{"id":29538,"date":"2024-11-18T02:30:46","date_gmt":"2024-11-18T02:30:46","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=29538"},"modified":"2024-11-18T02:37:59","modified_gmt":"2024-11-18T02:37:59","slug":"%d8%a7%d9%84%d8%ae%d8%b7%d9%88%d8%b7-%d8%a7%d9%84%d9%85%d9%82%d8%a7%d8%b1%d8%a8%d8%a9%d8%8c-%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d9%88%d8%aa%d9%82%d9%86%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%aa%d9%85","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d8%ae%d8%b7%d9%88%d8%b7-%d8%a7%d9%84%d9%85%d9%82%d8%a7%d8%b1%d8%a8%d8%a9%d8%8c-%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d9%88%d8%aa%d9%82%d9%86%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d8%aa%d9%85\/","title":{"rendered":"\u0627\u0644\u062e\u0637\u0648\u0637 \u0627\u0644\u0645\u0642\u0627\u0631\u0628\u0629\u060c \u0627\u0644\u062d\u062f\u0648\u062f \u0648\u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u064a"},"content":{"rendered":"<style>\n    p {\n    text-align:justify;\n    }\n<\/style>\n<h1 style=\"text-align:center;\">\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a\u060c \u0627\u0644\u062d\u062f\u0648\u062f \u0648\u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u064a<\/h1>\n<p style=\"text-align:center;\"><em><strong>\u0645\u0644\u062e\u0635:<\/strong><br \/>\n\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629 \u062a\u062a\u0645 \u0645\u0646\u0627\u0642\u0634\u0629 \u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0648\u0627\u0644\u0645\u0635\u0637\u0644\u062d\u0627\u062a \u0627\u0644\u063a\u0627\u0644\u0628\u0629 \u0641\u064a \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u062f\u0648\u0627\u0644. \u064a\u062a\u0645 \u0627\u0633\u062a\u0643\u0634\u0627\u0641 \u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0623\u0641\u0642\u064a\u0629\u060c \u0627\u0644\u062a\u064a \u062a\u0648\u0635\u0641 \u0633\u0644\u0648\u0643 \u0627\u0644\u062f\u0627\u0644\u0629 \u0639\u0646\u062f\u0645\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u064a\u0645\u064a\u0644 \u0625\u0644\u0649 \u0627\u0644\u0645\u0627\u0644\u0627\u0646\u0647\u0627\u064a\u0629\u061b \u0648\u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0631\u0623\u0633\u064a\u0629\u060c \u0627\u0644\u062a\u064a \u062a\u062f\u0644 \u0639\u0644\u0649 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629 \u0639\u0646\u062f\u0645\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u064a\u0642\u062a\u0631\u0628 \u0645\u0646 \u0642\u064a\u0645 \u0645\u0639\u064a\u0646\u0629\u061b \u0648\u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0645\u0627\u0626\u0644\u0629\u060c \u0627\u0644\u0647\u0627\u0645\u0629 \u0641\u064a \u062d\u0627\u0644\u0629 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0646\u0633\u0628\u064a\u0629 \u0639\u0646\u062f\u0645\u0627 \u064a\u0641\u0648\u0642 \u062f\u0631\u062c\u0629 \u0627\u0644\u0628\u0633\u0637 \u062f\u0631\u062c\u0629 \u0627\u0644\u0645\u0642\u0627\u0645. \u064a\u062a\u0645 \u0643\u0630\u0644\u0643 \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u0635\u0637\u0644\u062d \u0627\u0644\u063a\u0627\u0644\u0628 \u0644\u062f\u0627\u0644\u0629\u060c \u0627\u0644\u0630\u064a \u064a\u0648\u0641\u0631 \u062a\u0642\u0631\u064a\u0628\u0627 \u0644\u0642\u064a\u0645 \u0643\u0628\u064a\u0631\u0629 \u0623\u0648 \u0642\u0631\u064a\u0628\u0629 \u0645\u0646 \u0642\u064a\u0645 \u0645\u0639\u064a\u0646\u0629 \u0644\u0644\u0645\u062a\u063a\u064a\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span>.<\/em><\/p>\n<p style=\"text-align:center;\"><strong>\u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0645<\/strong><br \/>\n\u0639\u0646\u062f \u0627\u0646\u062a\u0647\u0627\u0621 \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0633\u064a\u0643\u0648\u0646 \u0627\u0644\u0637\u0627\u0644\u0628 \u0642\u0627\u062f\u0631\u0627 \u0639\u0644\u0649:\n<\/p>\n<ol>\n<li><strong>\u0627\u0633\u062a\u064a\u0639\u0627\u0628<\/strong> \u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0623\u0641\u0642\u064a\u0629 \u0648\u062a\u0637\u0628\u064a\u0642\u0647\u0627 \u0641\u064a \u062a\u062d\u0644\u064a\u0644 \u0633\u0644\u0648\u0643 \u0627\u0644\u062f\u0648\u0627\u0644 \u0639\u0646\u062f\u0645\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u064a\u0645\u064a\u0644 \u0625\u0644\u0649 \u0627\u0644\u0645\u0627\u0644\u0627\u0646\u0647\u0627\u064a\u0629.<\/li>\n<li><strong>\u062a\u062d\u062f\u064a\u062f<\/strong> \u0627\u0644\u0634\u0631\u0648\u0637 \u0644\u0648\u062c\u0648\u062f \u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0631\u0623\u0633\u064a\u0629 \u0648\u062a\u0637\u0628\u064a\u0642\u0647\u0627 \u0641\u064a \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u062a\u064a \u0644\u0647\u0627 \u062d\u062f\u0648\u062f \u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629 \u0639\u0646\u062f\u0645\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u064a\u0642\u062a\u0631\u0628 \u0645\u0646 \u0642\u064a\u0645 \u0645\u0639\u064a\u0646\u0629.