{"id":29748,"date":"2024-11-27T12:00:15","date_gmt":"2024-11-27T12:00:15","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=29748"},"modified":"2024-11-27T17:36:33","modified_gmt":"2024-11-27T17:36:33","slug":"%d8%a7%d9%84%d9%85%d8%b4%d8%aa%d9%82%d8%a9-%d9%83%d8%ad%d8%af-%d9%84%d8%af%d8%a7%d9%84%d8%a9","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d9%85%d8%b4%d8%aa%d9%82%d8%a9-%d9%83%d8%ad%d8%af-%d9%84%d8%af%d8%a7%d9%84%d8%a9\/","title":{"rendered":"\u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0643\u062d\u062f \u0644\u062f\u0627\u0644\u0629"},"content":{"rendered":"<style>\np {\n    text-align: justify;\n}\n<\/style>\n<h1 style=\"text-align:center;\">\u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0643\u062d\u062f \u0644\u062f\u0627\u0644\u0629<\/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\u060c \u0633\u0646\u0633\u062a\u0643\u0634\u0641 \u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0643\u0623\u062f\u0627\u0629 \u0631\u064a\u0627\u0636\u064a\u0629 \u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u062a\u063a\u064a\u0631\u0627\u062a \u0641\u064a \u0627\u0644\u062f\u0648\u0627\u0644. \u0633\u0646\u0628\u062f\u0623 \u0645\u0646 \u0645\u064a\u0644 \u0627\u0644\u062e\u0637 \u0627\u0644\u0642\u0627\u0637\u0639\u060c \u0648\u0645\u0639 \u0623\u062e\u0630 \u0627\u0644\u062d\u062f \u0639\u0646\u062f\u0645\u0627 \u062a\u0642\u062a\u0631\u0628 \u0627\u0644\u0646\u0642\u0627\u0637\u060c \u0633\u0646\u0639\u0631\u0641 \u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0643\u0645\u064a\u0644 \u0627\u0644\u062e\u0637 \u0627\u0644\u0645\u0645\u0627\u0633. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u0646\u062f\u0631\u0633 \u062e\u0635\u0627\u0626\u0635\u0647\u0627 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0648\u0642\u0648\u0627\u0639\u062f\u0647\u0627 \u0645\u062b\u0644 \u0627\u0644\u062c\u0645\u0639\u060c \u0648\u0627\u0644\u0636\u0631\u0628\u060c \u0648\u0627\u0644\u0642\u0633\u0645\u0629\u060c \u0627\u0644\u062a\u064a \u062a\u0639\u062f \u0623\u0633\u0627\u0633\u064a\u0629 \u0644\u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u0645\u0634\u062a\u0642\u0627\u062a \u0641\u064a \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u062f\u0648\u0627\u0644 \u0648\u0627\u0644\u0638\u0648\u0627\u0647\u0631 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0629.<\/em><\/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\u0627\u064b \u0639\u0644\u0649:\n<\/p>\n<ol>\n<li><strong>\u0641\u0647\u0645<\/strong> \u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0643\u062d\u062f \u064a\u0635\u0641 \u0627\u0644\u062a\u063a\u064a\u0631 \u0627\u0644\u0644\u062d\u0638\u064a \u0641\u064a \u062f\u0627\u0644\u0629 \u0648\u0643\u0645\u064a\u0644 \u0627\u0644\u062e\u0637 \u0627\u0644\u0645\u0645\u0627\u0633 \u0644\u0645\u0646\u062d\u0646\u0649 \u0639\u0646\u062f \u0646\u0642\u0637\u0629.<\/li>\n<li><strong>\u0634\u0631\u062d<\/strong> \u0643\u064a\u0641 \u0623\u0646 \u0627\u0634\u062a\u0642\u0627\u0642\u064a\u0629 \u0627\u0644\u062f\u0648\u0627\u0644 \u062a\u062a\u0636\u0645\u0646 \u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u062a\u0647\u0627.<\/li>\n<li><strong>\u0625\u062b\u0628\u0627\u062a<\/strong> \u0627\u0644\u0642\u0648\u0627\u0639\u062f \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0644\u0644\u0627\u0634\u062a\u0642\u0627\u0642 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0631\u0633\u0645\u064a.