{"id":29574,"date":"2024-11-18T17:33:37","date_gmt":"2024-11-18T17:33:37","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=29574"},"modified":"2024-11-18T17:33:37","modified_gmt":"2024-11-18T17:33:37","slug":"%d8%a7%d9%84%d8%ad%d8%af-%d9%88%d8%a7%d9%84%d8%a7%d8%b3%d8%aa%d9%85%d8%b1%d8%a7%d8%b1%d9%8a%d8%a9","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d8%ad%d8%af-%d9%88%d8%a7%d9%84%d8%a7%d8%b3%d8%aa%d9%85%d8%b1%d8%a7%d8%b1%d9%8a%d8%a9\/","title":{"rendered":"\u0627\u0644\u062d\u062f \u0648\u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629"},"content":{"rendered":"<style>\np {\ntext-align:justify;\n}\n<\/style>\n<p><center><\/p>\n<h1>\u0627\u0644\u062d\u062f \u0648\u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629<\/h1>\n<p><\/center><\/p>\n<p style=\"text-align:center;\"><em><strong>\u0627\u0644\u0645\u0644\u062e\u0635:<\/strong><\/em><br \/>\n\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0646\u062a\u0646\u0627\u0648\u0644 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0628\u064a\u0646 \u0627\u0644\u062d\u062f \u0648\u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0641\u064a \u0627\u0644\u062f\u0627\u0644\u0629\u060c \u0628\u062f\u0621\u064b\u0627 \u0628\u062a\u0641\u0633\u064a\u0631 \u0628\u062f\u064a\u0647\u064a \u0648\u0631\u0633\u0645\u064a \u0644\u0647\u0630\u0627 \u0627\u0644\u0645\u0641\u0647\u0648\u0645. \u0646\u0633\u062a\u0643\u0634\u0641 \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0641\u064a \u0646\u0642\u0637\u0629 \u0648\u0641\u064a \u0645\u062c\u0645\u0648\u0639\u0629\u060c \u0645\u0639 \u0634\u0631\u062d \u0627\u0644\u0634\u0631\u0648\u0637 \u0627\u0644\u0644\u0627\u0632\u0645\u0629 \u0644\u0643\u064a \u062a\u0643\u0648\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0645\u0633\u062a\u0645\u0631\u0629. \u0643\u0645\u0627 \u0646\u0633\u062a\u0639\u0631\u0636 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u062c\u0628\u0631\u064a\u0629 \u0644\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u0633\u062a\u0645\u0631\u0629\u060c \u0628\u0645\u0627 \u0641\u064a \u0630\u0644\u0643 \u0627\u0644\u062c\u0645\u0639\u060c \u0627\u0644\u0636\u0631\u0628\u060c \u0627\u0644\u0642\u0633\u0645\u0629 \u0648\u062a\u0643\u0648\u064a\u0646 \u0627\u0644\u062f\u0648\u0627\u0644. \u0641\u064a \u0627\u0644\u0646\u0647\u0627\u064a\u0629\u060c \u064a\u062a\u0645 \u062d\u0644 \u0623\u0645\u062b\u0644\u0629 \u0639\u0645\u0644\u064a\u0629 \u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u062f\u0648\u0627\u0644 \u0645\u062e\u062a\u0644\u0641\u0629 \u0648\u062d\u0633\u0627\u0628 \u0627\u0644\u062d\u062f\u0648\u062f\u060c \u0648\u0631\u0628\u0637\u0647\u0627 \u0628\u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629.\n<\/p>\n<p style=\"text-align:center;\"><strong>\u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0645:<\/strong><br \/>\n\u0641\u064a \u0646\u0647\u0627\u064a\u0629 \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0633\u064a\u0643\u0648\u0646 \u0627\u0644\u0637\u0627\u0644\u0628 \u0642\u0627\u062f\u0631\u064b\u0627 \u0639\u0644\u0649:<\/p>\n<ol>\n<li><strong>\u062a\u062d\u0644\u064a\u0644<\/strong> \u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u062f\u0627\u0644\u0629 \u0641\u064a \u0646\u0642\u0637\u0629 \u0639\u0646 \u0637\u0631\u064a\u0642 \u0627\u0644\u062a\u062d\u0642\u0642 \u0645\u0646 \u0627\u0644\u0634\u0631\u0648\u0637 \u0627\u0644\u0645\u062d\u062f\u062f\u0629.<\/li>\n<li><strong>\u062a\u0642\u064a\u064a\u0645<\/strong> \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0627\u0644\u062f\u0627\u0644\u0629 \u0645\u0633\u062a\u0645\u0631\u0629 \u0641\u064a \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0639\u064a\u0646\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0631\u0633\u0645\u064a \u0644\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629.