u0432\u043e\u0432 \u0444\u0443\u043d\u043a\u0446\u0438\u0439. \u041a\u0430\u043a\u043e\u0432\u044b \u0432\u0441\u0435 \u0432\u0438\u0434\u044b \u0440\u0430\u0437\u0440\u044b\u0432\u043e\u0432? \u0420\u0430\u0437\u043b\u0438\u0447\u0430\u044e\u0442 \u0442\u0440\u0438 \u0442\u0438\u043f\u0430 \u0440\u0430\u0437\u0440\u044b\u0432\u043e\u0432, \u0430 \u0438\u043c\u0435\u043d\u043d\u043e: \u041f\u0440\u0435\u043e\u0434\u043e\u043b\u0438\u043c\u044b\u0439 \u0440\u0430\u0437\u0440\u044b\u0432 : \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 \u043d\u0435 \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u044e\u0442 \u0441\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u041d\u0435\u0438\u0437\u0431\u0435\u0436\u043d\u044b\u0439 \u0440\u0430\u0437\u0440\u044b\u0432 \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0433\u043e \u0441\u043a\u0430\u0447\u043a\u0430 : \u0411\u043e\u043a\u043e\u0432\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ru\/%d1%82%d0%b8%d0%bf%d1%8b-%d1%80%d0%b0%d0%b7%d1%80%d1%8b%d0%b2%d0%be%d0%b2\/\"> <span class=\"screen-reader-text\">\u0422\u0438\u043f\u044b \u0440\u0430\u0437\u0440\u044b\u0432\u043e\u0432<\/span> \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 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