<\/li>\n<li><strong>\u0627\u0633\u062a\u062e\u062f\u0627\u0645<\/strong> \u062e\u0635\u0627\u0626\u0635 \u062c\u0628\u0631 \u0627\u0644\u0645\u0634\u062a\u0642\u0627\u062a (\u0627\u0644\u062c\u0645\u0639\u060c \u0627\u0644\u0636\u0631\u0628\u060c \u0648\u0627\u0644\u0642\u0633\u0645\u0629) \u0641\u064a \u0645\u0633\u0627\u0626\u0644 \u0631\u064a\u0627\u0636\u064a\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\"><strong>\u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u0645\u0634\u062a\u0642\u0629<\/strong><\/a><br \/>\n<a href=\"#2\">\u0645\u064a\u0644 \u0627\u0644\u062e\u0637 \u0627\u0644\u0642\u0627\u0637\u0639<\/a><br \/>\n<a href=\"#3\">\u0627\u0644\u0627\u0646\u062a\u0642\u0627\u0644 \u0625\u0644\u0649 \u0627\u0644\u062d\u062f: \u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0648\u0645\u064a\u0644 \u0627\u0644\u062e\u0637 \u0627\u0644\u0645\u0645\u0627\u0633<\/a><br \/>\n<a href=\"#4\">\u062a\u0639\u0631\u064a\u0641 \u0628\u062f\u064a\u0644<\/a><br \/>\n<a href=\"#5\"><strong>\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0645\u0634\u062a\u0642\u0627\u062a<\/strong><\/a><br \/>\n<a href=\"#6\">\u0627\u0644\u0627\u0634\u062a\u0642\u0627\u0642\u064a\u0629 \u062a\u062a\u0636\u0645\u0646 \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629<\/a><br \/>\n<a href=\"#\">\u062c\u0628\u0631 \u0627\u0644\u0645\u0634\u062a\u0642\u0627\u062a<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/TFxATgmYvkY\" 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\u0641\u0647\u0648\u0645 \u0627\u0644\u0645\u0634\u062a\u0642\u0629<\/h2>\n<p>\u062a\u062a\u0645\u064a\u0632 \u0627\u0644\u0637\u0628\u064a\u0639\u0629 \u0628\u0627\u0644\u062a\u063a\u064a\u0631 \u0627\u0644\u0645\u0633\u062a\u0645\u0631\u060c \u0648\u0627\u0644\u0623\u062f\u0627\u0629 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0627\u0644\u0623\u0643\u062b\u0631 \u0623\u0647\u0645\u064a\u0629 \u0644\u062d\u0633\u0627\u0628 \u0648\u0641\u0647\u0645 \u0647\u0630\u0627 \u0627\u0644\u062a\u063a\u064a\u0631 \u0647\u064a \u0627\u0644\u0645\u0634\u062a\u0642\u0629. \u062a\u0646\u0628\u0639 \u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0645\u0646 \u0637\u0631\u062d \u0627\u0644\u0633\u0624\u0627\u0644 \u00ab\u0645\u0627\u0630\u0627 \u0633\u064a\u062d\u062f\u062b \u0644\u0642\u064a\u0645\u0629 \u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u0639\u0646\u062f\u0645\u0627 \u064a\u062a\u0645 \u0632\u064a\u0627\u062f\u0629 \u0623\u0648 \u062a\u0642\u0644\u064a\u0644 \u0627\u0644\u0645\u062a\u063a\u064a\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0628\u0645\u0642\u062f\u0627\u0631 \u0635\u063a\u064a\u0631 \u062c\u062f\u0627\u064b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta x<\/span><\/span>\u061f\u00bb. \u064a\u0638\u0647\u0631 \u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0643\u062d\u062f \u0644\u062f\u0627\u0644\u0629 \u0623\u062b\u0646\u0627\u0621 \u062a\u062d\u0644\u064a\u0644 \u0647\u0630\u0627 \u0627\u0644\u0633\u0624\u0627\u0644.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h3>\u0645\u064a\u0644 \u0627\u0644\u062e\u0637 \u0627\u0644\u0642\u0627\u0637\u0639<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=TFxATgmYvkY&amp;t=164s\" target=\"_blank\" rel=\"noopener\"><strong>\u0644\u0646\u0623\u062e\u0630 \u0641\u064a \u0627\u0644\u0627\u0639\u062a\u0628\u0627\u0631 \u062f\u0627\u0644\u0629<\/strong><\/a> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u0645\u0642\u064a\u0645\u0629 \u0639\u0646\u062f \u0646\u0642\u0637\u062a\u064a\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0 + \\Delta x<\/span><\/span>. \u0623\u064a \u062e\u0637 \u064a\u0642\u0637\u0639 \u0646\u0642\u0637\u062a\u064a\u0646 \u0645\u0646 \u0645\u0646\u062d\u0646\u0649 \u064a\u0633\u0645\u0649 \u00ab\u0627\u0644\u062e\u0637 \u0627\u0644\u0642\u0627\u0637\u0639\u00bb\u060c \u0643\u0645\u0627 \u064a\u0638\u0647\u0631 \u0641\u064a \u0627\u0644\u0634\u0643\u0644.