<\/li>\n<li><strong>\u062a\u062d\u0644\u064a\u0644<\/strong> \u0638\u0647\u0648\u0631 \u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0645\u0627\u0626\u0644\u0629 \u0641\u064a \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0646\u0633\u0628\u064a\u0629 \u0639\u0646\u062f\u0645\u0627 \u064a\u0641\u0648\u0642 \u062f\u0631\u062c\u0629 \u0627\u0644\u0628\u0633\u0637 \u062f\u0631\u062c\u0629 \u0627\u0644\u0645\u0642\u0627\u0645.<\/li>\n<li><strong>\u062a\u0637\u0628\u064a\u0642<\/strong> \u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u0645\u0635\u0637\u0644\u062d \u0627\u0644\u063a\u0627\u0644\u0628 \u0644\u062a\u0642\u0631\u064a\u0628 \u0633\u0644\u0648\u0643 \u0627\u0644\u062f\u0648\u0627\u0644 \u0641\u064a \u0642\u064a\u0645 \u0643\u0628\u064a\u0631\u0629 \u0644\u0644\u0645\u062a\u063a\u064a\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0623\u0648 \u0642\u0631\u064a\u0628\u0629 \u0645\u0646 \u0642\u064a\u0645 \u0645\u0639\u064a\u0646\u0629.<\/li>\n<li><strong>\u062a\u0648\u0636\u064a\u062d<\/strong> \u0643\u064a\u0641 \u064a\u0633\u0627\u0647\u0645 \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0648\u0627\u0644\u0645\u0635\u0637\u0644\u062d\u0627\u062a \u0627\u0644\u063a\u0627\u0644\u0628\u0629 \u0641\u064a \u0641\u0647\u0645 \u0627\u0644\u0633\u0644\u0648\u0643 \u0627\u0644\u0639\u0627\u0645 \u0644\u0644\u062f\u0648\u0627\u0644.<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong><u>\u0641\u0647\u0631\u0633 \u0627\u0644\u0645\u062d\u062a\u0648\u064a\u0627\u062a<\/u>:<\/strong><br \/>\n<a href=\"#1\">\u0645\u0642\u062f\u0645\u0629<\/a><br \/>\n<a href=\"#2\">\u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0623\u0641\u0642\u064a\u0629 \u0648\u0627\u0644\u062d\u062f\u0648\u062f \u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629<\/a><br \/>\n<a href=\"#3\">\u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0631\u0623\u0633\u064a\u0629 \u0648\u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629<\/a><br \/>\n<a href=\"#4\">\u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0645\u0627\u0626\u0644\u0629\u060c \u0627\u0644\u0645\u0646\u062d\u0646\u064a\u0627\u062a \u0648\u0627\u0644\u0645\u0635\u0637\u0644\u062d\u0627\u062a \u0627\u0644\u063a\u0627\u0644\u0628\u0629<\/a><br \/>\n<a href=\"#5\">\u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629<\/a><br \/>\n<a href=\"#6\">\u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u0642\u062a\u0631\u062d\u0629<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/Ekd0oSvMbfE\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u0645\u0642\u062f\u0645\u0629<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=Ekd0oSvMbfE&amp;t=98s\" target=\"_blank\" rel=\"noopener\"><strong>\u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062a\u064a \u0642\u0645\u0646\u0627 \u0628\u0645\u0631\u0627\u062c\u0639\u062a\u0647\u0627<\/strong><\/a> \u062d\u062a\u0649 \u0627\u0644\u0622\u0646 \u062a\u0633\u0645\u062d \u0644\u0646\u0627 \u0628\u062a\u0639\u0631\u064a\u0641 \u0628\u0639\u0636 \u0627\u0644\u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0645\u0641\u064a\u062f\u0629 \u0644\u0641\u0647\u0645 \u0627\u0644\u0633\u0644\u0648\u0643 \u0627\u0644\u0639\u0627\u0645 \u0644\u0644\u062f\u0648\u0627\u0644\u060c \u0648\u0647\u064a \u0627\u0644\u0645\u0635\u0637\u0644\u062d\u0627\u062a \u0627\u0644\u063a\u0627\u0644\u0628\u0629 \u0648\u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0623\u0641\u0642\u064a\u0629 \u0648\u0627\u0644\u0631\u0623\u0633\u064a\u0629\u061b \u0648\u0647\u064a\u060c \u0644\u0646\u0642\u0648\u0644\u060c \u0645\u0646\u062d\u0646\u064a\u0627\u062a \u064a\u062a\u0645 \u0627\u0644\u0627\u0642\u062a\u0631\u0627\u0628 \u0645\u0646\u0647\u0627 \u0645\u0639 \u062a\u0632\u0627\u064a\u062f \u0642\u064a\u0645 \u0627\u0644\u0645\u062a\u063a\u064a\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span>.