{"id":26,"date":"2023-09-17T11:07:18","date_gmt":"2023-09-17T11:07:18","guid":{"rendered":"https:\/\/mathority.org\/ar\/%d8%a3%d9%86%d9%88%d8%a7%d8%b9-%d8%a7%d9%84%d8%a7%d9%86%d9%82%d8%b7%d8%a7%d8%b9%d8%a7%d8%aa\/"},"modified":"2023-09-17T11:07:18","modified_gmt":"2023-09-17T11:07:18","slug":"%d8%a3%d9%86%d9%88%d8%a7%d8%b9-%d8%a7%d9%84%d8%a7%d9%86%d9%82%d8%b7%d8%a7%d8%b9%d8%a7%d8%aa","status":"publish","type":"post","link":"https:\/\/mathority.org\/ar\/%d8%a3%d9%86%d9%88%d8%a7%d8%b9-%d8%a7%d9%84%d8%a7%d9%86%d9%82%d8%b7%d8%a7%d8%b9%d8%a7%d8%aa\/","title":{"rendered":"\u0623\u0646\u0648\u0627\u0639 \u0627\u0644\u0627\u0646\u0642\u0637\u0627\u0639\u0627\u062a"},"content":{"rendered":"<p style=\";text-align:right;direction:rtl\">\u0647\u0646\u0627 \u0633\u0648\u0641 \u062a\u0643\u062a\u0634\u0641 \u0623\u0646\u0648\u0627\u0639 \u0627\u0644\u0627\u0646\u0642\u0637\u0627\u0639\u0627\u062a \u0627\u0644\u0645\u0648\u062c\u0648\u062f\u0629. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0631\u0624\u064a\u0629 \u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u062c\u0645\u064a\u0639 \u0623\u0646\u0648\u0627\u0639 \u0627\u0646\u0642\u0637\u0627\u0639\u0627\u062a \u0627\u0644\u0648\u0638\u0627\u0626\u0641 \u0648\u0633\u062a\u0643\u0648\u0646 \u0642\u0627\u062f\u0631\u064b\u0627 \u0639\u0644\u0649 \u0627\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u0649 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u0645\u062d\u0644\u0648\u0644\u0629 \u0639\u0644\u0649 \u0623\u0646\u0648\u0627\u0639 \u0627\u0646\u0642\u0637\u0627\u0639\u0627\u062a \u0627\u0644\u0648\u0638\u0627\u0626\u0641. <\/p>\n<p style=\";text-align:right;direction:rtl\"><strong><\/strong><\/p>\n<p style=\";text-align:right;direction:rtl\"><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center;text-align:right;direction:rtl\">\n<div id=\"ezoic-pub-ad-placeholder-104\" style=\";text-align:right;direction:rtl\"><strong> <\/strong><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"%c2%bfcuales-son-todos-los-tipos-de-discontinuidades\"><\/span> \u0645\u0627 \u0647\u064a \u062c\u0645\u064a\u0639 \u0623\u0646\u0648\u0627\u0639 \u0627\u0644\u0627\u0646\u0642\u0637\u0627\u0639\u0627\u062a\u061f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0647\u0646\u0627\u0643 \u062b\u0644\u0627\u062b\u0629 \u0623\u0646\u0648\u0627\u0639 \u0645\u0646 \u0627\u0644\u0627\u0646\u0642\u0637\u0627\u0639\u0627\u062a\u060c \u0648\u0647\u064a:<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0644\u0627\u0646\u0642\u0637\u0627\u0639 \u0627\u0644\u0630\u064a \u064a\u0645\u0643\u0646 \u062a\u062c\u0646\u0628\u0647<\/strong> : \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0644\u0644\u062f\u0627\u0644\u0629 \u0639\u0646\u062f \u0646\u0642\u0637\u0629 \u0645\u0627 \u0644\u0627 \u062a\u062a\u0637\u0627\u0628\u0642 \u0645\u0639 \u0642\u064a\u0645\u0629 \u0627\u0644\u0648\u0638\u064a\u0641\u0629.<\/li>\n<li style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0642\u0637\u0627\u0639 \u0627\u0644\u0642\u0641\u0632 \u0627\u0644\u0645\u062d\u062f\u0648\u062f \u0627\u0644\u0630\u064a \u0644\u0627 \u0645\u0641\u0631 \u0645\u0646\u0647<\/strong> : \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0644\u0644\u062f\u0627\u0644\u0629 \u0639\u0646\u062f \u0646\u0642\u0637\u0629 \u0645\u0627 \u0645\u062e\u062a\u0644\u0641\u0629.<\/li>\n<li style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0642\u0637\u0627\u0639 \u0627\u0644\u0642\u0641\u0632\u0629 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629 \u0627\u0644\u062d\u062a\u0645\u064a\u0629<\/strong> : \u0623\u062d\u062f \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0644\u0644\u062f\u0627\u0644\u0629 \u064a\u0639\u0637\u064a \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629 \u0623\u0648 \u063a\u064a\u0631 \u0645\u0648\u062c\u0648\u062f.<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0644\u0625\u0643\u0645\u0627\u0644 \u0641\u0647\u0645 \u0627\u0644\u0645\u0641\u0627\u0647\u064a\u0645\u060c \u0633\u0646\u0634\u0631\u062d \u0643\u0644 \u0646\u0648\u0639 \u0645\u0646 \u0623\u0646\u0648\u0627\u0639 \u0639\u062f\u0645 \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0628\u0645\u0632\u064a\u062f \u0645\u0646 \u0627\u0644\u062a\u0641\u0635\u064a\u0644 \u0648\u0633\u0646\u0631\u0649 \u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0627\u0644\u062f\u0648\u0627\u0644 \u0630\u0627\u062a \u0627\u0644\u0623\u0646\u0648\u0627\u0639 \u0627\u0644\u062b\u0644\u0627\u062b\u0629 \u0645\u0646 \u0627\u0646\u0642\u0637\u0627\u0639\u0627\u062a \u0627\u0644\u0627\u062a\u0635\u0627\u0644.