<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/--KZ1YA55iug\/YI_jLiez_RI\/AAAAAAAAFCs\/xYcWyzwUaf88McAiTNK7l6tOSZQKyZFdwCLcBGAsYHQ\/s0\/graficosecante.PNG\" alt=\"\u062e\u0637 \u0642\u0627\u0637\u0639\" class=\" aligncenter lazyload\" width=\"397\" height=\"233\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/--KZ1YA55iug\/YI_jLiez_RI\/AAAAAAAAFCs\/xYcWyzwUaf88McAiTNK7l6tOSZQKyZFdwCLcBGAsYHQ\/s0\/graficosecante.PNG\" alt=\"\u062e\u0637 \u0642\u0627\u0637\u0639\" class=\" aligncenter lazyload\" width=\"397\" height=\"233\" \/><\/noscript><\/p>\n<p>\u0645\u064a\u0644 \u0647\u0630\u0627 \u0627\u0644\u062e\u0637 \u0627\u0644\u0642\u0627\u0637\u0639 \u0647\u0648<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{\\Delta f(x_0)}{\\Delta x} = \\dfrac{f(x_0 + \\Delta x) - f(x_0)}{\\Delta x}<\/span><\/span><\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h3>\u0627\u0644\u0627\u0646\u062a\u0642\u0627\u0644 \u0625\u0644\u0649 \u0627\u0644\u062d\u062f: \u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0648\u0645\u064a\u0644 \u0627\u0644\u062e\u0637 \u0627\u0644\u0645\u0645\u0627\u0633<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=TFxATgmYvkY&amp;t=278s\" target=\"_blank\" rel=\"noopener\"><strong>\u0625\u0630\u0627 \u0627\u0639\u062a\u0628\u0631\u0646\u0627 \u0627\u0644\u062e\u0637 \u0627\u0644\u0642\u0627\u0637\u0639 \u0644\u0645\u0646\u062d\u0646\u0649<\/strong><\/a> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y=f(x)<\/span><\/span> \u0627\u0644\u0630\u064a \u064a\u0645\u0631 \u0639\u0628\u0631 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0 + \\Delta x<\/span><\/span>\u060c \u062b\u0645 \u0623\u062e\u0630\u0646\u0627 \u0627\u0644\u062d\u062f \u062d\u064a\u062b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta x<\/span><\/span> \u064a\u0645\u064a\u0644 \u0625\u0644\u0649 \u0627\u0644\u0635\u0641\u0631\u060c \u0641\u0625\u0646\u0646\u0627 \u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u0627\u0644\u062e\u0637 \u0627\u0644\u0645\u0645\u0627\u0633 \u0627\u0644\u0630\u064a \u064a\u0645\u0631 \u0628\u0627\u0644\u0646\u0642\u0637\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(x_0, f(x_0)).<\/span><\/span><\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-8wCxY7adTBw\/YI_kfLeezzI\/AAAAAAAAFC0\/o6nKbRKv1SISYU3Rx7ML5Rly29edqey3ACLcBGAsYHQ\/s0\/grafico%2Brecta%2Btangente.PNG\" alt=\"\u0631\u0633\u0645 \u0628\u064a\u0627\u0646\u064a \u0644\u0644\u062e\u0637 \u0627\u0644\u0645\u0645\u0627\u0633\" class=\" aligncenter lazyload\" width=\"464\" height=\"268\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-8wCxY7adTBw\/YI_kfLeezzI\/AAAAAAAAFC0\/o6nKbRKv1SISYU3Rx7ML5Rly29edqey3ACLcBGAsYHQ\/s0\/grafico%2Brecta%2Btangente.PNG\" alt=\"\u0631\u0633\u0645 \u0628\u064a\u0627\u0646\u064a \u0644\u0644\u062e\u0637 \u0627\u0644\u0645\u0645\u0627\u0633\" class=\" aligncenter lazyload\" width=\"464\" height=\"268\" \/><\/noscript><\/p>\n<p>\u0645\u0646 \u0647\u0646\u0627 \u062a\u0646\u0634\u0623 \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0631\u0633\u0645\u064a \u0644\u0644\u0645\u0634\u062a\u0642\u0629 \u0644\u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u0639\u0646\u062f \u0646\u0642\u0637\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u0643\u062d\u062f:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\dfrac{df(x_0)}{dx}:= \\lim_{\\Delta x \\to 0}\\dfrac{\\Delta f(x_0)}{\\Delta x} = \\lim_{\\Delta x \\to 0} \\dfrac{f(x_0 + \\Delta x) - f(x_0)}{\\Delta x}<\/span><\/span><\/p>\n<p>\u0648\u0647\u0630\u0627 \u064a\u0645\u062b\u0644 \u0623\u064a\u0636\u0627\u064b \u0645\u064a\u0644 \u0627\u0644\u062e\u0637 \u0627\u0644\u0645\u0645\u0627\u0633 \u0627\u0644\u0630\u064a \u064a\u0645\u0631 \u0628\u0627\u0644\u0646\u0642\u0637\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0.