{"id":27941,"date":"2024-08-16T13:00:37","date_gmt":"2024-08-16T13:00:37","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27941"},"modified":"2024-08-15T22:27:58","modified_gmt":"2024-08-15T22:27:58","slug":"%d9%86%d8%b8%d8%b1%d9%8a%d8%a9-%d8%a7%d9%84%d8%b3%d8%a7%d9%86%d8%af%d9%88%d9%8a%d8%aa%d8%b4-%d9%84%d8%ad%d8%b3%d8%a7%d8%a8-%d8%a7%d9%84%d9%86%d9%87%d8%a7%d9%8a%d8%a7%d8%aa","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ar\/%d9%86%d8%b8%d8%b1%d9%8a%d8%a9-%d8%a7%d9%84%d8%b3%d8%a7%d9%86%d8%af%d9%88%d9%8a%d8%aa%d8%b4-%d9%84%d8%ad%d8%b3%d8%a7%d8%a8-%d8%a7%d9%84%d9%86%d9%87%d8%a7%d9%8a%d8%a7%d8%aa\/","title":{"rendered":"\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0633\u0627\u0646\u062f\u0648\u064a\u062a\u0634 \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a"},"content":{"rendered":"<p><center><\/p>\n<h1>\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0633\u0627\u0646\u062f\u0648\u064a\u062a\u0634 \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a<\/h1>\n<p><em><strong>\u0645\u0644\u062e\u0635:<\/strong><br \/>\n\u062a\u0642\u062f\u0645 \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629 \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0633\u0627\u0646\u062f\u0648\u064a\u062a\u0634\u060c \u0648\u0647\u064a \u0623\u062f\u0627\u0629 \u0631\u0626\u064a\u0633\u064a\u0629 \u0641\u064a \u062d\u0633\u0627\u0628 \u0627\u0644\u062a\u0641\u0627\u0636\u0644 \u0648\u0627\u0644\u062a\u0643\u0627\u0645\u0644 \u0644\u062a\u0642\u064a\u064a\u0645 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u0635\u0639\u0628\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062f\u0648\u0627\u0644 \u0623\u0628\u0633\u0637 \u062a\u0642\u064a\u062f \u0645\u0646 \u0627\u0644\u0623\u0639\u0644\u0649 \u0648\u0627\u0644\u0623\u0633\u0641\u0644. \u062a\u064f\u0642\u062f\u0645 \u0627\u0644\u062d\u0635\u0629 \u0634\u0631\u062d\u064b\u0627 \u0631\u0633\u0648\u0645\u064a\u064b\u0627 \u0648\u0625\u062b\u0628\u0627\u062a\u064b\u0627 \u0631\u0633\u0645\u064a\u064b\u0627\u060c \u064a\u0644\u064a\u0647\u0645\u0627 \u0623\u0645\u062b\u0644\u0629 \u0639\u0645\u0644\u064a\u0629. \u0627\u0644\u0647\u062f\u0641 \u0647\u0648 \u0623\u0646 \u064a\u0641\u0647\u0645 \u0627\u0644\u0637\u0644\u0627\u0628 \u0643\u064a\u0641\u064a\u0629 \u062a\u0637\u0628\u064a\u0642 \u0647\u0630\u0647 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0628\u0634\u0643\u0644 \u0623\u0643\u062b\u0631 \u0643\u0641\u0627\u0621\u0629.<\/em><\/p>\n<p><strong>\u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0645:<\/strong><br \/>\n\u0639\u0646\u062f \u0625\u0643\u0645\u0627\u0644 \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<ul style=\"text-align:left;\">\n<li><strong>\u0641\u0647\u0645<\/strong> \u0641\u0627\u0626\u062f\u0629 \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0633\u0627\u0646\u062f\u0648\u064a\u062a\u0634 \u0641\u064a \u062d\u0633\u0627\u0628 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a.<\/li>\n<li><strong>\u062a\u062d\u062f\u064a\u062f<\/strong> \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u062a\u064a \u064a\u0645\u0643\u0646\u0647\u0627 \u062a\u0642\u064a\u062f \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u0633\u062a\u0647\u062f\u0641\u0629 \u0644\u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u0646\u0638\u0631\u064a\u0629.<\/li>\n<li><strong>\u062a\u0637\u0628\u064a\u0642<\/strong> \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0633\u0627\u0646\u062f\u0648\u064a\u062a\u0634 \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u0635\u0639\u0628\u0629.<\/li>\n<li><strong>\u062a\u0635\u0648\u0631<\/strong> \u0645\u0641\u0647\u0648\u0645 \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0633\u0627\u0646\u062f\u0648\u064a\u062a\u0634 \u0631\u0633\u0648\u0645\u064a\u064b\u0627.