{"id":29100,"date":"2021-08-19T13:00:22","date_gmt":"2021-08-19T13:00:22","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=29100"},"modified":"2024-09-22T09:26:47","modified_gmt":"2024-09-22T09:26:47","slug":"%d9%85%d8%ac%d8%a7%d9%84-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%8c-%d9%85%d8%ac%d8%a7%d9%84-%d8%a7%d9%84%d9%82%d9%8a%d9%85-%d9%88%d8%a7%d9%84%d8%b1%d8%b3%d9%85-%d8%a7%d9%84%d8%a8%d9%8a%d8%a7","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%ac%d8%a7%d9%84-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%8c-%d9%85%d8%ac%d8%a7%d9%84-%d8%a7%d9%84%d9%82%d9%8a%d9%85-%d9%88%d8%a7%d9%84%d8%b1%d8%b3%d9%85-%d8%a7%d9%84%d8%a8%d9%8a%d8%a7\/","title":{"rendered":"\u0645\u062c\u0627\u0644 \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u060c \u0645\u062c\u0627\u0644 \u0627\u0644\u0642\u064a\u0645 \u0648\u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a &#8211; \u0627\u0644\u0645\u0642\u062a\u0631\u062d\u0629 \u0648\u0627\u0644\u0645\u062d\u0644\u0629"},"content":{"rendered":"<p><center><\/p>\n<h1>\u0645\u062c\u0627\u0644 \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u060c \u0645\u062c\u0627\u0644 \u0627\u0644\u0642\u064a\u0645 \u0648\u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a &#8211; \u0627\u0644\u0645\u0642\u062a\u0631\u062d\u0629 \u0648\u0627\u0644\u0645\u062d\u0644\u0629<\/h1>\n<p><em><strong>\u0627\u0644\u0645\u0644\u062e\u0635:<\/strong><br \/>\n   \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u062f\u0631\u0633\u060c \u0646\u062a\u062f\u0631\u0628 \u0639\u0644\u0649 \u0643\u064a\u0641\u064a\u0629 \u062a\u062d\u062f\u064a\u062f \u0645\u062c\u0627\u0644 \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u060c \u0645\u062c\u0627\u0644 \u0627\u0644\u0642\u064a\u0645 \u0648\u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a \u0644\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u062c\u0628\u0631\u064a\u0629 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0648\u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0627\u0644\u0645\u062d\u0644\u0648\u0644\u0629\u060c \u0645\u0639 \u0627\u0644\u062a\u0623\u0643\u064a\u062f \u0639\u0644\u0649 \u0623\u0647\u0645\u064a\u0629 \u0627\u0644\u0645\u0645\u0627\u0631\u0633\u0629 \u0644\u0625\u062a\u0642\u0627\u0646 \u0647\u0630\u0647 \u0627\u0644\u062a\u0642\u0646\u064a\u0627\u062a.<br \/>\n   <\/em><\/p>\n<p>   <strong>\u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0645:<\/strong><br \/>\n   \u0628\u0646\u0647\u0627\u064a\u0629 \u0647\u0630\u0627 \u0627\u0644\u062f\u0631\u0633 \u0633\u064a\u0643\u0648\u0646 \u0627\u0644\u0637\u0627\u0644\u0628 \u0642\u0627\u062f\u0631\u0627\u064b \u0639\u0644\u0649:<\/p>\n<ol style=\"text-align:left;\">\n<li><strong>\u0641\u0647\u0645<\/strong> \u0643\u064a\u0641\u064a\u0629 \u062a\u062d\u062f\u064a\u062f \u0645\u062c\u0627\u0644 \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0644\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u062c\u0628\u0631\u064a\u0629.<\/li>\n<li><strong>\u062a\u062d\u062f\u064a\u062f<\/strong> \u0645\u062c\u0627\u0644 \u0627\u0644\u0642\u064a\u0645 \u0644\u0623\u0646\u0648\u0627\u0639 \u0645\u062e\u062a\u0644\u0641\u0629 \u0645\u0646 \u0627\u0644\u062f\u0648\u0627\u0644.<\/li>\n<li><strong>\u062a\u0645\u062b\u064a\u0644<\/strong> \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a \u0644\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u062c\u0628\u0631\u064a\u0629 \u0641\u064a \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u062f\u064a\u0643\u0627\u0631\u062a\u064a.<\/li>\n<li><strong>\u062a\u0637\u0628\u064a\u0642<\/strong> \u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u062a\u0628\u0633\u064a\u0637 \u0644\u062d\u0644 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0623\u0643\u062b\u0631 \u062a\u0639\u0642\u064a\u062f\u0627\u064b.