<\/li>\n<li><strong>\u0625\u062b\u0628\u0627\u062a<\/strong> \u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u062f\u0627\u0644\u0629 \u0628\u0646\u0627\u0621\u064b \u0639\u0644\u0649 \u062e\u0635\u0627\u0626\u0635\u0647\u0627 \u0627\u0644\u062c\u0628\u0631\u064a\u0629.<\/li>\n<li><strong>\u062a\u0635\u0646\u064a\u0641<\/strong> \u0646\u0642\u0627\u0637 \u0627\u0644\u0627\u0646\u0642\u0637\u0627\u0639 \u0625\u0644\u0649 \u0623\u0646\u0648\u0627\u0639 \u0645\u062e\u062a\u0644\u0641\u0629 \u0648\u0641\u0642\u064b\u0627 \u0644\u0644\u0634\u0631\u0648\u0637 \u063a\u064a\u0631 \u0627\u0644\u0645\u062a\u062d\u0642\u0642\u0629.<\/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\">\u0627\u0644\u0645\u0642\u062f\u0645\u0629<\/a><br \/>\n<a href=\"#2\">\u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0641\u064a \u0646\u0642\u0637\u0629<\/a><br \/>\n<a href=\"#3\">\u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0641\u064a \u0645\u062c\u0645\u0648\u0639\u0629<\/a><br \/>\n<a href=\"#4\">\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u0633\u062a\u0645\u0631\u0629<\/a><br \/>\n<a href=\"#5\">\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/4kehfJcyPRg\" 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>\u0627\u0644\u0645\u0642\u062f\u0645\u0629<\/h2>\n<p ><a href=\"https:\/\/www.youtube.com\/watch?v=4kehfJcyPRg&amp;t=109s\" target=\"_blank\" rel=\"noopener\"><strong>\u0645\u0646 \u0627\u0644\u0646\u0627\u062d\u064a\u0629 \u0627\u0644\u0628\u062f\u064a\u0647\u064a\u0629\u060c \u062a\u064f\u0641\u0647\u0645 \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629<\/strong><\/a> \u0641\u064a \u0627\u0644\u062f\u0627\u0644\u0629 \u0643\u062e\u0627\u0635\u064a\u0629 \u062a\u0633\u0645\u062d \u0628\u0631\u0633\u0645 \u0645\u0646\u062d\u0646\u0627\u0647\u0627 \u00ab\u062f\u0648\u0646 \u0631\u0641\u0639 \u0627\u0644\u0642\u0644\u0645\u00bb. \u0647\u0630\u0647 \u0627\u0644\u0641\u0643\u0631\u0629 \u0627\u0644\u062a\u064a \u064a\u0633\u0647\u0644 \u0641\u0647\u0645\u0647\u0627 \u0628\u062d\u062f \u0630\u0627\u062a\u0647\u0627 \u0644\u064a\u0633\u062a \u0643\u0627\u0641\u064a\u0629 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0647\u062f\u0641 \u0647\u0648 \u0627\u0644\u0635\u0631\u0627\u0645\u0629 \u0641\u064a \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0631\u064a\u0627\u0636\u064a. \u064a\u062c\u0628 \u062a\u062d\u0642\u064a\u0642 \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u062f\u0646\u0649 \u0645\u0646 \u0627\u0644\u0634\u0631\u0648\u0637 \u0627\u0644\u0631\u0633\u0645\u064a\u0629. \u0645\u0646 \u0627\u0644\u0646\u0627\u062d\u064a\u0629 \u0627\u0644\u0631\u0633\u0645\u064a\u0629\u060c \u062a\u0631\u062a\u0628\u0637 \u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0627\u0644\u062f\u0648\u0627\u0644 \u0628\u0634\u0643\u0644 \u0648\u062b\u064a\u0642 \u0628\u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u062d\u062f\u060c \u0648\u0647\u0630\u0627 \u0645\u0627 \u0633\u0646\u062f\u0631\u0633\u0647 \u0628\u0627\u0644\u062a\u0641\u0635\u064a\u0644.