<\/span><\/span><\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h3>\u062a\u0639\u0631\u064a\u0641 \u0628\u062f\u064a\u0644<\/h3>\n<p>\u0637\u0631\u064a\u0642\u0629 \u0628\u062f\u064a\u0644\u0629 \u0644\u062a\u0642\u062f\u064a\u0645 \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0643\u062d\u062f \u064a\u0645\u0643\u0646 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647\u0627 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0627\u0633\u062a\u0628\u062f\u0627\u0644 \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p dir=\"ltr\" style=\"text-align:center\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\nx_i &amp;= x_0\\\\\n\nx_f &amp;= x_i + \\Delta x\n\n\\end{array}\n\n<\/span>\n<p>\u0648\u0628\u0630\u0644\u0643 \u0646\u062c\u062f \u0623\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta x = x_f - x_i<\/span><\/span> \u0648\u064a\u0635\u0628\u062d \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0639\u0644\u0649 \u0627\u0644\u0634\u0643\u0644 \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p dir=\"ltr\" style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\displaystyle \\dfrac{df(x_i)}{dx} &amp;=\\displaystyle \\lim_{\\Delta x \\to 0}\\dfrac{ f(x_i + \\Delta x) - f(x_i)}{\\Delta x}\\\\ \\\\\n\n&amp;=\\displaystyle \\lim_{x_f - x_i \\to 0} \\dfrac{f(x_f) - f(x_i)}{x_f - x_i}\\\\ \\\\\n\n&amp;=\\displaystyle  \\lim_{x_f \\to x_i } \\dfrac{f(x_f) - f(x_i)}{x_f - x_i}\n\n\\end{array}\n\n<\/span>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-GLyWOue8OUs\/YJAHOc_lTOI\/AAAAAAAAFC8\/3IV-onfsq9QC4nyweccS4ZN_O-JlWVz8wCLcBGAsYHQ\/s0\/definicion%2Bderivada%2Bcomo%2Blimite.PNG\" alt=\"\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0643\u062d\u062f \u0645\u0646 \u0645\u064a\u0644 \u0627\u0644\u062e\u0637\u0648\u0637 \u0627\u0644\u0642\u0627\u0637\u0639\u0629\" class=\" aligncenter lazyload\" width=\"469\" height=\"243\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-GLyWOue8OUs\/YJAHOc_lTOI\/AAAAAAAAFC8\/3IV-onfsq9QC4nyweccS4ZN_O-JlWVz8wCLcBGAsYHQ\/s0\/definicion%2Bderivada%2Bcomo%2Blimite.PNG\" alt=\"\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0643\u062d\u062f \u0645\u0646 \u0645\u064a\u0644 \u0627\u0644\u062e\u0637\u0648\u0637 \u0627\u0644\u0642\u0627\u0637\u0639\u0629\" class=\" aligncenter lazyload\" width=\"469\" height=\"243\" \/><\/noscript><\/p>\n<p>\u0643\u0644 \u0645\u0646 \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u064a\u0646 \u0645\u0643\u0627\u0641\u0626\u0627\u0646 \u0648\u064a\u0645\u0643\u0646 \u0627\u0644\u062a\u0628\u062f\u064a\u0644 \u0628\u064a\u0646\u0647\u0645\u0627 \u062d\u0633\u0628 \u0645\u0627 \u064a\u0646\u0627\u0633\u0628 \u0627\u0644\u0633\u064a\u0627\u0642.