<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"discontinuidad-evitable\"><\/span> \u0627\u0646\u0642\u0637\u0627\u0639 \u064a\u0645\u0643\u0646 \u062a\u062c\u0646\u0628\u0647 <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\"><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center;text-align:right;direction:rtl\">\n<div id=\"ezoic-pub-ad-placeholder-105\" style=\";text-align:right;direction:rtl\"><strong> <\/strong><\/div>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"><strong>\u0627\u0644\u0627\u0646\u0642\u0637\u0627\u0639 \u0627\u0644\u0630\u064a \u064a\u0645\u0643\u0646 \u062a\u062c\u0646\u0628\u0647<\/strong> \u0647\u0648 \u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u0627\u0646\u0642\u0637\u0627\u0639 \u0627\u0644\u0630\u064a \u064a\u0643\u0648\u0646 \u0644\u0647 \u062f\u0627\u0644\u0629 \u0639\u0646\u062f \u0646\u0642\u0637\u0629 \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u062d\u062f \u0645\u0648\u062c\u0648\u062f\u064b\u0627 \u0639\u0646\u062f \u062a\u0644\u0643 \u0627\u0644\u0646\u0642\u0637\u0629 \u0648\u0644\u0643\u0646\u0647 \u0644\u0627 \u064a\u062a\u0637\u0627\u0628\u0642 \u0645\u0639 \u0642\u064a\u0645\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0623\u0648 \u0623\u0646 \u0635\u0648\u0631\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u063a\u064a\u0631 \u0645\u0648\u062c\u0648\u062f\u0629. <\/p>\n<p style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\">\n<div class=\"wp-block-column is-vertically-aligned-top is-layout-flow\" style=\";text-align:right;direction:rtl\">\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=\"\u0627\u0646\u0642\u0637\u0627\u0639 \u0627\u0644\u0648\u0638\u064a\u0641\u0629 \u0627\u0644\u0630\u064a \u064a\u0645\u0643\u0646 \u062a\u062c\u0646\u0628\u0647\" class=\"wp-image-1400\" width=\"276\" height=\"259\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0644\u0647\u0630\u0647 \u0627\u0644\u062f\u0627\u0644\u0629 \u0645\u062a\u0633\u0627\u0648\u064a\u0629 \u0645\u0639 \u0628\u0639\u0636\u0647\u0627 \u0627\u0644\u0628\u0639\u0636\u060c \u0648\u0644\u0643\u0646\u0647\u0627 \u062a\u062e\u062a\u0644\u0641 \u0639\u0646 \u0642\u064a\u0645\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0639\u0646\u062f \u062a\u0644\u0643 \u0627\u0644\u0646\u0642\u0637\u0629. \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0627\u0644\u0648\u0638\u064a\u0641\u0629 \u062a\u0645\u062b\u0644 \u0627\u0646\u0642\u0637\u0627\u0639\u064b\u0627 \u064a\u0645\u0643\u0646 \u062a\u062c\u0646\u0628\u0647. <\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\">\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=\"\u0627\u0646\u0642\u0637\u0627\u0639 \u064a\u0645\u0643\u0646 \u062a\u062c\u0646\u0628\u0647 \u0644\u0648\u0638\u064a\u0641\u0629 \u0628\u062f\u0648\u0646 \u0635\u0648\u0631\u0629\" class=\"wp-image-1401\" width=\"276\" height=\"259\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062f\u0627\u0644\u0629 \u0641\u064a \u0627\u0644\u0645\u062b\u0627\u0644 \u0627\u0644\u0633\u0627\u0628\u0642 \u0644\u0647\u0627 \u0627\u0646\u0642\u0637\u0627\u0639 \u064a\u0645\u0643\u0646 \u062a\u062c\u0646\u0628\u0647 \u0644\u0623\u0646 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0639\u0646\u062f x=a \u0644\u0647\u0627 \u0646\u0641\u0633 \u0627\u0644\u0642\u064a\u0645\u0629\u060c \u0644\u0643\u0646 \u0635\u0648\u0631\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0639\u0646\u062f \u0647\u0630\u0647 \u0627\u0644\u0646\u0642\u0637\u0629 \u063a\u064a\u0631 \u0645\u0648\u062c\u0648\u062f\u0629.<\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0627\u0646\u0638\u0631:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ar\/\u0627\u0644\u062d\u062f\u0648\u062f-\u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629\/\">\u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0644\u0644\u062f\u0627\u0644\u0629<\/a><\/span> <\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"discontinuidad-inevitable-de-salto-finito\"><\/span> \u0627\u0644\u0627\u0646\u0642\u0637\u0627\u0639 \u0627\u0644\u062d\u062a\u0645\u064a \u0644\u0644\u0642\u0641\u0632\u0629 \u0627\u0644\u0645\u062d\u062f\u0648\u062f\u0629 <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\"><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center;text-align:right;direction:rtl\">\n<div id=\"ezoic-pub-ad-placeholder-106\" style=\";text-align:right;direction:rtl\"><strong> <\/strong><\/div>\n<p style=\";text-align:right;direction:rtl\"><strong><br \/><\/strong><\/p>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"><strong>\u0627\u0646\u0642\u0637\u0627\u0639 \u0627\u0644\u0642\u0641\u0632 \u0627\u0644\u0645\u062d\u062f\u0648\u062f \u0627\u0644\u062d\u062a\u0645\u064a<\/strong> \u0647\u0648 \u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u0627\u0646\u0642\u0637\u0627\u0639 \u0627\u0644\u0630\u064a \u064a\u0642\u062f\u0645 \u062f\u0627\u0644\u0629 \u0639\u0646\u062f \u0646\u0642\u0637\u0629 \u0639\u0646\u062f\u0645\u0627 \u062a\u0643\u0648\u0646 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0644\u0644\u062f\u0627\u0644\u0629 \u0639\u0646\u062f \u062a\u0644\u0643 \u0627\u0644\u0646\u0642\u0637\u0629 \u063a\u064a\u0631 \u0645\u062a\u0633\u0627\u0648\u064a\u0629.