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0623\u0641\u0642\u064a\u0629 \u0648\u0627\u0644\u062d\u062f\u0648\u062f \u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=Ekd0oSvMbfE&amp;t=137s\" target=\"_blank\" rel=\"noopener\"><strong>\u0625\u0630\u0627 \u0643\u0627\u0646\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u062f\u0627\u0644\u0629 \u0645\u0639\u0631\u0641\u0629 \u0639\u0644\u0649<\/strong><\/a> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">]a,+\\infty[<\/span><\/span>\u060c \u0644\u0628\u0639\u0636 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\in\\mathbb{R}<\/span><\/span>\u060c \u0641\u0625\u0646\u0647 \u064a\u0645\u0643\u0646 \u062d\u0633\u0627\u0628 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0644 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u0639\u0646\u062f\u0645\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u064a\u0645\u064a\u0644 \u0625\u0644\u0649 \u0627\u0644\u0645\u0627\u0644\u0627\u0646\u0647\u0627\u064a\u0629. \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0647\u0630\u0647 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0645\u0648\u062c\u0648\u062f\u0629\u060c \u0641\u0625\u0646 \u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637 \u0627\u0644\u0623\u0641\u0642\u064a \u0625\u0644\u0649 \u0627\u0644\u064a\u0645\u064a\u0646 \u064a\u0639\u0631\u0641 \u0643\u062e\u0637 \u0645\u0639\u0627\u062f\u0644\u0629<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A_+(x) = L^+<\/span><\/span><\/p>\n<p>\u062d\u064a\u062b<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to+\\infty}f(x) = L^+<\/span><\/span><\/p>\n<p>\u0648\u0628\u0627\u0644\u0645\u062b\u0644\u060c \u064a\u064f\u0639\u0631\u0641 \u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637 \u0627\u0644\u0623\u0641\u0642\u064a \u0625\u0644\u0649 \u0627\u0644\u064a\u0633\u0627\u0631 \u0628\u062e\u0637 \u0645\u0639\u0627\u062f\u0644\u0629<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A_-(x) = L^-<\/span><\/span><\/p>\n<p>\u0639\u0646\u062f\u0645\u0627<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to-\\infty}f(x) = L^-<\/span><\/span><\/p>\n<p>\u062a\u0633\u0627\u0639\u062f \u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0623\u0641\u0642\u064a\u0629 \u0641\u064a \u0648\u0635\u0641 \u0633\u0644\u0648\u0643 \u0627\u0644\u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u0639\u0646\u062f\u0645\u0627 \u062a\u0632\u062f\u0627\u062f \u0642\u064a\u0645 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0628\u0644\u0627 \u062d\u062f\u0648\u062f.<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-ckBGkFWse2w\/YH1GWClIciI\/AAAAAAAAE6s\/zZ_se7yShqMLiEHKNT_jkgAWuK9cme5wwCLcBGAsYHQ\/s0\/as%25C3%25ADntotahorizontal.PNG\" alt=\"\u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0623\u0641\u0642\u064a\u0629\" class=\"aligncenter lazyload\" width=\"478\" height=\"290\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-ckBGkFWse2w\/YH1GWClIciI\/AAAAAAAAE6s\/zZ_se7yShqMLiEHKNT_jkgAWuK9cme5wwCLcBGAsYHQ\/s0\/as%25C3%25ADntotahorizontal.PNG\" alt=\"\u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0623\u0641\u0642\u064a\u0629\" class=\"aligncenter lazyload\" width=\"478\" height=\"290\" \/><\/noscript><\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0631\u0623\u0633\u064a\u0629 \u0648\u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=Ekd0oSvMbfE&amp;t=277s\" target=\"_blank\" rel=\"noopener\"><strong>\u0628\u0627\u0644\u0645\u062b\u0644 \u0644\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0623\u0641\u0642\u064a\u0629\u060c<\/strong><\/a> \u062a\u064f\u0639\u0631\u0641 \u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0631\u0623\u0633\u064a\u0629 \u0644\u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u0643\u062e\u0637 \u0645\u0639\u0627\u062f\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x=a<\/span><\/span> \u0639\u0646\u062f\u0645\u0627<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to a}f(x) = +\\infty<\/span><\/span><\/p>\n<p>\u0648\u064a\u0643\u0648\u0646 \u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637 \u0631\u0623\u0633\u064a\u0627\u064b \u0625\u0644\u0649 \u0627\u0644\u0623\u0633\u0641\u0644 \u0625\u0630\u0627<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to a}f(x) = -\\infty<\/span><\/span><\/p>\n<p>\u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u062a\u0643\u0648\u0646 \u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0645\u0646 \u0627\u0644\u064a\u0645\u064a\u0646 \u0623\u0648 \u0645\u0646 \u0627\u0644\u064a\u0633\u0627\u0631 \u062d\u0633\u0628 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0627\u0644\u0645\u0639\u0646\u064a\u0629.