<\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0645\u0634\u062a\u0642\u0627\u062a<\/h2>\n<p>\u064a\u064f\u0642\u0627\u0644 \u0625\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u0627\u0634\u062a\u0642\u0627\u0642 \u0639\u0646\u062f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u062d\u062f \u0627\u0644\u062a\u0627\u0644\u064a \u0645\u0648\u062c\u0648\u062f\u0627\u064b:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{f(x_0 + \\Delta x) - f(x_0)}{\\Delta x}<\/span><\/span><\/p>\n<p>\u0648\u0633\u0646\u0642\u0648\u0644 \u0625\u0646\u0647\u0627 \u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u0627\u0634\u062a\u0642\u0627\u0642 \u0641\u064a \u0645\u062c\u0645\u0648\u0639\u0629 <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span> \u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u062d\u062f \u0645\u064f\u0639\u0631\u0651\u064e\u0641\u0627\u064b \u0628\u0634\u0643\u0644 \u062c\u064a\u062f \u0644\u0643\u0644 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0 \\in I.<\/span><\/span> \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u0627\u0634\u062a\u0642\u0627\u0642 \u062a\u0645\u062a\u0644\u0643 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p><a name=\"6\"><\/a><\/p>\n<h3>\u0627\u0644\u0627\u0634\u062a\u0642\u0627\u0642\u064a\u0629 \u062a\u0639\u0646\u064a \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=TFxATgmYvkY&amp;t=526s\" target=\"_blank\" rel=\"noopener\"><strong>\u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0627\u0644\u062f\u0627\u0644\u0629 \u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u0627\u0634\u062a\u0642\u0627\u0642 \u0639\u0646\u062f <\/strong><\/a><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span>\u060c \u0641\u0625\u0646\u0647\u0627 \u062a\u0643\u0648\u0646 \u0645\u0633\u062a\u0645\u0631\u0629 \u0639\u0646\u062f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span>. \u064a\u0645\u0643\u0646\u0646\u0627 \u0625\u062b\u0628\u0627\u062a \u0630\u0644\u0643 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u062d\u062c\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p>\u0644\u0643\u064a \u062a\u0643\u0648\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u0645\u0633\u062a\u0645\u0631\u0629 \u0639\u0646\u062f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u064a\u062c\u0628 \u0623\u0646 \u064a\u062a\u062d\u0642\u0642:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to x_0}f(x) = f(x_0) <\/span><\/span><\/p>\n<p>\u0625\u0630\u0627 \u0641\u062d\u0635\u0646\u0627 \u0627\u0644\u062c\u0627\u0646\u0628 \u0627\u0644\u0623\u064a\u0633\u0631 \u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629\u060c \u0633\u0646\u062c\u062f \u0623\u0646:<\/p>\n<p><span dir=\"ltr\"><\/p>\n<p dir=\"ltr\" style=\"text-align:center\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\displaystyle \\lim_{x\\to x_0} f(x) &amp;= \\displaystyle \\lim_{x\\to x_0} \\left[ f(x) + f(x_0) - f(x_0) \\right] \\\\ \\\\\n\n&amp;= \\displaystyle \\lim_{x\\to x_0} \\left[f(x_0) + \\left( f(x)  - f(x_0) \\right) \\right] \\\\ \\\\\n\n&amp;= \\displaystyle \\lim_{x\\to x_0} \\left[f(x_0) + \\left( \\dfrac{f(x)  - f(x_0)}{x- x_0} \\right)(x-x_0)  \\right] \\\\ \\\\\n\n&amp;=f(x_0) +\\displaystyle \\lim_{x\\to x_0} \\left[ \\left( \\dfrac{f(x)  - f(x_0)}{x- x_0} \\right)(x-x_0) \\right] \\\\ \\\\\n\n\\end{array}\n\n<\/span>\n<p><><\/p>\n<p>\u0645\u0646 \u0647\u0646\u0627 \u0646\u062c\u062f \u0623\u0646\u0647 \u0644\u0643\u064a \u062a\u0643\u0648\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u0645\u0633\u062a\u0645\u0631\u0629 \u0639\u0646\u062f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span>\u060c \u064a\u062c\u0628 \u0623\u0646 \u064a\u0643\u0648\u0646 \u0627\u0644\u062d\u062f \u0639\u0644\u0649 \u0627\u0644\u062c\u0647\u0629 \u0627\u0644\u064a\u0645\u0646\u0649 \u0645\u062d\u062f\u062f\u0627\u064b \u0628\u0634\u0643\u0644 \u062c\u064a\u062f\u061b \u0648\u0647\u0630\u0627 \u064a\u062a\u062d\u0642\u0642 \u0625\u0630\u0627 \u0648\u0641\u0642\u0637 \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 x_0} \\dfrac{f(x) - f(x_0)}{x-x_0} =\\dfrac{df(x_0)}{dx}<\/span><\/span><\/p>\n<p>\u0628\u0639\u0628\u0627\u0631\u0629 \u0623\u062e\u0631\u0649\u060c \u0625\u0630\u0627 \u0643\u0627\u0646\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u0627\u0634\u062a\u0642\u0627\u0642 \u0639\u0646\u062f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span>. \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0625\u0630\u0627 \u0643\u0627\u0646\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u0627\u0634\u062a\u0642\u0627\u0642 \u0639\u0646\u062f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span>\u060c \u0641\u0625\u0646\u0647\u0627 \u062a\u0643\u0648\u0646 \u0645\u0633\u062a\u0645\u0631\u0629 \u0639\u0646\u062f \u062a\u0644\u0643 \u0627\u0644\u0646\u0642\u0637\u0629.<\/p>\n<p><a name=\"7\"><\/a><\/p>\n<h3>\u062c\u0628\u0631 \u0627\u0644\u0645\u0634\u062a\u0642\u0627\u062a<\/h3>\n<p>\u0644\u062a\u0643\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u0648<span class=\"katex-eq\" data-katex-display=\"false\">g<\/span> \u062f\u0627\u0644\u062a\u064a\u0646 \u0642\u0627\u0628\u0644\u062a\u064a\u0646 \u0644\u0644\u0627\u0634\u062a\u0642\u0627\u0642 \u0639\u0646\u062f \u062c\u0645\u064a\u0639 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x \\in I<\/span><\/span>\u060c \u0648\u0644\u062a\u0643\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha,\\beta\\in\\mathbb{R}.<\/span><\/span> \u0625\u0630\u0646 \u064a\u062a\u062d\u0642\u0642:<\/p>\n<ol>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{d}{dx} \\left( \\alpha f(x) \\pm \\beta g(x) \\right) = \\alpha \\dfrac{df(x)}{dx} \\pm \\beta\\dfrac{dg(x)}{dx}<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{d}{dx} \\left( f(x) g(x) \\right) = \\dfrac{df(x)}{dx}g(x) + f(x)\\dfrac{dg(x)}{dx}<\/span><\/span><\/li>\n<li>\u0625\u0630\u0627 \u0643\u0627\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g(x)\\neq 0<\/span><\/span>\u060c \u0641\u0625\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{d}{dx} \\left( \\dfrac{f(x)}{g(x)} \\right) = \\dfrac{\\dfrac{df(x)}{dx}g(x) - f(x) \\dfrac{dg(x)}{dx} }{\\left[g(x)\\right]^2}<\/span><\/span><\/li>\n<\/ol>\n<p>\u0643\u0645\u0627 \u0646\u0631\u0649\u060c \u0641\u0625\u0646 \u062c\u0628\u0631 \u0627\u0644\u0645\u0634\u062a\u0642\u0627\u062a \u0644\u064a\u0633 \u0628\u062f\u064a\u0647\u064a\u0627\u064b \u0643\u0645\u0627 \u0642\u062f \u064a\u0628\u062f\u0648 \u0644\u0644\u0648\u0647\u0644\u0629 \u0627\u0644\u0623\u0648\u0644\u0649\u061b \u0648\u0645\u0639 \u0630\u0644\u0643\u060c \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0628\u0631\u0647\u0627\u0646 \u0647\u0630\u0647 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0628\u0633\u0647\u0648\u0644\u0629 \u0646\u0633\u0628\u064a\u0629 \u0645\u0646 \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0645\u0634\u062a\u0642\u0627\u062a \u0643\u062d\u062f\u0648\u062f.