<\/li>\n<li><strong>\u0625\u062b\u0628\u0627\u062a<\/strong> \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0633\u0627\u0646\u062f\u0648\u064a\u062a\u0634 \u0628\u0634\u0643\u0644 \u0631\u0633\u0645\u064a.<\/li>\n<\/ul>\n<p><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\u0641\u0643\u0631\u0629 \u0627\u0644\u0631\u0633\u0648\u0645\u064a\u0629 \u0644\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0633\u0627\u0646\u062f\u0648\u064a\u062a\u0634<\/a><br \/>\n<a href=\"#3\">\u0625\u062b\u0628\u0627\u062a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0633\u0627\u0646\u062f\u0648\u064a\u062a\u0634<\/a><br \/>\n<a href=\"#4\">\u0623\u0645\u062b\u0644\u0629<\/a><\/p>\n<p><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/24G_qlEwL9M\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\n<\/center><\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u0645\u0642\u062f\u0645\u0629<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=24G_qlEwL9M&amp;t=158s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u062a\u0643\u0645\u0646 \u0641\u0627\u0626\u062f\u0629 \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0633\u0627\u0646\u062f\u0648\u064a\u062a\u0634 \u0641\u064a \u0633\u0647\u0648\u0644\u0629 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647\u0627 \u0644\u062d\u0633\u0627\u0628 \u0628\u0639\u0636 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u0635\u0639\u0628\u0629<\/span><\/strong><\/a> \u0645\u0646 \u062e\u0644\u0627\u0644 \u0623\u062e\u0631\u0649 \u0623\u0628\u0633\u0637. \u0627\u0644\u0633\u0628\u0628 \u0641\u064a \u062a\u0633\u0645\u064a\u062a\u0647\u0627 \u0647\u0648 \u0623\u0646\u0647 \u0628\u062f\u0644\u0627\u064b \u0645\u0646 \u062d\u0633\u0627\u0628 \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0645\u0628\u0627\u0634\u0631\u0629 \u0639\u0646\u062f\u0645\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\to x_0<\/span><\/span>\u060c \u064a\u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0632\u0648\u062c \u0622\u062e\u0631 \u0645\u0646 \u0627\u0644\u062f\u0648\u0627\u0644\u060c \u0648\u0627\u062d\u062f\u0629 \u062a\u0642\u064a\u062f \u0645\u0646 \u0627\u0644\u0623\u0639\u0644\u0649 \u0648\u0627\u0644\u0623\u062e\u0631\u0649 \u0645\u0646 \u0627\u0644\u0623\u0633\u0641\u0644\u060c \u0648\u0646\u0647\u0627\u064a\u062a\u0647\u0645\u0627 \u0639\u0646\u062f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u062a\u062a\u0637\u0627\u0628\u0642 \u0648\u062a\u0643\u0648\u0646 \u0633\u0647\u0644\u0629 \u0627\u0644\u062d\u0635\u0648\u0644. \u0628\u0645\u0627 \u0623\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0623\u0635\u0644\u064a\u0629 \u062a\u0642\u0639 \u062f\u0627\u0626\u0645\u064b\u0627 \u0628\u064a\u0646 \u0627\u0644\u062f\u0648\u0627\u0644\u064a\u0646\u060c \u0641\u0647\u064a \u0645\u062b\u0644 \u00ab\u0627\u0644\u062c\u0628\u0646 \u0628\u064a\u0646 \u0634\u0631\u064a\u062d\u062a\u064a \u0627\u0644\u062e\u0628\u0632\u00bb.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u0627\u0644\u0641\u0643\u0631\u0629 \u0627\u0644\u0631\u0633\u0648\u0645\u064a\u0629 \u0644\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0633\u0627\u0646\u062f\u0648\u064a\u062a\u0634<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=24G_qlEwL9M&amp;t=206s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0641\u064a \u0627\u0644\u0648\u0627\u0642\u0639\u060c \u0627\u0644\u0641\u0643\u0631\u0629 \u0627\u0644\u062a\u064a \u062a\u0644\u062e\u0635 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0628\u0633\u064a\u0637\u0629 \u0644\u0644\u063a\u0627\u064a\u0629.