<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-ptEipMpyIhc\/YH1VDclyMxI\/AAAAAAAAE60\/LmzpK2HAU7oLpswJQy5_TLIv9jSf9whDwCLcBGAsYHQ\/s0\/asintotavertical.PNG\" alt=\"\u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637 \u0627\u0644\u0631\u0623\u0633\u064a\" class=\" aligncenter lazyload\" width=\"428\" height=\"283\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-ptEipMpyIhc\/YH1VDclyMxI\/AAAAAAAAE60\/LmzpK2HAU7oLpswJQy5_TLIv9jSf9whDwCLcBGAsYHQ\/s0\/asintotavertical.PNG\" alt=\"\u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637 \u0627\u0644\u0631\u0623\u0633\u064a\" class=\" aligncenter lazyload\" width=\"428\" height=\"283\" \/><\/noscript><\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0645\u0627\u0626\u0644\u0629\u060c \u0627\u0644\u0645\u0646\u062d\u0646\u064a\u0627\u062a \u0648\u0627\u0644\u0645\u0635\u0637\u0644\u062d\u0627\u062a \u0627\u0644\u063a\u0627\u0644\u0628\u0629<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=Ekd0oSvMbfE&amp;t=400s\" target=\"_blank\" rel=\"noopener\"><strong>\u0623\u0628\u0633\u0637 \u0638\u0647\u0648\u0631 \u0644\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0645\u0627\u0626\u0644\u0629<\/strong><\/a> \u064a\u062d\u062f\u062b \u0639\u0646\u062f \u0627\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0646\u0633\u0628\u064a\u0629<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\dfrac{P(x)}{Q(x)}<\/span><\/span><\/p>\n<p>\u062d\u064a\u062b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Q(x)<\/span><\/span> \u0647\u0645\u0627 \u0643\u062b\u064a\u0631\u0627\u062a \u062d\u062f\u0648\u062f. \u0639\u0646\u062f\u0645\u0627 \u062a\u0643\u0648\u0646 \u062f\u0631\u062c\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span><\/span> \u0623\u0643\u0628\u0631 \u0645\u0646 \u062f\u0631\u062c\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Q(x)<\/span><\/span>\u060c \u064a\u0645\u0643\u0646 \u0625\u062c\u0631\u0627\u0621 \u0642\u0633\u0645\u0629 \u0643\u062b\u064a\u0631\u0627\u062a \u0627\u0644\u062d\u062f\u0648\u062f \u0644\u064a\u0643\u0648\u0646 \u0627\u0644\u0646\u0627\u062a\u062c \u0634\u064a\u0626\u064b\u0627 \u0645\u0646 \u0627\u0644\u0634\u0643\u0644<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\dfrac{P(x)}{Q(x)} = C(x) + \\dfrac{r(x)}{Q(x)}<\/span><\/span><\/p>\n<p>\u062d\u064a\u062b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span><\/span> \u0647\u0648 \u062e\u0627\u0631\u062c \u0627\u0644\u0642\u0633\u0645\u0629 \u0648<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r(x)<\/span><\/span> \u0647\u0648 \u0627\u0644\u0628\u0627\u0642\u064a. \u0625\u0630\u0627 \u0643\u0627\u0646\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span><\/span> \u0644\u0647\u0627 \u062f\u0631\u062c\u0629 \u062a\u062a\u062c\u0627\u0648\u0632 \u062f\u0631\u062c\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Q(x)<\/span><\/span> \u0628\u0648\u062d\u062f\u0629 \u0648\u0627\u062d\u062f\u0629\u060c \u0641\u0625\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span><\/span> \u0633\u064a\u0643\u0648\u0646 \u0645\u0646 \u0627\u0644\u062f\u0631\u062c\u0629 \u0627\u0644\u0623\u0648\u0644\u0649\u060c \u0623\u064a \u0633\u064a\u0643\u0648\u0646 \u0644\u0647 \u0634\u0643\u0644 \u062e\u0637 \u0648\u064a\u0642\u0627\u0644 \u0625\u0646\u0647 \u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637 \u0645\u0627\u0626\u0644 \u0644\u0644\u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span>.<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-wRTmSl2Z3HE\/YH1dSl-noDI\/AAAAAAAAE68\/og2lPX_ydUUGlxYnn5hgj2mNCSeAPoQKACLcBGAsYHQ\/s0\/asintotaoblicua.PNG\" alt=\"\u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637 \u0627\u0644\u0645\u0627\u0626\u0644\" class=\" aligncenter lazyload\" width=\"404\" height=\"239\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-wRTmSl2Z3HE\/YH1dSl-noDI\/AAAAAAAAE68\/og2lPX_ydUUGlxYnn5hgj2mNCSeAPoQKACLcBGAsYHQ\/s0\/asintotaoblicua.PNG\" alt=\"\u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637 \u0627\u0644\u0645\u0627\u0626\u0644\" class=\" aligncenter lazyload\" width=\"404\" height=\"239\" \/><\/noscript><\/p>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=Ekd0oSvMbfE&amp;t=633s\" target=\"_blank\" rel=\"noopener\"><strong>\u0628\u0634\u0643\u0644 \u0639\u0627\u0645\u060c \u0625\u0630\u0627 \u0643\u0627\u0646\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span><\/span> \u0644\u0647\u0627 \u062f\u0631\u062c\u0629<\/strong><\/a> \u062a\u062a\u062c\u0627\u0648\u0632 \u062f\u0631\u062c\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Q(x)<\/span><\/span> \u0628\u0623\u064a \u0645\u0642\u062f\u0627\u0631\u060c \u0641\u0625\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span><\/span> \u0633\u064a\u0643\u0648\u0646 \u0644\u0647 \u062f\u0631\u062c\u0629 \u062a\u0633\u0627\u0648\u064a \u0627\u0644\u0641\u0631\u0642 \u0628\u064a\u0646 \u062f\u0631\u062c\u0627\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Q(x)<\/span><\/span>\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0633\u064a\u0643\u0648\u0646 \u0641\u064a \u0627\u0644\u0639\u0627\u062f\u0629 \u0645\u0646\u062d\u0646\u064d \u0643\u062b\u064a\u0631 \u0627\u0644\u062d\u062f\u0648\u062f. \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629 \u0644\u0627 \u064a\u064f\u0639\u062a\u0628\u0631 