<\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0644\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0627\u0644\u0645\u062d\u062f\u062f\u0629 \u0645\u062a\u0639\u062f\u062f \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0639\u0646\u062f \u0646\u0642\u0637\u0629 \u062a\u063a\u064a\u064a\u0631 \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0645\u062e\u062a\u0644\u0641\u0629\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0644\u0647\u0627 \u0627\u0646\u0642\u0637\u0627\u0639 \u0642\u0641\u0632\u0629 \u0645\u062d\u062f\u0648\u062f \u0644\u0627 \u0645\u0641\u0631 \u0645\u0646\u0647 \u0639\u0646\u062f \u062a\u0644\u0643 \u0627\u0644\u0646\u0642\u0637\u0629. <\/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=\"\u0627\u0644\u0627\u0646\u0642\u0637\u0627\u0639 \u0627\u0644\u062d\u062a\u0645\u064a \u0644\u0644\u0642\u0641\u0632\u0629 \u0627\u0644\u0645\u062d\u062f\u0648\u062f\u0629\" class=\"wp-image-1406\" width=\"275\" height=\"258\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u064a\u0638\u0647\u0631 \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0639\u062f\u0645 \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0639\u0645\u0648\u0645\u064b\u0627 \u0641\u064a \u0627\u0644\u0648\u0638\u0627\u0626\u0641 \u0627\u0644\u0645\u062d\u062f\u062f\u0629 \u0628\u0627\u0644\u0642\u0637\u0639 (\u0623\u0648 \u0628\u0627\u0644\u0642\u0637\u0639).<\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0627\u0646\u0638\u0631:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ar\">\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u062f\u0627\u0644\u0629 \u0645\u062a\u0639\u062f\u062f\u0629 \u0627\u0644\u062a\u0639\u0631\u064a\u0641<\/a><\/span> <\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"discontinuidad-inevitable-de-salto-infinito\"><\/span> \u0627\u0644\u0642\u0641\u0632\u0629 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629 \u0627\u0646\u0642\u0637\u0627\u0639 \u0644\u0627 \u0645\u0641\u0631 \u0645\u0646\u0647 <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\"><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center;text-align:right;direction:rtl\">\n<div id=\"ezoic-pub-ad-placeholder-107\" style=\";text-align:right;direction:rtl\"><strong> <\/strong><\/div>\n<\/div>\n<p style=\";text-align:right;direction:rtl\">\u0625\u0646 <strong>\u0627\u0646\u0642\u0637\u0627\u0639 \u0627\u0644\u0642\u0641\u0632\u0629 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629 \u0627\u0644\u062d\u062a\u0645\u064a\u0629<\/strong> \u0647\u0648 \u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u0627\u0646\u0642\u0637\u0627\u0639 \u0644\u0647 \u0648\u0638\u064a\u0641\u0629 \u0641\u064a \u0628\u0639\u0636 \u0627\u0644\u0623\u062d\u064a\u0627\u0646 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0623\u062d\u062f \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0639\u0646\u062f \u062a\u0644\u0643 \u0627\u0644\u0646\u0642\u0637\u0629 \u0644\u0627 \u0646\u0647\u0627\u0626\u064a\u064b\u0627 \u0623\u0648 \u063a\u064a\u0631 \u0645\u0648\u062c\u0648\u062f. <\/p>\n<p style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\" style=\";text-align:right;direction:rtl\">\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u064a\u0633\u0631 \u0644\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u064a\u0639\u0637\u064a \u0639\u062f\u062f\u0627 \u062d\u0642\u064a\u0642\u064a\u0627\u060c \u0648\u0644\u0643\u0646 \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u064a\u0645\u0646 \u064a\u0639\u0637\u064a \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629. \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0627\u0644\u0648\u0638\u064a\u0641\u0629 \u062a\u0642\u062f\u0645 \u0627\u0646\u0642\u0637\u0627\u0639\u064b\u0627 \u0644\u0627 \u0646\u0647\u0627\u0626\u064a\u064b\u0627 \u0644\u0644\u0642\u0641\u0632\u0629. <\/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=\"\u0627\u0646\u0642\u0637\u0627\u0639 \u0627\u0644\u0642\u0641\u0632 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\" class=\"wp-image-1411\" width=\"276\" height=\"259\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u064a\u0645\u0643\u0646\u0643 \u0623\u062f\u0646\u0627\u0647 \u0631\u0624\u064a\u0629 \u062f\u0627\u0644\u0629 \u0628\u064a\u0627\u0646\u064a\u0629 \u064a\u0639\u0637\u064a \u062d\u062f\u0627\u0647\u0627 \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0627\u0646 \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0644\u0647\u0627 \u0627\u0646\u0642\u0637\u0627\u0639 \u0644\u0627 \u0646\u0647\u0627\u0626\u064a \u0641\u064a \u0627\u0644\u0642\u0641\u0632. <\/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=\"\u0627\u0646\u0642\u0637\u0627\u0639 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629 \u0644\u0647\" class=\"wp-image-1412\" width=\"276\" height=\"259\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\"> \u064a\u062d\u062f\u062b \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u0627\u0646\u0642\u0637\u0627\u0639 \u0639\u0627\u062f\u0629\u064b \u0641\u064a <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ar\/\u0648\u0638\u064a\u0641\u0629-\u0639\u0642\u0644\u0627\u0646\u064a\u0629\/\">\u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0639\u0642\u0644\u0627\u0646\u064a\u0629 (\u0623\u0648 \u0627\u0644\u0643\u0633\u0631\u064a\u0629)<\/a><\/span> . <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-tipos-de-discontinuidades\"><\/span> \u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629 \u0639\u0644\u0649 \u0623\u0646\u0648\u0627\u0639 \u0627\u0644\u0627\u0646\u0642\u0637\u0627\u0639\u0627\u062a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062a\u0645\u0631\u064a\u0646 1 <\/h3>\n<p style=\";text-align:right;direction:rtl\"><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center;text-align:right;direction:rtl\">\n<div id=\"ezoic-pub-ad-placeholder-108\" style=\";text-align:right;direction:rtl\"><strong> <\/strong><\/div>\n<p style=\";text-align:right;direction:rtl\"><strong><br \/><\/strong><\/p>\n<\/div>\n<p style=\";text-align:right;direction:rtl\">\u062d\u062f\u062f \u0646\u0648\u0639 \u0627\u0646\u0642\u0637\u0627\u0639 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u062a\u0639\u062f\u062f\u0629 \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0639\u0646\u062f \u0627\u0644\u0646\u0642\u0637\u0629 x=3: <\/p>\n<p style=\";text-align:right;direction:rtl\">\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.&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;65&#8243; width=&#8221;232&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/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;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0645\u062c\u0627\u0644 \u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0623\u0648\u0644 \u0645\u0646 \u0627\u0644\u062f\u0627\u0644\u0629<\/p>\n<p style=\";text-align:right;direction:rtl\">\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> \u0645\u062b\u0644 \u0627\u0644\u0642\u0637\u0639\u0629 \u0627\u0644\u062b\u0627\u0646\u064a\u0629<\/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> \u060c \u0643\u0644\u0647\u0627 \u0623\u0631\u0642\u0627\u0645 \u062d\u0642\u064a\u0642\u064a\u0629 \u0644\u0623\u0646\u0647\u0627 \u062f\u0648\u0627\u0644 \u0645\u062a\u0639\u062f\u062f\u0629 \u0627\u0644\u062d\u062f\u0648\u062f.<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0625\u0630\u0646 \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0648\u062d\u064a\u062f\u0629 \u0627\u0644\u062a\u064a \u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u0643\u0648\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0639\u0646\u062f\u0647\u0627 \u063a\u064a\u0631 \u0645\u062a\u0635\u0644\u0629 \u0647\u064a \u0646\u0642\u0637\u0629 \u062a\u0648\u0642\u0641 \u0627\u0644\u062f\u0627\u0644\u0629 \u0645\u062a\u0639\u062f\u062f\u0629 \u0627\u0644\u062a\u0639\u0631\u064a\u0641. \u0648\u0644\u0630\u0644\u0643 \u0633\u0648\u0641 \u0646\u0642\u0648\u0645 \u0628\u062d\u0633\u0627\u0628 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0645\u0631\u062d\u0644\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062d\u062f\u0627\u0646 \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0627\u0646 \u0639\u0646\u062f x=3 \u064a\u0639\u0637\u064a\u0627\u0646 \u0646\u062a\u0627\u0626\u062c \u0645\u062e\u062a\u0644\u0641\u0629. \u0648\u0644\u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0627\u0644\u0646\u0642\u0637\u0629 x=3 \u0647\u064a \u0627\u0646\u0642\u0637\u0627\u0639 \u0642\u0641\u0632\u0629 \u0645\u062d\u062f\u0648\u062f \u0644\u0627 \u0645\u0641\u0631 \u0645\u0646\u0647.