<\/p>\n<p><span style=\"color: #000080;\">\u0627\u0644\u0628\u0631\u0647\u0627\u0646:<\/span><\/p>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=TFxATgmYvkY&amp;t=925s\" target=\"_blank\" rel=\"noopener\"><strong>\u0628\u0631\u0647\u0627\u0646 \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u062c\u0645\u0639<\/strong><\/a> \u0647\u0648 \u0643\u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p dir=\"ltr\" style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\dfrac{d}{dx}\\left(\\alpha f(x) \\pm \\beta g(x) \\right) &amp; =\\displaystyle \\lim_{\\Delta x\\to 0} \\dfrac{\\left[\\alpha f(x+\\Delta x) \\pm \\beta g(x+ \\Delta x)\\right] - \\left[\\alpha f(x) \\pm \\beta g(x) \\right]}{\\Delta x} \\\\ \\\\\n\n&amp;= \\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{ \\left[\\alpha f(x+\\Delta x) - \\alpha f(x)\\right] \\pm \\left[\\beta g(x+\\Delta x) - \\beta g(x)\\right]}{\\Delta x} \\\\ \\\\\n\n&amp;= \\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{ \\alpha \\left[ f(x+\\Delta x) -  f(x)\\right] \\pm  \\beta  \\left[ g(x+\\Delta x) - g(x)\\right]}{\\Delta x} \\\\ \\\\\n\n&amp;= \\displaystyle \\alpha \\lim_{\\Delta x \\to 0} \\dfrac{f(x+\\Delta x) -  f(x)}{\\Delta x} \\pm \\beta \\lim_{\\Delta x \\to 0} \\dfrac{ g(x+\\Delta x) -  g(x)}{\\Delta x} \\\\ \\\\\n\n&amp;= \\alpha \\dfrac{df(x)}{dx} \\pm \\beta \\dfrac{dg(x)}{dx}\n\n\\end{array}\n\n<\/span>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=TFxATgmYvkY&amp;t=1059s\" target=\"_blank\" rel=\"noopener\"><strong>\u0623\u0645\u0627 \u0628\u0631\u0647\u0627\u0646 \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u062c\u062f\u0627\u0621<\/strong><\/a> \u0641\u0647\u0648 \u0623\u0643\u062b\u0631 \u062a\u0639\u0642\u064a\u062f\u0627\u064b \u0642\u0644\u064a\u0644\u0627\u064b \u0648\u0644\u0643\u0646\u0647 \u0645\u0628\u0627\u0634\u0631:<\/p>\n<p dir=\"ltr\" style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\dfrac{d}{dx}\\left[f(x)g(x)\\right] &amp;= \\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{f(x+\\Delta x) g(x+\\Delta x) -  f(x) g(x)}{\\Delta x} \\\\ \\\\\n\n&amp;= \\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{f(x+\\Delta x) g(x+\\Delta x) + \\color{red}f(x)g(x+\\Delta x) - f(x)g(x+\\Delta x) \\color{black} - f(x) g(x)}{\\Delta x} \\\\ \\\\\n\n&amp;= \\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{\\left[f(x+\\Delta x) - f(x) \\right] g(x+\\Delta x) + f(x) \\left[g(x+\\Delta x)  - g(x)\\right]}{\\Delta x} \\\\ \\\\\n\n&amp;=\\displaystyle \\lim_{\\Delta x \\to 0} g(x+\\Delta x) \\dfrac{f(x+\\Delta x) - f(x)}{\\Delta x} + f(x)\\lim_{\\Delta x \\to 0} \\dfrac{g(x+\\Delta x) - g(x)}{\\Delta x}\\\\ \\\\\n\n&amp;=\\displaystyle \\lim_{\\Delta x \\to 0} g(x+\\Delta x)\\lim_{\\Delta x \\to 0} \\dfrac{f(x+\\Delta x) - f(x)}{\\Delta x} + f(x)\\lim_{\\Delta x \\to 0} \\dfrac{g(x+\\Delta x) - g(x)}{\\Delta x}\\\\ \\\\\n\n&amp;= g(x) \\dfrac{df(x)}{dx} + f(x)\\dfrac{dg(x)}{dx}\n\n\\end{array}\n\n<\/span>\n<p>\u0647\u0646\u0627 \u0627\u0633\u062a\u0641\u062f\u0646\u0627 \u0645\u0646 \u062d\u0642\u064a\u0642\u0629 \u0623\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">g<\/span> \u062f\u0627\u0644\u0629 \u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u0627\u0634\u062a\u0642\u0627\u0642 \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0645\u0633\u062a\u0645\u0631\u0629\u060c \u0645\u0645\u0627 \u064a\u0639\u0646\u064a \u0623\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{\\Delta x\\to 0 } g(x+\\Delta x) = g(x)<\/span><\/span>. \u0648\u0627\u0633\u062a\u062e\u062f\u0645\u0646\u0627 \u062c\u0628\u0631 \u0627\u0644\u062d\u062f\u0648\u062f \u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0627\u0644\u0628\u0631\u0647\u0627\u0646.