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span><\/span> \u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u064b\u0627\u060c \u0639\u0644\u0649 \u0627\u0644\u0631\u063a\u0645 \u0645\u0646 \u0623\u0646 \u0627\u0644\u0633\u0644\u0648\u0643 \u0627\u0644\u0639\u0627\u0645 \u0644\u0644\u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u0633\u064a\u0643\u0648\u0646 \u00ab\u0627\u0644\u0627\u0642\u062a\u0631\u0627\u0628 \u0628\u0634\u0643\u0644 \u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u064a\u00bb \u0645\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span><\/span> \u0639\u0646\u062f\u0645\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\to\\pm\\infty<\/span><\/span>. \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629\u060c \u064a\u064f\u0642\u0627\u0644 \u0625\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span><\/span> \u0647\u0648 <strong>\u0627\u0644\u0645\u0635\u0637\u0644\u062d \u0627\u0644\u063a\u0627\u0644\u0628 \u0644\u0644\u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u0644\u0642\u064a\u0645 \u0643\u0628\u064a\u0631\u0629 \u0644\u0644\u0645\u062a\u063a\u064a\u0631 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/span>.<\/strong><\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-IEYO071tTuY\/YH1fjR-WWnI\/AAAAAAAAE7E\/ga2rZ02i8QU5R1IMvQB9rpgFuDknAGfbACLcBGAsYHQ\/s0\/terminoDominante.PNG\" alt=\"\u0627\u0644\u0645\u0635\u0637\u0644\u062d \u0627\u0644\u063a\u0627\u0644\u0628 \u0648\u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637 \u0627\u0644\u0631\u0623\u0633\u064a\" class=\" aligncenter lazyload\" width=\"479\" height=\"437\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-IEYO071tTuY\/YH1fjR-WWnI\/AAAAAAAAE7E\/ga2rZ02i8QU5R1IMvQB9rpgFuDknAGfbACLcBGAsYHQ\/s0\/terminoDominante.PNG\" alt=\"\u0627\u0644\u0645\u0635\u0637\u0644\u062d \u0627\u0644\u063a\u0627\u0644\u0628 \u0648\u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637 \u0627\u0644\u0631\u0623\u0633\u064a\" class=\" aligncenter lazyload\" width=\"479\" height=\"437\" \/><\/noscript><\/p>\n<p>\u0645\u0646 \u0627\u0644\u0645\u0645\u0643\u0646 \u0623\u064a\u0636\u064b\u0627 \u0627\u0644\u062a\u062d\u062f\u062b \u0639\u0646 \u0627\u0644\u0645\u0635\u0637\u0644\u062d \u0627\u0644\u063a\u0627\u0644\u0628 \u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0648\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0642\u0631\u064a\u0628\u064b\u0627 \u0645\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\in\\mathbb{R}<\/span><\/span>.<\/p>\n<p>\u0625\u0630\u0627 \u0643\u0627\u0646\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = P(x)\/Q(x) = C(x) + r(x)\/Q(x)<\/span><\/span>\u060c \u062d\u064a\u062b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(x),<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Q(x),<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r(x)<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span><\/span> \u0643\u0644\u0647\u0627 \u0643\u062b\u064a\u0631\u0627\u062a \u062d\u062f\u0648\u062f. \u0625\u0630\u0627 \u0643\u0627\u0646\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to a}f(x) = \\infty<\/span><\/span>\u060c \u0641\u0625\u0646 \u0627\u0644\u0628\u0627\u0642\u064a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r(x)\/Q(x)<\/span><\/span> \u064a\u064f\u0639\u062a\u0628\u0631 <strong>\u0627\u0644\u0645\u0635\u0637\u0644\u062d \u0627\u0644\u063a\u0627\u0644\u0628 \u0644\u0644\u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u0628\u0627\u0644\u0642\u0631\u0628 \u0645\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x=a<\/span><\/span>.<\/strong><\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629<\/h2>\n<h3><strong>\u0627\u0644\u062a\u0645\u0631\u064a\u0646 1:<\/strong><\/h3>\n<p>\u062d\u062f\u062f \u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0623\u0641\u0642\u064a\u0629 \u0648\u0627\u0644\u0631\u0623\u0633\u064a\u0629 \u0644\u0644\u062f\u0627\u0644\u0629<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\dfrac{3x + 1}{x - 2}<\/span><\/span><\/p>\n<p><strong>\u0627\u0644\u062d\u0644:<\/strong><\/p>\n<p>\u0644\u0625\u064a\u062c\u0627\u062f <strong>\u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637 \u0627\u0644\u0623\u0641\u0642\u064a<\/strong>\u060c \u0646\u0642\u0648\u0645 \u0628\u062d\u0633\u0627\u0628 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0644<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u0639\u0646\u062f\u0645\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x \\to \\pm\\infty<\/span><\/span>:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x \\to \\pm\\infty} \\dfrac{3x + 1}{x - 2} = 3<\/span><\/span><\/p>\n<p>\u0644\u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637 \u0627\u0644\u0623\u0641\u0642\u064a \u0647\u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y = 3<\/span><\/span>.