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u062a\u0645\u0631\u064a\u0646 2<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0623\u0648\u062c\u062f \u0646\u0648\u0639 \u0627\u0644\u0627\u0646\u0642\u0637\u0627\u0639 \u0627\u0644\u0630\u064a \u062a\u0638\u0647\u0631\u0647 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0643\u0633\u0631\u064a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0639\u0646\u062f \u0646\u0642\u0627\u0637 \u0644\u0627 \u062a\u0646\u062a\u0645\u064a \u0625\u0644\u0649 \u0645\u062c\u0627\u0644\u0647\u0627: <\/p>\n<p style=\";text-align:right;direction:rtl\">\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;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0645\u0646\u0637\u0642\u064a\u064b\u0627\u060c \u0644\u062d\u0644 \u0647\u0630\u0627 \u0627\u0644\u062a\u0645\u0631\u064a\u0646\u060c \u0639\u0644\u064a\u0643 \u0623\u0648\u0644\u064b\u0627 \u0625\u064a\u062c\u0627\u062f \u0645\u062c\u0627\u0644 \u0627\u0644\u062f\u0627\u0644\u0629. \u0648\u0628\u0645\u0627 \u0623\u0646 \u0647\u0630\u0647 \u062f\u0627\u0644\u0629 \u0639\u0642\u0644\u0627\u0646\u064a\u0629\u060c \u0641\u0625\u0646\u0646\u0627 \u0646\u062c\u0639\u0644 \u0627\u0644\u0645\u0642\u0627\u0645 \u064a\u0633\u0627\u0648\u064a 0 \u0648\u0646\u062d\u0644 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0646\u0627\u062a\u062c\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0633\u062a\u0643\u0648\u0646 \u0645\u062a\u0635\u0644\u0629 \u0641\u064a \u062c\u0645\u064a\u0639 \u0627\u0644\u0646\u0642\u0627\u0637 \u0628\u0627\u0633\u062a\u062b\u0646\u0627\u0621 x=-2\u060c \u0644\u0630\u0644\u0643 \u062f\u0639\u0648\u0646\u0627 \u0646\u0631\u0649 \u0645\u0627 \u0647\u0648 \u0646\u0648\u0639 \u0639\u062f\u0645 \u0627\u0644\u0627\u062a\u0635\u0627\u0644 \u0647\u0648 \u0627\u0644\u0646\u0642\u0637\u0629 x=-2. \u0644\u0644\u0642\u064a\u0627\u0645 \u0628\u0630\u0644\u0643\u060c \u0646\u062d\u0633\u0628 \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0639\u0646\u062f \u0627\u0644\u0646\u0642\u0637\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"> \u0644\u0643\u0646\u0646\u0627 \u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u0639\u062f\u0645 \u062a\u062d\u062f\u064a\u062f \u0635\u0641\u0631\u064a \u0628\u064a\u0646 \u0627\u0644\u0635\u0641\u0631\u060c \u0644\u0630\u0644\u0643 \u0646\u0642\u0648\u0645 \u0628\u062a\u062d\u0644\u064a\u0644 \u0643\u062b\u064a\u0631\u0627\u062a \u062d\u062f\u0648\u062f \u0627\u0644\u0628\u0633\u0637 \u0648\u0627\u0644\u0645\u0642\u0627\u0645 \u0648\u0646\u0628\u0633\u0637:<\/p>\n<p style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0622\u0646 \u0646\u062d\u0644 \u0627\u0644\u062d\u062f:<\/p>\n<p style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0641\u0625\u0646 \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0639\u0646\u062f \u0627\u0644\u0646\u0642\u0637\u0629 x=-2 \u0645\u0648\u062c\u0648\u062f\u0629 \u0648\u062a\u0639\u0637\u064a -4. \u0627\u0644\u0622\u0646 \u062f\u0639\u0648\u0646\u0627 \u0646\u062a\u062d\u0642\u0642 \u0645\u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0645\u0648\u062c\u0648\u062f\u064b\u0627 <\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"> \u0639\u0646\u062f \u062d\u0633\u0627\u0628 \u0635\u0648\u0631\u0629 \u0627\u0644\u062f\u0627\u0644\u0629\u060c \u0644\u0627 \u064a\u0645\u0643\u0646 \u062a\u0628\u0633\u064a\u0637 \u0639\u062f\u0645 \u0627\u0644\u062a\u0639\u064a\u064a\u0646 0\/0 \u0648\u0644\u064a\u0633 \u0644\u0647 \u062d\u0644. \u0644\u0630\u0627<\/p>\n<p style=\";text-align:right;direction:rtl\">\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> \u063a\u064a\u0631 \u0645\u0648\u062c\u0648\u062f.<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0627\u0644\u062e\u062a\u0627\u0645\u060c \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0639\u0646\u062f x=-2 \u0645\u0648\u062c\u0648\u062f\u0629\u060c \u0648\u0644\u0643\u0646<\/p>\n<p style=\";text-align:right;direction:rtl\">\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> \u0644\u0627. \u0644\u0630\u0644\u0643\u060c x=-2 \u0647\u0648 \u0627\u0646\u0642\u0637\u0627\u0639 \u064a\u0645\u0643\u0646 \u062a\u062c\u0646\u0628\u0647.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062a\u0645\u0631\u064a\u0646 3 <\/h3>\n<p style=\";text-align:right;direction:rtl\"><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center;text-align:right;direction:rtl\">\n<div id=\"ezoic-pub-ad-placeholder-110\" style=\";text-align:right;direction:rtl\"><strong> <\/strong><\/div>\n<p style=\";text-align:right;direction:rtl\"><strong><br \/><\/strong><\/p>\n<\/div>\n<p style=\";text-align:right;direction:rtl\">\u062a\u062d\u0644\u064a\u0644 \u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0627\u0644\u0648\u0638\u064a\u0641\u0629 \u0627\u0644\u0639\u0642\u0644\u0627\u0646\u064a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\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;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u0645\u0639\u0631\u0641\u0629 \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u062f\u0627\u0644\u0629 \u0645\u062a\u0635\u0644\u0629\u060c \u0639\u0644\u064a\u0646\u0627 \u0623\u0648\u0644\u064b\u0627 \u062d\u0633\u0627\u0628 \u0645\u062c\u0627\u0644\u0647\u0627. \u0648\u0644\u0630\u0644\u0643\u060c \u0641\u0625\u0646\u0646\u0627 \u0646\u062c\u0639\u0644 \u0645\u0642\u0627\u0645 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0643\u0633\u0631\u064a\u0629 \u064a\u0633\u0627\u0648\u064a \u0627\u0644\u0635\u0641\u0631 \u0644\u0645\u0639\u0631\u0641\u0629 \u0627\u0644\u0646\u0642\u0627\u0637 \u0627\u0644\u062a\u064a \u0644\u0627 \u062a\u0646\u062a\u0645\u064a \u0625\u0644\u0649 \u0627\u0644\u0645\u062c\u0627\u0644: <\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0633\u062a\u0643\u0648\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0645\u062a\u0635\u0644\u0629 \u0641\u064a \u062c\u0645\u064a\u0639 \u0627\u0644\u0646\u0642\u0627\u0637 \u0628\u0627\u0633\u062a\u062b\u0646\u0627\u0621 x=5. \u0644\u0630\u0644\u0643 \u062f\u0639\u0648\u0646\u0627 \u0646\u0631\u0649 \u0645\u0627 \u0647\u0648 \u0646\u0648\u0639 \u0639\u062f\u0645 \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 x=5 \u0639\u0646 \u0637\u0631\u064a\u0642 \u062d\u0633\u0627\u0628 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0639\u0646\u062f \u0647\u0630\u0647 \u0627\u0644\u0646\u0642\u0637\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"> \u0646\u062c\u062f \u0623\u0646\u0641\u0633\u0646\u0627 \u0645\u0639 \u0639\u062f\u0645 \u062a\u062d\u062f\u064a\u062f \u0631\u0642\u0645 \u0645\u0642\u0633\u0648\u0645\u064b\u0627 \u0639\u0644\u0649 0. \u0644\u0630\u0644\u0643 \u0646\u062d\u0633\u0628 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0644\u0644\u062f\u0627\u0644\u0629 \u0639\u0646\u062f x=5: <\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u064a\u0633\u0631 \u0644\u0644\u062f\u0627\u0644\u0629 \u0639\u0646\u062f x=5 \u064a\u0639\u0637\u064a \u0633\u0627\u0644\u0628 \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629 \u0648\u0627\u0644\u062d\u062f \u0627\u0644\u0623\u064a\u0645\u0646 \u064a\u0639\u0637\u064a \u0632\u0627\u0626\u062f \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629. \u0648\u0644\u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0644\u0647\u0627 \u0627\u0646\u0642\u0637\u0627\u0639 \u0644\u0627 \u0646\u0647\u0627\u0626\u064a \u0644\u0627 \u0645\u0641\u0631 \u0645\u0646\u0647 \u0639\u0646\u062f x = 5\u060c \u062d\u064a\u062b \u0623\u0646 \u062d\u062f\u064b\u0627 \u062c\u0627\u0646\u0628\u064a\u064b\u0627 \u0648\u0627\u062d\u062f\u064b\u0627 \u0639\u0644\u0649 \u0627\u0644\u0623\u0642\u0644 \u0639\u0646\u062f \u0647\u0630\u0647 \u0627\u0644\u0646\u0642\u0637\u0629 \u064a\u0645\u064a\u0644 \u0625\u0644\u0649 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062a\u0645\u0631\u064a\u0646 4<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u062d\u062f\u062f \u062c\u0645\u064a\u0639 \u0627\u0646\u0642\u0637\u0627\u0639\u0627\u062a \u0627\u0644\u062f\u0627\u0644\u0629 \u0645\u062a\u0639\u062f\u062f\u0629 \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0645\u0648\u0636\u062d\u0629 \u0641\u064a \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a \u0627\u0644\u062a\u0627\u0644\u064a: <\/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=\"\u062d\u0644 \u0627\u0644\u062a\u0645\u0631\u064a\u0646 \u062d\u0627\u0644\u0627\u062a \u0627\u0646\u0642\u0637\u0627\u0639 \u0627\u0644\u0648\u0638\u0627\u0626\u0641\" 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;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u0631\u0633\u0645 \u0627\u0644\u062f\u0627\u0644\u0629 \u064a\u062c\u0628 \u0639\u0644\u064a\u0643 \u0631\u0641\u0639 \u0642\u0644\u0645 \u0627\u0644\u0631\u0635\u0627\u0635 \u0639\u0646\u062f x=-2\u060c \u0639\u0646\u062f x=1 \u0648\u0639\u0646\u062f x=4. \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0627\u0644\u0648\u0638\u064a\u0641\u0629 \u0645\u062a\u0642\u0637\u0639\u0629 \u0639\u0646\u062f \u0647\u0630\u0647 \u0627\u0644\u0646\u0642\u0627\u0637 \u0627\u0644\u062b\u0644\u0627\u062b.<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0639\u0646\u062f x=-2\u060c \u062d\u062f \u0627\u0644\u062c\u0627\u0646\u0628 \u0627\u0644\u0623\u064a\u0633\u0631 \u0647\u0648 +\u221e \u0648\u062d\u062f \u0627\u0644\u062c\u0627\u0646\u0628 \u0627\u0644\u0623\u064a\u0645\u0646 \u0647\u0648 3. \u0644\u0630\u0627\u060c \u0646\u0638\u0631\u064b\u0627 \u0644\u0623\u0646 \u0623\u062d\u062f \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0644\u0627 \u0646\u0647\u0627\u0626\u064a\u060c \u0641\u0625\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0644\u0647\u0627 \u0627\u0646\u0642\u0637\u0627\u0639 \u0642\u0641\u0632 \u0644\u0627 \u0646\u0647\u0627\u0626\u064a \u0644\u0627 \u0645\u0641\u0631 \u0645\u0646\u0647 \u0639\u0646\u062f x=-2.