<\/span> <\/strong><\/a>\u0644\u0646\u0641\u0631\u0636 \u0623\u0646\u0646\u0627 \u0646\u0631\u064a\u062f \u062d\u0633\u0627\u0628 \u0646\u0647\u0627\u064a\u0629 \u0635\u0639\u0628\u0629<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x \\to x_0}f(x)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0639\u0627\u062f\u0629\u064b \u0645\u0627 \u064a\u062a\u0645 \u0627\u0644\u0627\u0633\u062a\u0639\u0627\u0646\u0629 \u0628\u0643\u0644 \u0645\u0639\u0631\u0641\u062a\u0646\u0627 \u0641\u064a \u062c\u0628\u0631 \u0627\u0644\u062f\u0648\u0627\u0644 \u0644\u0645\u062d\u0627\u0648\u0644\u0629 <strong>\u062a\u0628\u0633\u064a\u0637\u0647\u0627 \u062d\u062a\u0649 \u0646\u062a\u0645\u0643\u0646 \u0645\u0646 \u062a\u0642\u064a\u064a\u0645\u0647\u0627<\/strong>. \u0648\u0645\u0639 \u0630\u0644\u0643\u060c \u0641\u064a \u0628\u0639\u0636 \u0627\u0644\u0623\u062d\u064a\u0627\u0646 \u064a\u0643\u0648\u0646 \u0627\u0644\u0646\u0647\u062c \u0627\u0644\u0645\u062e\u062a\u0644\u0641 \u0623\u0643\u062b\u0631 \u0643\u0641\u0627\u0621\u0629. \u0644\u0646\u0641\u062a\u0631\u0636 \u0623\u0646 \u0644\u062f\u064a\u0646\u0627 \u0641\u062a\u0631\u0629 \u0645\u063a\u0644\u0642\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I<\/span><\/span> \u0628\u062d\u064a\u062b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0 \\in I<\/span><\/span> \u0648\u0647\u0646\u0627\u0643 \u0623\u064a\u0636\u064b\u0627 \u062f\u0627\u0644\u062a\u0627\u0646 \u0623\u062e\u0631\u064a\u0627\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m(x)<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">M(x)<\/span><\/span> \u062a\u0644\u0628\u064a\u0627\u0646 \u0627\u0644\u0639\u0644\u0627\u0642\u0629<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\forall x\\in I)(m(x)\\leq f(x) \\leq M(x) )<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0648\u0623\u064a\u0636\u064b\u0627<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to x_0} m(x) = \\lim_{x\\to x_0} M(x) = L<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0625\u0630\u0646 \u0633\u064a\u062a\u062d\u0642\u0642<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to x_0} f(x) = L<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0647\u0630\u0627 \u0645\u0627 \u064a\u0645\u0643\u0646\u0646\u0627 \u0631\u0624\u064a\u062a\u0647 \u0641\u064a \u0627\u0644\u0635\u0648\u0631\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629.<\/p>\n<p><center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-gjBfVdaLj-k\/YGDXVUQBqDI\/AAAAAAAAEvg\/d2sNJdweVaoB64O5e2qfBxjZGIyIyGOxgCLcBGAsYHQ\/s0\/teorema%2Bdel%2Bsandwich.PNG\" alt=\"\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0633\u0627\u0646\u062f\u0648\u064a\u062a\u0634\" class=\"alignnone size-full lazyload\" width=\"513\" height=\"407\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-gjBfVdaLj-k\/YGDXVUQBqDI\/AAAAAAAAEvg\/d2sNJdweVaoB64O5e2qfBxjZGIyIyGOxgCLcBGAsYHQ\/s0\/teorema%2Bdel%2Bsandwich.PNG\" alt=\"\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0633\u0627\u0646\u062f\u0648\u064a\u062a\u0634\" class=\"alignnone size-full lazyload\" width=\"513\" height=\"407\" \/><\/noscript><\/center><\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u0625\u062b\u0628\u0627\u062a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0633\u0627\u0646\u062f\u0648\u064a\u062a\u0634<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=24G_qlEwL9M&amp;t=404s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0644\u0625\u062b\u0628\u0627\u062a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0633\u0627\u0646\u062f\u0648\u064a\u062a\u0634<\/span><\/strong><\/a>\u060c \u0633\u0646\u062a\u0628\u0639 \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(1)<\/span><\/span><\/td>\n<p>><\/p>\n<td><span style=\"background-color: #90ff90;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in I<\/span><\/span><\/span>; <strong>\u0641\u0631\u0636\u064a\u0629<\/strong><\/td>\n<\/tr>\n<tr>\n<\n\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(2)<\/span><\/span><\/td>\n<td><span style=\"background-color: #90ff90;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to