<\/p>\n<p>\u0644\u0625\u064a\u062c\u0627\u062f <strong>\u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637 \u0627\u0644\u0631\u0623\u0633\u064a<\/strong>\u060c \u0646\u062d\u062f\u062f \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u062a\u064a \u062a\u062c\u0639\u0644 \u0627\u0644\u0645\u0642\u0627\u0645 \u064a\u0633\u0627\u0648\u064a \u0635\u0641\u0631\u060c \u0623\u064a \u0639\u0646\u062f\u0645\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x = 2<\/span><\/span>.<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x \\to 2^\\pm} \\dfrac{3x + 1}{x - 2} = \\pm\\infty<\/span><\/span><\/p>\n<p>\u0647\u0630\u0627 \u064a\u062f\u0644 \u0639\u0644\u0649 \u0648\u062c\u0648\u062f \u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637 \u0631\u0623\u0633\u064a \u0639\u0646\u062f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x = 2<\/span><\/span>.<\/p>\n<p><strong>\u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0627\u0644\u0646\u0647\u0627\u0626\u064a\u0629:<\/strong> \u0627\u0644\u062f\u0627\u0644\u0629 \u0644\u062f\u064a\u0647\u0627 \u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637 \u0623\u0641\u0642\u064a \u0639\u0646\u062f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y = 3<\/span><\/span> \u0648\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637 \u0631\u0623\u0633\u064a \u0639\u0646\u062f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x = 2<\/span><\/span>.<\/p>\n<h3><strong>\u0627\u0644\u062a\u0645\u0631\u064a\u0646 2:<\/strong><\/h3>\n<p>\u0623\u0648\u062c\u062f \u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0623\u0641\u0642\u064a\u0629 \u0648\u0627\u0644\u0645\u0627\u0626\u0644\u0629\u060c \u0625\u0646 \u0648\u062c\u062f\u062a\u060c \u0644\u0644\u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g(x) = \\frac{2x^2 + 3x + 4}{x + 1}<\/span><\/span>.<\/p>\n<p><strong>\u0627\u0644\u062d\u0644:<\/strong><\/p>\n<p>\u0623\u0648\u0644\u0627\u060c \u0646\u0628\u062d\u062b \u0639\u0646 <strong>\u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637 \u0627\u0644\u0623\u0641\u0642\u064a<\/strong> \u0628\u062d\u0633\u0627\u0628 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0639\u0646\u062f\u0645\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x \\to \\pm\\infty<\/span><\/span>. \u0628\u0645\u0627 \u0623\u0646 \u062f\u0631\u062c\u0629 \u0627\u0644\u0628\u0633\u0637 \u0623\u0643\u0628\u0631 \u0645\u0646 \u062f\u0631\u062c\u0629 \u0627\u0644\u0645\u0642\u0627\u0645\u060c \u0644\u0627 \u064a\u0648\u062c\u062f \u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637 \u0623\u0641\u0642\u064a.<\/p>\n<p>\u0644\u0625\u064a\u062c\u0627\u062f <strong>\u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637 \u0627\u0644\u0645\u0627\u0626\u0644<\/strong>\u060c \u0646\u0642\u0648\u0645 \u0628\u0642\u0633\u0645\u0629 \u0643\u062b\u064a\u0631\u0627\u062a \u0627\u0644\u062d\u062f\u0648\u062f \u0648\u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{2x^2 + 3x + 4}{x + 1} = 2x + 1 + \\dfrac{3}{x + 1}<\/span><\/span><\/p>\n<p>\u0644\u0630\u0644\u0643\u060c \u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637 \u0627\u0644\u0645\u0627\u0626\u0644 \u0647\u0648 \u0627\u0644\u062e\u0637 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y = 2x + 1<\/span><\/span>\u060c \u0648\u0647\u0648 \u0627\u0644\u0645\u0635\u0637\u0644\u062d \u0627\u0644\u063a\u0627\u0644\u0628 \u0644\u0644\u062f\u0627\u0644\u0629.<\/p>\n<p><strong>\u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0627\u0644\u0646\u0647\u0627\u0626\u064a\u0629:<\/strong> \u0627\u0644\u062f\u0627\u0644\u0629 \u0644\u064a\u0633 \u0644\u062f\u064a\u0647\u0627 \u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637 \u0623\u0641\u0642\u064a\u060c \u0648\u0644\u0643\u0646 \u0644\u062f\u064a\u0647\u0627 \u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637 \u0645\u0627\u0626\u0644 \u064a\u0633\u0627\u0648\u064a \u0627\u0644\u062e\u0637 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y = 2x + 1<\/span><\/span>.<\/p>\n<h3><strong>\u0627\u0644\u062a\u0645\u0631\u064a\u0646 3:<\/strong><\/h3>\n<p>\u0627\u062d\u0633\u0628 \u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637 \u0627\u0644\u0631\u0623\u0633\u064a \u0644\u0644\u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h(x) = \\frac{5}{x^2 - 4}<\/span><\/span>.