<\/p>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=TFxATgmYvkY&amp;t=162s\" target=\"_blank\" rel=\"noopener\"><strong>\u0623\u062e\u064a\u0631\u0627\u064b\u060c \u0628\u0631\u0647\u0627\u0646 \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u0642\u0633\u0645\u0629<\/strong><\/a> \u064a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0646\u062a\u064a\u062c\u0629 \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u062c\u062f\u0627\u0621. \u0644\u062a\u0643\u0646 \u062f\u0627\u0644\u0629 \u0628\u0627\u0644\u0634\u0643\u0644 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k(x) = f(x)\/g(x)<\/span><\/span>\u060c \u062d\u064a\u062b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g(x)\\neq 0<\/span><\/span>. \u0648\u0645\u0646 \u0647\u0646\u0627 \u0646\u062c\u062f:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\dfrac{df(x)}{dx}= \\dfrac{d}{dx}(k(x)g(x)) = \\dfrac{dk(x)}{dx}g(x) + k(x)\\dfrac{dg(x)}{dx}<\/span><\/span><\/p>\n<p>\u0627\u0644\u0622\u0646\u060c \u0628\u062d\u0644 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{dk(x)}{dx}<\/span><\/span> \u0646\u062c\u062f:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{dk(x)}{dx}g(x) = \\dfrac{df(x)}{dx} - k(x)\\dfrac{dg(x)}{dx} = \\dfrac{d}{dx}f(x) - \\dfrac{f(x)}{g(x)}\\dfrac{dg(x)}{dx} <\/span><\/span><\/p>\n<p>\u0648\u0645\u0646 \u0647\u0646\u0627:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\dfrac{d}{dx}\\left(\\dfrac{f(x)}{g(x)}\\right)\n\n &amp;= \\dfrac{dk(x)}{dx} =\\dfrac{1}{g(x)} \\dfrac{df(x)}{dx} - \\dfrac{f(x)}{\\left[g(x)\\right]^2}\\dfrac{dg(x)}{dx} \\\\ \\\\\n\n&amp; = \\dfrac{\\dfrac{df(x)}{dx}g(x) - f(x) \\dfrac{dg(x)}{dx}}{[g(x)]^2}\n\n\\end{array}\n\n<\/span>\n<p>\u0648\u0647\u0648 \u0627\u0644\u0645\u0637\u0644\u0648\u0628 \u0625\u062b\u0628\u0627\u062a\u0647.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0643\u062d\u062f \u0644\u062f\u0627\u0644\u0629 \u0645\u0644\u062e\u0635: \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0633\u0646\u0633\u062a\u0643\u0634\u0641 \u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0643\u0623\u062f\u0627\u0629 \u0631\u064a\u0627\u0636\u064a\u0629 \u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u062a\u063a\u064a\u0631\u0627\u062a \u0641\u064a \u0627\u0644\u062f\u0648\u0627\u0644. \u0633\u0646\u0628\u062f\u0623 \u0645\u0646 \u0645\u064a\u0644 \u0627\u0644\u062e\u0637 \u0627\u0644\u0642\u0627\u0637\u0639\u060c \u0648\u0645\u0639 \u0623\u062e\u0630 \u0627\u0644\u062d\u062f \u0639\u0646\u062f\u0645\u0627 \u062a\u0642\u062a\u0631\u0628 \u0627\u0644\u0646\u0642\u0627\u0637\u060c \u0633\u0646\u0639\u0631\u0641 \u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0643\u0645\u064a\u0644 \u0627\u0644\u062e\u0637 \u0627\u0644\u0645\u0645\u0627\u0633. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u0646\u062f\u0631\u0633 \u062e\u0635\u0627\u0626\u0635\u0647\u0627 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0648\u0642\u0648\u0627\u0639\u062f\u0647\u0627 \u0645\u062b\u0644 \u0627\u0644\u062c\u0645\u0639\u060c \u0648\u0627\u0644\u0636\u0631\u0628\u060c \u0648\u0627\u0644\u0642\u0633\u0645\u0629\u060c \u0627\u0644\u062a\u064a \u062a\u0639\u062f \u0623\u0633\u0627\u0633\u064a\u0629 \u0644\u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u0645\u0634\u062a\u0642\u0627\u062a \u0641\u064a \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u062f\u0648\u0627\u0644 \u0648\u0627\u0644\u0638\u0648\u0627\u0647\u0631 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0629. \u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0645 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":29706,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":1,"footnotes":""},"categories":[860,565],"tags":[],"class_list":["post-29748","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 - 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