<\/li>\n<\/ol>\n<p>   <\/center><\/p>\n<h2>\u0643\u064a\u0641\u064a\u0629 \u0625\u062a\u0642\u0627\u0646 \u0627\u0644\u062a\u0642\u0646\u064a\u0627\u062a<\/h2>\n<p style=\"text-align: justify;\">\u0644\u0625\u062a\u0642\u0627\u0646 \u0627\u0644\u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u0633\u0645\u062d \u0628\u062a\u062d\u062f\u064a\u062f \u0645\u062c\u0627\u0644 \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u060c \u0645\u062c\u0627\u0644 \u0627\u0644\u0642\u064a\u0645 \u0648\u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a\u060c \u0639\u0644\u0649 \u0627\u0644\u0623\u0642\u0644 \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0645\u0633\u062a\u0648\u0649\u060c \u0644\u064a\u0633 \u0645\u0646 \u0627\u0644\u0636\u0631\u0648\u0631\u064a \u0645\u0631\u0627\u062c\u0639\u0629 \u0627\u0644\u0645\u0632\u064a\u062f \u0645\u0646 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u062a\u064a \u0642\u0645\u0646\u0627 \u0628\u062a\u063a\u0637\u064a\u062a\u0647\u0627 \u0628\u0627\u0644\u0641\u0639\u0644. \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0645\u0631\u062d\u0644\u0629\u060c \u0645\u0646 \u0627\u0644\u0623\u0641\u0636\u0644 \u0627\u0644\u0642\u064a\u0627\u0645 \u0628\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646\u060c \u0648\u0623\u0641\u0636\u0644 \u0637\u0631\u064a\u0642\u0629 \u0644\u0644\u062a\u0645\u0631\u064a\u0646 \u0647\u064a \u0627\u062e\u062a\u0631\u0627\u0639 \u062a\u0645\u0627\u0631\u064a\u0646 \u0639\u0634\u0648\u0627\u0626\u064a\u0629. \u0628\u0647\u0630\u0647 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0641\u0642\u0637 \u0633\u062a\u062a\u0639\u0631\u0641 \u062d\u0642\u064b\u0627 \u0639\u0644\u0649 \u062d\u062f\u0648\u062f \u0627\u0644\u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u062a\u064a \u062f\u0631\u0633\u0646\u0627\u0647\u0627 \u062d\u062a\u0649 \u0627\u0644\u0622\u0646 \u0648\u0633\u062a\u0637\u0648\u0631 \u0627\u0644\u062d\u062f\u0633 \u0627\u0644\u0630\u064a \u0633\u064a\u0645\u0643\u0646\u0643 \u0645\u0646 \u0627\u0644\u0639\u0645\u0644 \u0628\u0645\u0647\u0627\u0631\u0629.<\/p>\n<p style=\"text-align: justify;\">\u0645\u0627 \u0633\u0646\u0641\u0639\u0644\u0647 \u0627\u0644\u0622\u0646 \u0647\u0648 \u0628\u0627\u0644\u0636\u0628\u0637 \u0647\u0630\u0627: \u0633\u0623\u062e\u062a\u0631\u0639 \u0628\u0639\u0636 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064a\u0629 \u0648\u0633\u0623\u062d\u0644\u0647\u0627 \u0628\u0642\u062f\u0631 \u0645\u0627 \u062a\u0633\u0645\u062d \u0628\u0647 \u0627\u0644\u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u0645\u062a \u0645\u0631\u0627\u062c\u0639\u062a\u0647\u0627\u061b \u0625\u0630\u0627 \u0644\u0645 \u064a\u0643\u0646 \u0645\u0646 \u0627\u0644\u0645\u0645\u0643\u0646 \u062d\u0644\u0647\u0627 \u0628\u0647\u0630\u0647 \u0627\u0644\u062a\u0642\u0646\u064a\u0627\u062a\u060c \u0641\u0633\u0623\u0634\u0631\u062d \u0627\u0644\u0646\u0642\u0627\u0637 \u0627\u0644\u062a\u064a \u062a\u0641\u0634\u0644 \u0641\u064a\u0647\u0627 \u0648\u0644\u0645\u0627\u0630\u0627.<\/p>\n<h3>\u062a\u0645\u0627\u0631\u064a\u0646 \u0639\u0645\u0644\u064a\u0629:<\/h3>\n<p style=\"text-align: justify;\">\u062d\u062f\u062f \u0645\u062c\u0627\u0644 \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u060c \u0645\u062c\u0627\u0644 \u0627\u0644\u0642\u064a\u0645 \u0648\u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a \u0644\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<ol style=\"text-align: justify;\">\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a(x) = \\displaystyle \\frac{x^3 - 3x^2 + 5x - 1}{x^2 + 2x - 1}<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b(x) = \\displaystyle \\frac{4x^4 + 2x^3 - 5x^2 - 2x - 2}{2x^2 - x - 