<\/p>\n<p><strong>\u0627\u0644\u062d\u0644:<\/strong><\/p>\n<p>\u0644\u0625\u064a\u062c\u0627\u062f <strong>\u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637 \u0627\u0644\u0631\u0623\u0633\u064a<\/strong>\u060c \u0646\u062d\u062f\u062f \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u062a\u064a \u062a\u062c\u0639\u0644 \u0627\u0644\u0645\u0642\u0627\u0645 \u064a\u0633\u0627\u0648\u064a \u0635\u0641\u0631\u060c \u0623\u064a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x^2 - 4 = 0<\/span><\/span>. \u0647\u0630\u0627 \u064a\u062d\u062f\u062b \u0639\u0646\u062f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x = \\pm 2<\/span><\/span>.<\/p>\n<p>\u0646\u0642\u0648\u0645 \u0628\u062a\u0642\u064a\u064a\u0645 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0644\u0643\u0644 \u0642\u064a\u0645\u0629:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x \\to 2^\\pm} \\dfrac{5}{x^2 - 4} = \\pm\\infty<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x \\to -2^\\pm} \\dfrac{5}{x^2 - 4} = \\pm\\infty<\/span><\/span><\/p>\n<p><strong>\u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0627\u0644\u0646\u0647\u0627\u0626\u064a\u0629:<\/strong> \u0627\u0644\u062f\u0627\u0644\u0629 \u0644\u062f\u064a\u0647\u0627 \u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0631\u0623\u0633\u064a\u0629 \u0639\u0646\u062f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x = 2<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x = -2<\/span><\/span>.<\/p>\n<p><a name=\"6\"><\/a><\/p>\n<h2>\u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u0642\u062a\u0631\u062d\u0629<\/h2>\n<ol>\n<li>\u062d\u0644\u0644 \u0627\u0644\u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\frac{2x^2 - 3x + 1}{x^2 + x - 2}<\/span><\/span>. \u062d\u062f\u062f \u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0623\u0641\u0642\u064a\u0629 \u0648\u0627\u0644\u0631\u0623\u0633\u064a\u0629 \u0648\u0627\u0644\u0645\u0627\u0626\u0644\u0629\u060c \u0625\u0646 \u0648\u062c\u062f\u062a. \u0627\u0634\u0631\u062d \u0643\u0644 \u062e\u0637\u0648\u0629 \u0644\u062a\u0639\u0632\u064a\u0632 \u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0648\u062d\u0633\u0627\u0628 \u0627\u0644\u062d\u062f\u0648\u062f.<\/li>\n<li>\u0642\u064a\u0651\u0645 \u0627\u0644\u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g(x) = \\frac{3x^3 + 2x}{x^2 + 1}<\/span><\/span>. \u062d\u062f\u062f \u0627\u0644\u0645\u0635\u0637\u0644\u062d \u0627\u0644\u063a\u0627\u0644\u0628 \u0639\u0646\u062f\u0645\u0627 \u064a\u0645\u064a\u0644 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0625\u0644\u0649 \u0627\u0644\u0645\u0627\u0644\u0627\u0646\u0647\u0627\u064a\u0629. \u062b\u0645 \u062a\u062d\u0642\u0642 \u0645\u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0647\u0646\u0627\u0643 \u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637 \u0645\u0627\u0626\u0644\u060c \u0645\u0628\u0631\u0631\u0627\u064b \u0625\u062c\u0627\u0628\u062a\u0643.<\/li>\n<li>\u0635\u0645\u0645 \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u062a\u0642\u0631\u064a\u0628\u064a \u0644\u0644\u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h(x) = \\frac{5x - 4}{x + 1}<\/span><\/span>. \u062a\u0636\u0645\u064a\u0646 \u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0623\u0641\u0642\u064a\u0629 \u0648\u0627\u0644\u0631\u0623\u0633\u064a\u0629 \u0648\u0627\u0644\u0645\u0627\u0626\u0644\u0629 (\u0625\u0646 \u0648\u062c\u062f\u062a) \u0648\u062a\u062d\u0644\u064a\u0644 \u0633\u0644\u0648\u0643 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h(x)<\/span><\/span> \u0644\u0642\u064a\u0645 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0627\u0644\u0642\u0635\u0648\u0649.<\/li>\n<li>\u062a\u062d\u0642\u0642 \u0645\u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0627\u0644\u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k(x) = \\frac{x^2 - 4x + 3}{x^2 - 1}<\/span><\/span> \u0644\u062f\u064a\u0647\u0627 \u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0631\u0623\u0633\u064a\u0629. \u0646\u0627\u0642\u0634 \u062f\u0648\u0631 \u0627\u0644\u0645\u0635\u0637\u0644\u062d\u0627\u062a \u0627\u0644\u063a\u0627\u0644\u0628\u0629 \u0641\u064a \u062a\u062d\u0644\u064a\u0644 \u0646\u0647\u0627\u064a\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k(x)<\/span><\/span> \u0639\u0646\u062f \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u062a\u064a \u062a\u0645\u064a\u0644 \u0641\u064a\u0647\u0627 \u0627\u0644\u062f\u0627\u0644\u0629 \u0625\u0644\u0649 \u0627\u0644\u0645\u0627\u0644\u0627\u0646\u0647\u0627\u064a\u0629.