x_0} m(x) = L<\/span><\/span><\/span> ; <strong>\u0641\u0631\u0636\u064a\u0629<\/strong><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\forall \\epsilon \\gt 0)(\\exists \\delta_1 \\gt 0) (|x-x_0|\\lt \\delta_1 \\rightarrow |m(x) -L| \\lt \\epsilon )<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(3)<\/span><\/span><\/td>\n<td><span style=\"background-color: #90ff90;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to x_0} M(x) = L<\/span><\/span><\/span> ; <strong>\u0641\u0631\u0636\u064a\u0629<\/strong><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\forall \\epsilon \\gt 0)(\\exists \\delta_2 \\gt 0) (|x-x_0|\\lt \\delta_2 \\rightarrow |M(x) -L| \\lt \\epsilon )<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(4)<\/span><\/span><\/td>\n<td><span style=\"background-color: #90ff90;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\forall x \\in I)(m(x) \\leq f(x) \\leq M(x) )<\/span><\/span><\/span>; <strong>\u0641\u0631\u0636\u064a\u0629<\/strong><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(5)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\forall x \\in I)(m(x) - L \\leq f(x) - L \\leq M(x) - L )<\/span><\/span>; \u0645\u0646 (4)<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(6)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(|m(x) -L|\\lt \\epsilon) \\rightarrow (-\\epsilon \\lt m(x) - L \\lt \\epsilon)<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(7)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(|M(x) -L|\\lt \\epsilon ) \\rightarrow (-\\epsilon \\lt M(x) - L \\lt \\epsilon) <\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(8)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\forall \\epsilon \\gt 0)(\\exists \\delta \\gt 0) (|x-x_0|\\lt \\delta=\\min\\{\\delta_1,\\delta_2\\} \\rightarrow ( |M(x) -L| \\lt \\epsilon \\wedge |m(x) -L| \\lt \\epsilon ) )<\/span><\/span>; \u0645\u0646 (2,3)<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(9)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\forall \\epsilon \\gt 0)(\\exists \\delta \\gt 0) (|x-x_0|\\lt \\delta=\\min\\{\\delta_1,\\delta_2\\} \\rightarrow ( - \\epsilon \\lt f(x) - L \\lt \\epsilon ) )<\/span><\/span>; \u0645\u0646 (1,5,6,7,8)<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\forall \\epsilon \\gt 0)(\\exists \\delta \\gt 0) (|x-x_0|\\lt \\delta=\\min\\{\\delta_1,\\delta_2\\} \\rightarrow |f(x) - L| \\lt \\epsilon ) )<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to x_0}f(x) = L\\;\\blacksquare<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u0623\u0645\u062b\u0644\u0629<\/h2>\n<p style=\"text-align: justify; color: #000000;\">\u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0633\u0627\u0646\u062f\u0648\u064a\u062a\u0634\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u062d\u0633\u0627\u0628 \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0648\u0627\u0644 \u062d\u062a\u0649 \u0639\u0646\u062f\u0645\u0627 \u0644\u0627 \u062a\u0643\u0648\u0646 \u0644\u062f\u064a\u0646\u0627 \u062a\u0639\u0628\u064a\u0631\u0647\u0627 \u0627\u0644\u062c\u0628\u0631\u064a \u0627\u0644\u0635\u0631\u064a\u062d. \u0641\u064a\u0645\u0627 \u064a\u0644\u064a \u0628\u0639\u0636 \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0630\u0644\u0643:<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0645\u062b\u0627\u0644 \u0639\u0644\u0649 \u0630\u0644\u0643 \u064a\u062d\u062f\u062b \u0641\u064a \u0627\u0644\u062d\u0627\u0644\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<ul style=\"text-align: justify; color: #000000;\">\n<li>\u0625\u0630\u0627 \u0643\u0627\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{5-2x^2}\\leq f(x) \\leq \\sqrt{5-x^2}<\/span><\/span>\u060c \u0639\u0646\u062f\u0645\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-1\\leq x\\leq 1<\/span><\/span>. \u0645\u0627 \u0647\u064a \u0642\u064a\u0645\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 0}f(x)<\/span><\/span>? <a href=\"https:\/\/www.youtube.com\/watch?v=24G_qlEwL9M&amp;t=1082s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u0627\u0644\u062d\u0644]<\/span><\/strong><\/a><\/li>\n<\/ul>\n<p style=\"text-align: justify; color: #000000;\">\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0622\u062e\u0631 \u0639\u0645\u0644\u064a \u0644\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0633\u0627\u0646\u062f\u0648\u064a\u062a\u0634 \u064a\u062d\u062f\u062b \u0639\u0646\u062f\u0645\u0627 \u0644\u0627 \u062a\u0643\u0648\u0646 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0646\u0641\u0633\u0647\u0627 \u0648\u0627\u0636\u062d\u0629 \u0645\u0642\u0627\u0631\u0646\u0629 \u0628\u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u0623\u062e\u0631\u0649 \u0627\u0644\u0623\u0628\u0633\u0637 \u0627\u0644\u062a\u064a \u062a\u0642\u064a\u062f\u0647\u0627 \u0645\u0646 \u0627\u0644\u0623\u0639\u0644\u0649 \u0648\u0627\u0644\u0623\u0633\u0641\u0644\u060c \u0643\u0645\u0627 \u0647\u0648 \u0627\u0644\u062d\u0627\u0644 \u0639\u0646\u062f \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062b\u0627\u0644 \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<ul style=\"text-align: justify; color: #000000;\">\n<li>\u0627\u062d\u0633\u0628: <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 0}\\dfrac{\\sin(x)}{x}<\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=24G_qlEwL9M&amp;t=1157s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u0627\u0644\u062d\u0644]<\/span><\/strong><\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0633\u0627\u0646\u062f\u0648\u064a\u062a\u0634 \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0645\u0644\u062e\u0635: \u062a\u0642\u062f\u0645 \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629 \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0633\u0627\u0646\u062f\u0648\u064a\u062a\u0634\u060c \u0648\u0647\u064a \u0623\u062f\u0627\u0629 \u0631\u0626\u064a\u0633\u064a\u0629 \u0641\u064a \u062d\u0633\u0627\u0628 \u0627\u0644\u062a\u0641\u0627\u0636\u0644 \u0648\u0627\u0644\u062a\u0643\u0627\u0645\u0644 \u0644\u062a\u0642\u064a\u064a\u0645 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u0635\u0639\u0628\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062f\u0648\u0627\u0644 \u0623\u0628\u0633\u0637 \u062a\u0642\u064a\u062f \u0645\u0646 \u0627\u0644\u0623\u0639\u0644\u0649 \u0648\u0627\u0644\u0623\u0633\u0641\u0644. \u062a\u064f\u0642\u062f\u0645 \u0627\u0644\u062d\u0635\u0629 \u0634\u0631\u062d\u064b\u0627 \u0631\u0633\u0648\u0645\u064a\u064b\u0627 \u0648\u0625\u062b\u0628\u0627\u062a\u064b\u0627 \u0631\u0633\u0645\u064a\u064b\u0627\u060c \u064a\u0644\u064a\u0647\u0645\u0627 \u0623\u0645\u062b\u0644\u0629 \u0639\u0645\u0644\u064a\u0629. \u0627\u0644\u0647\u062f\u0641 \u0647\u0648 \u0623\u0646 \u064a\u0641\u0647\u0645 \u0627\u0644\u0637\u0644\u0627\u0628 \u0643\u064a\u0641\u064a\u0629 \u062a\u0637\u0628\u064a\u0642 \u0647\u0630\u0647 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0628\u0634\u0643\u0644 \u0623\u0643\u062b\u0631 \u0643\u0641\u0627\u0621\u0629. \u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0645: \u0639\u0646\u062f \u0625\u0643\u0645\u0627\u0644 \u0647\u0630\u0647 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":27930,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":7,"footnotes":""},"categories":[860,565],"tags":[],"class_list":["post-27941","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>\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0633\u0627\u0646\u062f\u0648\u064a\u062a\u0634 \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u062a\u0639\u0644\u0645 \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 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