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h3>\u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0641\u064a \u0646\u0642\u0637\u0629<\/h3>\n<p ><a href=\"https:\/\/www.youtube.com\/watch?v=4kehfJcyPRg&amp;t=152s\" target=\"_blank\" rel=\"noopener\"><strong>\u0627\u0644\u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u062a\u0643\u0648\u0646 \u0645\u0633\u062a\u0645\u0631\u0629 \u0641\u064a \u0646\u0642\u0637\u0629<\/strong><\/a> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x=x_0<\/span><\/span> \u0625\u0630\u0627 \u0648\u0641\u0642\u0637 \u0625\u0630\u0627 \u062a\u062d\u0642\u0642\u062a \u0627\u0644\u0634\u0631\u0648\u0637 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<ul >\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u0645\u0639\u0631\u0641\u0629 \u0641\u064a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/li>\n<li>\u0627\u0644\u062d\u062f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to x_0} f(x)<\/span><\/span> \u0645\u0648\u062c\u0648\u062f<\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to x_0} f(x) = f(x_0)<\/span><\/span><\/li>\n<\/ul>\n<p >\u064a\u0645\u0643\u0646 \u062a\u0644\u062e\u064a\u0635 \u0630\u0644\u0643 \u0631\u064a\u0627\u0636\u064a\u064b\u0627 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\forall \\epsilon \\gt 0 \\right) \\left(\\exists \\delta \\gt 0 \\right) \\left(0\\lt |x-x_0|\\lt \\delta \\rightarrow |f(x) - f(x_0)|\\lt \\epsilon\\right)<\/span><\/span><\/p>\n<p >\u0647\u0630\u0627 \u0647\u0648 \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0644\u0644\u062d\u062f \u062d\u064a\u062b \u062a\u0645 \u0627\u0633\u062a\u0628\u062f\u0627\u0644 \u0627\u0644\u0642\u064a\u0645\u0629 \u00abL\u00bb \u0628\u0640 \u00abf(<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span>)\u00bb<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h3>\u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0641\u064a \u0645\u062c\u0645\u0648\u0639\u0629<\/h3>\n<p ><a href=\"https:\/\/www.youtube.com\/watch?v=4kehfJcyPRg&amp;t=462s\" target=\"_blank\" rel=\"noopener\"><strong>\u064a\u0645\u0643\u0646 \u062a\u0645\u062f\u064a\u062f \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629<\/strong><\/a> \u0645\u0646 \u0646\u0642\u0637\u0629 \u0648\u0627\u062d\u062f\u0629 \u0625\u0644\u0649 \u062c\u0645\u064a\u0639 \u0627\u0644\u0646\u0642\u0627\u0637 \u062f\u0627\u062e\u0644 \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0639\u064a\u0646\u0629. \u0646\u0642\u0648\u0644 \u0623\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u0645\u0633\u062a\u0645\u0631\u0629 \u062f\u0627\u062e\u0644 \u0645\u062c\u0645\u0648\u0639\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I\\subseteq Dom(f)<\/span><\/span> \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0645\u0633\u062a\u0645\u0631\u0629 \u0639\u0646\u062f \u062c\u0645\u064a\u0639 \u0627\u0644\u0646\u0642\u0627\u0637 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in I<\/span><\/span>. \u064a\u0645\u0643\u0646 \u062a\u0644\u062e\u064a\u0635 \u0630\u0644\u0643 \u0631\u064a\u0627\u0636\u064a\u064b\u0627 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\forall x_0 \\in I\\subseteq Dom(f) \\right)\\left(\\forall \\epsilon \\gt 0 \\right) \\left(\\exists \\delta \\gt 0 \\right) \\left(0\\lt |x-x_0|\\lt \\delta \\rightarrow |f(x) - f(x_0)|\\lt \\epsilon\\right)<\/span><\/span><\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h3>\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u0633\u062a\u0645\u0631\u0629<\/h3>\n<h4>\u0627\u0644\u062c\u0628\u0631 \u0627\u0644\u062e\u0627\u0635 \u0628\u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u0633\u062a\u0645\u0631\u0629<\/h4>\n<p ><a href=\"https:\/\/www.youtube.com\/watch?v=4kehfJcyPRg&amp;t=575s\" target=\"_blank\" rel=\"noopener\"><strong>\u0625\u0630\u0627 \u0643\u0627\u0646\u062a <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">g<\/span> \u062f\u0648\u0627\u0644 \u0645\u0633\u062a\u0645\u0631\u0629<\/strong><\/a> \u0639\u0644\u0649 