<\/p>\n<p style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"> \u062d\u062f \u0627\u0644\u062f\u0627\u0644\u0629 \u0639\u0646\u062f x=1 \u0647\u0648 0\u060c \u0648\u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u0642\u064a\u0645\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0639\u0646\u062f x=1 \u062a\u0633\u0627\u0648\u064a 2. \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u062a\u0645\u062b\u0644 \u0627\u0646\u0642\u0637\u0627\u0639\u064b\u0627 \u064a\u0645\u0643\u0646 \u062a\u062c\u0646\u0628\u0647 \u0639\u0646\u062f x=1. <\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"> \u0639\u0646\u062f x = 4\u060c \u062d\u062f \u0627\u0644\u062c\u0627\u0646\u0628 \u0627\u0644\u0623\u064a\u0633\u0631 \u0647\u0648 -3 \u0648\u062d\u062f \u0627\u0644\u062c\u0627\u0646\u0628 \u0627\u0644\u0623\u064a\u0645\u0646 \u0647\u0648 1. \u0644\u0630\u0644\u0643\u060c \u0646\u0638\u0631\u064b\u0627 \u0644\u0623\u0646 \u0627\u0644\u062d\u062f\u064a\u0646 \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u064a\u0646 \u0645\u062e\u062a\u0644\u0641\u0627\u0646 \u0648\u0644\u0627 \u064a\u0639\u0637\u064a \u0623\u064a \u0645\u0646\u0647\u0645\u0627 \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629\u060c \u0641\u0625\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0644\u0647\u0627 \u062d\u062a\u0645\u0627\u064b \u0627\u0646\u0642\u0637\u0627\u0639 \u0642\u0641\u0632 \u0645\u062d\u062f\u0648\u062f \u0639\u0646\u062f x =4. <\/p>\n<p style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\">\u0627\u0644\u062a\u0645\u0631\u064a\u0646 5<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0623\u0648\u062c\u062f \u062c\u0645\u064a\u0639 \u0627\u0644\u062e\u0637\u0648\u0637 \u0627\u0644\u0645\u0642\u0627\u0631\u0628\u0629 \u0648\u0627\u0644\u0627\u0646\u0642\u0637\u0627\u0639\u0627\u062a \u0644\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u0645\u062b\u0644\u0629 \u0641\u064a \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a \u0627\u0644\u062a\u0627\u0644\u064a: <\/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=\"\u062d\u0644 \u062a\u0645\u0631\u064a\u0646 \u062d\u0648\u0644 \u0623\u0646\u0648\u0627\u0639 \u0627\u0646\u0642\u0637\u0627\u0639\u0627\u062a \u0627\u0644\u062f\u0627\u0644\u0629\" 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;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> <strong><span style=\"text-decoration: underline;\">\u0627\u0644\u062e\u0637\u0648\u0637 \u0627\u0644\u0645\u0642\u0627\u0631\u0628\u0629<\/span><\/strong><\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062f\u0627\u0644\u0629 \u0642\u0631\u064a\u0628\u0629 \u062c\u062f\u064b\u0627 \u0645\u0646 \u0627\u0644\u062e\u0637 \u0627\u0644\u0631\u0623\u0633\u064a x=3 \u0648\u0644\u0643\u0646\u0647\u0627 \u0644\u0627 \u062a\u0644\u0645\u0633\u0647 \u0623\u0628\u062f\u064b\u0627. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0627\u0644\u062d\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a \u0627\u0644\u0623\u064a\u0633\u0631 \u0639\u0646\u062f x=3 \u0647\u0648 +\u221e \u0648\u0627\u0644\u062d\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a \u0627\u0644\u0623\u064a\u0645\u0646 \u0647\u0648 -\u221e. \u0644\u0630\u0644\u0643\u060c x=3 \u0647\u0648 \u062e\u0637 \u0645\u0642\u0627\u0631\u0628 \u0639\u0645\u0648\u062f\u064a.<\/p>\n<p style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"> \u0648\u064a\u062d\u062f\u062b \u0646\u0641\u0633 \u0627\u0644\u0634\u064a\u0621 \u0645\u0639 \u0627\u0644\u062e\u0637 \u0627\u0644\u0623\u0641\u0642\u064a y=-1\u060c \u062d\u064a\u062b \u062a\u0642\u062a\u0631\u0628 \u0627\u0644\u062f\u0627\u0644\u0629 \u0643\u062b\u064a\u0631\u064b\u0627 \u0645\u0646 y=-1 \u0648\u0644\u0643\u0646\u0647\u0627 \u0644\u0627 \u062a\u062a\u062c\u0627\u0648\u0632\u0647 \u0623\u0628\u062f\u064b\u0627. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0639\u0646\u062f\u0645\u0627 \u062a\u0642\u062a\u0631\u0628 x \u0645\u0646 +\u221e \u0648-\u221e \u0647\u064a -1. \u0644\u0630\u0644\u0643\u060c y=-1 \u0647\u0648 \u062e\u0637 \u0645\u0642\u0627\u0631\u0628 \u0623\u0641\u0642\u064a.