<\/li>\n<li>\u0627\u0633\u062a\u0643\u0634\u0641 \u0627\u0644\u0645\u0635\u0637\u0644\u062d\u0627\u062a \u0627\u0644\u063a\u0627\u0644\u0628\u0629 \u0644\u0644\u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m(x) = \\frac{2x^4 + 3x^2 - x + 5}{x^3 - x^2 + 2}<\/span><\/span>. \u062d\u062f\u062f \u0633\u0644\u0648\u0643 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m(x)<\/span><\/span> \u0639\u0646\u062f\u0645\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x \\to \\pm\\infty<\/span><\/span>\u060c \u0648\u0627\u0633\u062a\u0646\u062a\u062c \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0627\u0644\u062f\u0627\u0644\u0629 \u062a\u0642\u062a\u0631\u0628 \u0645\u0646 \u0645\u0646\u062d\u0646\u0649 \u0643\u062b\u064a\u0631 \u0627\u0644\u062d\u062f\u0648\u062f \u0628\u062f\u0644\u0627\u064b \u0645\u0646 \u062e\u0637 \u0645\u0633\u062a\u0642\u064a\u0645.<\/li>\n<li>\u0635\u063a \u062f\u0627\u0644\u0629 \u0646\u0633\u0628\u064a\u0629 \u0645\u0646 \u0627\u062e\u062a\u064a\u0627\u0631\u0643 \u0648\u0648\u0635\u0641 \u0628\u0627\u0644\u062a\u0641\u0635\u064a\u0644 \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0623\u0641\u0642\u064a\u0629 \u0648\u0627\u0644\u0631\u0623\u0633\u064a\u0629 \u0648\u0627\u0644\u0645\u0627\u0626\u0644\u0629\u060c \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0627\u0644\u0645\u0635\u0637\u0644\u062d\u0627\u062a \u0627\u0644\u063a\u0627\u0644\u0628\u0629. \u0642\u062f\u0645 \u0646\u062a\u0627\u0626\u062c\u0643 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0631\u0633\u0648\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a\u0629 \u0644\u062a\u0635\u0648\u0631 \u0643\u0644 \u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a\u060c \u0627\u0644\u062d\u062f\u0648\u062f \u0648\u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u064a \u0645\u0644\u062e\u0635: \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629 \u062a\u062a\u0645 \u0645\u0646\u0627\u0642\u0634\u0629 \u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0648\u0627\u0644\u0645\u0635\u0637\u0644\u062d\u0627\u062a \u0627\u0644\u063a\u0627\u0644\u0628\u0629 \u0641\u064a \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u062f\u0648\u0627\u0644. \u064a\u062a\u0645 \u0627\u0633\u062a\u0643\u0634\u0627\u0641 \u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0623\u0641\u0642\u064a\u0629\u060c \u0627\u0644\u062a\u064a \u062a\u0648\u0635\u0641 \u0633\u0644\u0648\u0643 \u0627\u0644\u062f\u0627\u0644\u0629 \u0639\u0646\u062f\u0645\u0627 \u064a\u0645\u064a\u0644 \u0625\u0644\u0649 \u0627\u0644\u0645\u0627\u0644\u0627\u0646\u0647\u0627\u064a\u0629\u061b \u0648\u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0631\u0623\u0633\u064a\u0629\u060c \u0627\u0644\u062a\u064a \u062a\u062f\u0644 \u0639\u0644\u0649 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629 \u0639\u0646\u062f\u0645\u0627 \u064a\u0642\u062a\u0631\u0628 \u0645\u0646 \u0642\u064a\u0645 \u0645\u0639\u064a\u0646\u0629\u061b \u0648\u0627\u0644\u0623\u0633\u064a\u0645\u0628\u0637\u0648\u0637\u0627\u062a \u0627\u0644\u0645\u0627\u0626\u0644\u0629\u060c \u0627\u0644\u0647\u0627\u0645\u0629 \u0641\u064a \u062d\u0627\u0644\u0629 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0646\u0633\u0628\u064a\u0629 \u0639\u0646\u062f\u0645\u0627 \u064a\u0641\u0648\u0642 \u062f\u0631\u062c\u0629 \u0627\u0644\u0628\u0633\u0637 \u062f\u0631\u062c\u0629 \u0627\u0644\u0645\u0642\u0627\u0645. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":29511,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":15,"footnotes":""},"categories":[860,565],"tags":[],"class_list":["post-29538","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-860","category-565"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0627\u0644\u062e\u0637\u0648\u0637 \u0627\u0644\u0645\u0642\u0627\u0631\u0628\u0629\u060c \u0627\u0644\u062d\u062f\u0648\u062f \u0648\u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u064a - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u0633\u062a\u0633\u0627\u0639\u062f\u0643 \u0647\u0630\u0647 \u0627\u0644\u062f\u0644\u064a\u0644 \u0639\u0644\u0649 \u0641\u0647\u0645 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\u0627\u0644\u062d\u062f\u0648\u062f \u0648\u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u064a\" \/>\n<meta name=\"twitter:description\" content=\"\u0633\u062a\u0633\u0627\u0639\u062f\u0643 \u0647\u0630\u0647 \u0627\u0644\u062f\u0644\u064a\u0644 \u0639\u0644\u0649 \u0641\u0647\u0645 \u0627\u0644\u062e\u0637\u0648\u0637 \u0627\u0644\u0645\u0642\u0627\u0631\u0628\u0629 \u0627\u0644\u0623\u0641\u0642\u064a\u0629 \u0648\u0627\u0644\u0639\u0645\u0648\u062f\u064a\u0629 \u0648\u0627\u0644\u0645\u0627\u0626\u0644\u0629\u060c \u0648\u0643\u064a\u0641\u064a\u0629 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647\u0627 \u0645\u0646 \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u062d\u062f\u0648\u062f.\" \/>\n<meta name=\"twitter:image\" content=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/11\/asintotas.jpg\" \/>\n<meta name=\"twitter:creator\" content=\"@topuranos\" \/>\n<meta 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