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I\\subseteq Dom(f)\\cap Dom(g)<\/span><\/span> \u0641\u0625\u0646\u0646\u0627 \u0646\u062d\u0635\u0644 \u0639\u0644\u0649:<\/p>\n<ul >\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f\\pm g<\/span><\/span> \u0645\u0633\u062a\u0645\u0631\u0629 \u0641\u064a <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f\\cdot g<\/span><\/span> \u0645\u0633\u062a\u0645\u0631\u0629 \u0641\u064a <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span><\/li>\n<li>\u0625\u0630\u0627 \u0643\u0627\u0646\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha\\in\\mathbb{R}<\/span><\/span>\u060c \u0641\u0625\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha f<\/span><\/span> \u0645\u0633\u062a\u0645\u0631\u0629 \u0641\u064a <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f\/g<\/span><\/span> \u0645\u0633\u062a\u0645\u0631\u0629 \u0641\u064a <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span> \u0628\u0634\u0631\u0637 \u0623\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g\\neq 0<\/span><\/span><\/li>\n<li>\u0625\u0630\u0627 \u0643\u0627\u0646\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha,\\beta\\in\\mathbb{R}<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta\\neq 0<\/span><\/span>\u060c \u0641\u0625\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^{\\alpha\/\\beta}<\/span><\/span> \u0645\u0633\u062a\u0645\u0631\u0629 \u0641\u064a <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span> \u0628\u0634\u0631\u0637 \u0623\u0646 \u062a\u0643\u0648\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f^{\\alpha\/\\beta}<\/span><\/span> \u0645\u0639\u0631\u0641\u0629 \u062c\u064a\u062f\u064b\u0627 \u0641\u064a <span class=\"katex-eq\" data-katex-display=\"false\">I.<\/span><\/li>\n<\/ul>\n<p >\u062c\u0645\u064a\u0639 \u0647\u0630\u0647 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u062a\u064a \u0642\u062f \u062a\u0628\u062f\u0648 \u0635\u0639\u0628\u0629 \u0627\u0644\u0625\u062b\u0628\u0627\u062a \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0631\u0633\u0645\u064a \u0644\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629\u060c \u0647\u064a \u0641\u064a \u0627\u0644\u0648\u0627\u0642\u0639 \u0633\u0647\u0644\u0629 \u062c\u062f\u064b\u0627 \u0644\u0623\u0646\u0647\u0627 \u062a\u0642\u0631\u064a\u0628\u064b\u0627 \u0645\u0645\u0627\u062b\u0644\u0629 \u0644\u062c\u0628\u0631 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0630\u064a <a href=\"https:\/\/toposuranos.com\/la-definicion-de-limite-demostraciones-y-teoremas\/\" rel=\"noopener\" target=\"_blank\">\u0623\u062b\u0628\u062a\u0646\u0627\u0647 \u0628\u0627\u0644\u0641\u0639\u0644<\/a>\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0646\u0639\u0641\u0649 \u0645\u0646 \u0625\u062b\u0628\u0627\u062a\u0647\u0627 \u0645\u0631\u0629 \u0623\u062e\u0631\u0649.<\/p>\n<h5>\u062a\u0631\u0643\u064a\u0628 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u0633\u062a\u0645\u0631\u0629<\/h5>\n<p >\u0625\u0630\u0627 \u0643\u0627\u0646\u062a <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u0645\u0633\u062a\u0645\u0631\u0629 \u0641\u064a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I\\subseteq Dom(f)<\/span><\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">g<\/span> \u0645\u0633\u062a\u0645\u0631\u0629 \u0641\u064a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(I)<\/span><\/span>\u060c \u0641\u0625\u0646 \u062a\u0631\u0643\u064a\u0628 \u0627\u0644\u062f\u0648\u0627\u0644 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(g\\circ f)(x) = g(f(x))<\/span><\/span> \u064a\u0643\u0648\u0646 \u0645\u0633\u062a\u0645\u0631\u064b\u0627 \u0641\u064a <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span>. \u0647\u0630\u0627\u060c \u0643\u0645\u0627 \u0642\u062f \u064a\u064f\u062a\u0648\u0642\u0639\u060c \u0647\u0648 \u0646\u062a\u064a\u062c\u0629 \u0645\u0628\u0627\u0634\u0631\u0629 \u0644\u0642\u0648\u0627\u0646\u064a\u0646 \u0627\u0644\u062a\u0631\u0643\u064a\u0628 \u0627\u0644\u062e\u0627\u0635\u0629 \u0628\u062d\u062f\u0648\u062f \u0627\u0644\u062f\u0648\u0627\u0644.