<\/p>\n<p style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"> <strong><span style=\"text-decoration: underline;\">\u0627\u0644\u0627\u0646\u0642\u0637\u0627\u0639\u0627\u062a<\/span><\/strong><\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0639\u0646\u062f x=6 \u062a\u0645\u062a \u0645\u0642\u0627\u0637\u0639\u0629 \u0627\u0644\u0648\u0638\u064a\u0641\u0629 \u0628\u0633\u0628\u0628 \u0648\u062c\u0648\u062f \u0646\u0642\u0637\u0629 \u0645\u0641\u062a\u0648\u062d\u0629. \u0627\u0644\u062d\u062f \u0639\u0646\u062f\u0645\u0627 \u062a\u0642\u062a\u0631\u0628 x \u0645\u0646 6 \u0647\u0648 -1.4 \u0644\u0643\u0646 f(6)=1. \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0644\u0647\u0627 \u0627\u0646\u0642\u0637\u0627\u0639 \u064a\u0645\u0643\u0646 \u062a\u062c\u0646\u0628\u0647 \u0639\u0646\u062f x=6 \u0644\u0623\u0646 \u0642\u064a\u0645\u0629 \u0627\u0644\u062d\u062f \u0644\u0627 \u062a\u062a\u0637\u0627\u0628\u0642 \u0645\u0639 \u0642\u064a\u0645\u0629 \u0627\u0644\u062f\u0627\u0644\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\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 style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"> \u0639\u0646\u062f x=-3 \u0644\u0627 \u062a\u062a\u0637\u0627\u0628\u0642 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0648\u0644\u0627 \u0634\u064a\u0621 \u064a\u0639\u0637\u064a \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629. \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0644\u0647\u0627 \u0627\u0646\u0642\u0637\u0627\u0639 \u0642\u0641\u0632\u0629 \u0645\u062d\u062f\u0648\u062f \u0644\u0627 \u0645\u0641\u0631 \u0645\u0646\u0647 \u0639\u0646\u062f x=-3.<\/p>\n<p style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0627\u0644\u062f\u0627\u0644\u0629 \u0644\u0647\u0627 \u0627\u0646\u0642\u0637\u0627\u0639 \u0644\u0627 \u0646\u0647\u0627\u0626\u064a \u0644\u0627 \u0645\u0641\u0631 \u0645\u0646\u0647 \u0639\u0646\u062f x = 3\u060c \u0646\u0638\u0631\u064b\u0627 \u0644\u0623\u0646 \u062d\u062f\u064b\u0627 \u062c\u0627\u0646\u0628\u064a\u064b\u0627 \u0648\u0627\u062d\u062f\u064b\u0627 \u0639\u0644\u0649 \u0627\u0644\u0623\u0642\u0644 \u0639\u0646\u062f \u0647\u0630\u0647 \u0627\u0644\u0646\u0642\u0637\u0629 \u064a\u0624\u062f\u064a \u0625\u0644\u0649 \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629. <\/p>\n<p style=\";text-align:right;direction:rtl\">\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\" style=\";text-align:right;direction:rtl\"><\/div>\n<p style=\";text-align:right;direction:rtl\"><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center;text-align:right;direction:rtl\">\n<div id=\"ezoic-pub-ad-placeholder-109\" style=\";text-align:right;direction:rtl\"><strong> <\/strong><\/div>\n<p style=\";text-align:right;direction:rtl\"><strong><br \/><\/strong><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u0647\u0646\u0627 \u0633\u0648\u0641 \u062a\u0643\u062a\u0634\u0641 \u0623\u0646\u0648\u0627\u0639 \u0627\u0644\u0627\u0646\u0642\u0637\u0627\u0639\u0627\u062a \u0627\u0644\u0645\u0648\u062c\u0648\u062f\u0629. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0631\u0624\u064a\u0629 \u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u062c\u0645\u064a\u0639 \u0623\u0646\u0648\u0627\u0639 \u0627\u0646\u0642\u0637\u0627\u0639\u0627\u062a \u0627\u0644\u0648\u0638\u0627\u0626\u0641 \u0648\u0633\u062a\u0643\u0648\u0646 \u0642\u0627\u062f\u0631\u064b\u0627 \u0639\u0644\u0649 \u0627\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u0649 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u0645\u062d\u0644\u0648\u0644\u0629 \u0639\u0644\u0649 \u0623\u0646\u0648\u0627\u0639 \u0627\u0646\u0642\u0637\u0627\u0639\u0627\u062a \u0627\u0644\u0648\u0638\u0627\u0626\u0641. \u0645\u0627 \u0647\u064a \u062c\u0645\u064a\u0639 \u0623\u0646\u0648\u0627\u0639 \u0627\u0644\u0627\u0646\u0642\u0637\u0627\u0639\u0627\u062a\u061f \u0647\u0646\u0627\u0643 \u062b\u0644\u0627\u062b\u0629 \u0623\u0646\u0648\u0627\u0639 \u0645\u0646 \u0627\u0644\u0627\u0646\u0642\u0637\u0627\u0639\u0627\u062a\u060c \u0648\u0647\u064a: \u0627\u0644\u0627\u0646\u0642\u0637\u0627\u0639 \u0627\u0644\u0630\u064a \u064a\u0645\u0643\u0646 \u062a\u062c\u0646\u0628\u0647 : \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0644\u0644\u062f\u0627\u0644\u0629 \u0639\u0646\u062f \u0646\u0642\u0637\u0629 \u0645\u0627 \u0644\u0627 \u062a\u062a\u0637\u0627\u0628\u0642 \u0645\u0639 \u0642\u064a\u0645\u0629 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ar\/%d8%a3%d9%86%d9%88%d8%a7%d8%b9-%d8%a7%d9%84%d8%a7%d9%86%d9%82%d8%b7%d8%a7%d8%b9%d8%a7%d8%aa\/\"> <span class=\"screen-reader-text\">\u0623\u0646\u0648\u0627\u0639 \u0627\u0644\u0627\u0646\u0642\u0637\u0627\u0639\u0627\u062a<\/span> \u0642\u0631\u0627\u0621\u0629 \u0627\u0644\u0645\u0632\u064a\u062f &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-26","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"<!-- This site is optimized 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