<\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646<\/h2>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/R91vswfQT_Q\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<ol >\n<li>\u062d\u0644\u0644 \u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u062a\u0627\u0644\u064a\u0629<br \/>\n<table>\n<tbody>\n<tr>\n<td width=\"30\">a.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=\\dfrac{1}{x-2} - 3x<\/span><\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=33s\" target=\"_blank\" rel=\"noopener\"><strong>\u0627\u0644\u062d\u0644<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>b.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=\\dfrac{x+1}{x^2-4x+3}<\/span><\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=97s\" target=\"_blank\" rel=\"noopener\"><strong>\u0627\u0644\u062d\u0644<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>c.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=|x-1| + \\sin(x)<\/span><\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=215s\" target=\"_blank\" rel=\"noopener\"><strong>\u0627\u0644\u062d\u0644<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>d.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=\\dfrac{\\cos(x)}{x}<\/span><\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=450s\" target=\"_blank\" rel=\"noopener\"><strong>\u0627\u0644\u062d\u0644<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>e.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=csc(2x)<\/span><\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=564s\" target=\"_blank\" rel=\"noopener\"><strong>\u0627\u0644\u062d\u0644<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>f.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=\\dfrac{x\\tan(x)}{x^2 + 1}<\/span><\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=666s\" target=\"_blank\" rel=\"noopener\"><strong>\u0627\u0644\u062d\u0644<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>g.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=\\sqrt{2x + 3}<\/span><\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=784s\" target=\"_blank\" rel=\"noopener\"><strong>\u0627\u0644\u062d\u0644<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>h.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=\\dfrac{x+2}{\\cos(x)}<\/span><\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=917s\" target=\"_blank\" rel=\"noopener\"><strong>\u0627\u0644\u062d\u0644<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>i.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=\\dfrac{\\sqrt{x^4 + 1}}{1+\\sin^2(x)}<\/span><\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=952s\" target=\"_blank\" rel=\"noopener\"><strong>\u0627\u0644\u062d\u0644<\/strong><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>\u0627\u062d\u0633\u0628 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062a\u0627\u0644\u064a\u0629. \u0647\u0644 \u0627\u0644\u062f\u0648\u0627\u0644 \u0645\u0633\u062a\u0645\u0631\u0629 \u0641\u064a \u0627\u0644\u0646\u0642\u0627\u0637 \u0627\u0644\u062a\u064a \u062a\u0642\u062a\u0631\u0628 \u0645\u0646\u0647\u0627\u061f<br \/>\n<table>\n<tbody>\n<tr>\n<td width=\"30\">a.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to\\pi} \\sin(x -\\sin(x))<\/span><\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=1033s\" target=\"_blank\" rel=\"noopener\"><strong>\u0627\u0644\u062d\u0644<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>b.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to 0} \\sin\\left(\\dfrac{\\pi}{2}\\cos(\\tan(x)) \\right)<\/span><\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=1092s\" target=\"_blank\" rel=\"noopener\"><strong>\u0627\u0644\u062d\u0644<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>c.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to 1} \\sec\\left(x\\sec^2(x) - \\tan^2(x) -1 \\right)<\/span><\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=1162s\" target=\"_blank\" rel=\"noopener\"><strong>\u0627\u0644\u062d\u0644<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>d.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to 0} \\tan\\left(\\dfrac{\\pi}{4}\\cos\\left(\\sin\\left(x^{1\/3}\\right)\\right) \\right)<\/span><\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=1274s\" target=\"_blank\" rel=\"noopener\"><strong>\u0627\u0644\u062d\u0644<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>e.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to 0} \\cos\\left(\\dfrac{\\pi}{\\sqrt{19 - 3\\sec{2x}}} \\right)<\/span><\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=1424s\" target=\"_blank\" rel=\"noopener\"><strong>\u0627\u0644\u062d\u0644<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>f.<\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to \\pi\/6} \\sqrt{\\csc^2(x) + 5\\sqrt{3}\\tan(x)}<\/span><\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=1505s\" target=\"_blank\" rel=\"noopener\"><strong>\u0627\u0644\u062d\u0644<\/strong><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u0627\u0644\u062d\u062f \u0648\u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0627\u0644\u0645\u0644\u062e\u0635: \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0646\u062a\u0646\u0627\u0648\u0644 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0628\u064a\u0646 \u0627\u0644\u062d\u062f \u0648\u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0641\u064a \u0627\u0644\u062f\u0627\u0644\u0629\u060c \u0628\u062f\u0621\u064b\u0627 \u0628\u062a\u0641\u0633\u064a\u0631 \u0628\u062f\u064a\u0647\u064a \u0648\u0631\u0633\u0645\u064a \u0644\u0647\u0630\u0627 \u0627\u0644\u0645\u0641\u0647\u0648\u0645. \u0646\u0633\u062a\u0643\u0634\u0641 \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0641\u064a \u0646\u0642\u0637\u0629 \u0648\u0641\u064a \u0645\u062c\u0645\u0648\u0639\u0629\u060c \u0645\u0639 \u0634\u0631\u062d \u0627\u0644\u0634\u0631\u0648\u0637 \u0627\u0644\u0644\u0627\u0632\u0645\u0629 \u0644\u0643\u064a \u062a\u0643\u0648\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0645\u0633\u062a\u0645\u0631\u0629. \u0643\u0645\u0627 \u0646\u0633\u062a\u0639\u0631\u0636 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u062c\u0628\u0631\u064a\u0629 \u0644\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u0633\u062a\u0645\u0631\u0629\u060c \u0628\u0645\u0627 \u0641\u064a \u0630\u0644\u0643 \u0627\u0644\u062c\u0645\u0639\u060c \u0627\u0644\u0636\u0631\u0628\u060c \u0627\u0644\u0642\u0633\u0645\u0629 \u0648\u062a\u0643\u0648\u064a\u0646 \u0627\u0644\u062f\u0648\u0627\u0644. \u0641\u064a \u0627\u0644\u0646\u0647\u0627\u064a\u0629\u060c \u064a\u062a\u0645 \u062d\u0644 \u0623\u0645\u062b\u0644\u0629 \u0639\u0645\u0644\u064a\u0629 \u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 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