1}<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c(x) = \\displaystyle \\frac{x^5 + x^3 - x - 1}{x^2 - x - 1}<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">d(x) = \\displaystyle \\frac{3x^2 - 3x - 2}{\\sqrt{x^2 - 1}}<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">e(x) = \\displaystyle \\sqrt{\\frac{x^4 - x^2 - 11}{(x^2 - 1)\\sqrt{x^2 - x - 1}}}<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\displaystyle \\frac{(x^2 - 2x - 2)\\sqrt{7x^8 - 5x^4 - 2}}{x\\sqrt{5x^2 - 3x + 2}}<\/span><\/span><\/li>\n<\/ol>\n<h3>\u062d\u0644 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u0639\u0645\u0644\u064a\u0629:<\/h3>\n<p>   <center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/f2g4MVSvfSI\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n<p>   <center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/8nF10hKDbz4\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n<p>   <center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/MA9mvrEohpc\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n<h3>\u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u0642\u062a\u0631\u062d\u0629:<\/h3>\n<p style=\"text-align: justify;\">\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u0645\u0642\u062a\u0631\u062d\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0645\u0634\u0627\u0628\u0647\u0629 \u0644\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0644\u0647\u0627 \u0633\u0627\u0628\u0642\u064b\u0627\u061b \u0644\u0642\u062f \u0642\u0645\u062a \u0641\u0642\u0637 \u0628\u062a\u063a\u064a\u064a\u0631 \u0627\u0644\u0623\u0631\u0642\u0627\u0645. \u0627\u0644\u0647\u064a\u0643\u0644 \u0647\u0648 \u0646\u0641\u0633\u0647\u060c \u0644\u0630\u0627 \u0642\u062f \u062a\u0643\u0648\u0646 \u0627\u0644\u062d\u0644\u0648\u0644 \u0627\u0644\u0633\u0627\u0628\u0642\u0629 \u0645\u0641\u064a\u062f\u0629. \u0625\u0630\u0627 \u0643\u0646\u062a \u0644\u0627 \u062a\u0632\u0627\u0644 \u063a\u064a\u0631 \u0648\u0627\u062b\u0642 \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062a\u0642\u0646\u064a\u0627\u062a\u060c \u064a\u0645\u0643\u0646\u0643 \u062f\u0627\u0626\u0645\u064b\u0627 \u0627\u0644\u0627\u0639\u062a\u0645\u0627\u062f \u0639\u0644\u0649 \u0623\u062f\u0648\u0627\u062a \u0639\u0628\u0631 \u0627\u0644\u0625\u0646\u062a\u0631\u0646\u062a \u0645\u062b\u0644 <a href=\"https:\/\/www.wolframalpha.com\/\" rel=\"nofollow, noreferrer, noopener\" target=\"_blank\">WolframAlpha<\/a> \u0648 <a href=\"https:\/\/www.geogebra.org\/\" rel=\"nofollow, noreferrer, noopener\" target=\"_blank\">GeoGebra<\/a>. \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0644\u062f\u064a\u0643 \u0635\u0639\u0648\u0628\u0627\u062a \u0641\u064a \u0627\u0644\u062c\u0628\u0631\u060c \u0641\u0625\u0646 \u0645\u0631\u0627\u062c\u0639\u0629 \u0627\u0644\u062f\u0631\u0648\u0633 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0633\u062a\u0633\u0627\u0639\u062f\u0643:<\/p>\n<p style=\"text-align: justify;\">\u0643\u0645\u0627 \u0647\u0648 \u0627\u0644\u062d\u0627\u0644 \u0641\u064a \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u0633\u0627\u0628\u0642\u0629\u060c \u064a\u062c\u0628 \u0639\u0644\u064a\u0643 \u062d\u0633\u0627\u0628 \u0645\u062c\u0627\u0644 \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u060c \u0645\u062c\u0627\u0644 \u0627\u0644\u0642\u064a\u0645 \u0648\u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a.<\/p>\n<ol style=\"text-align: justify;\">\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a(x) = \\displaystyle \\frac{-5x^3 + 9x^2 - 7x - 2}{5x^2 + 3x + 9}<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b(x) = \\displaystyle \\frac{-8x^4 + 2x^3 + 4x^2 + 4x + 1}{3x^2 - 9x + 3}<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c(x) = \\displaystyle \\frac{-7x^5 + 9x^3 + 7x + 5}{-2x^2 - 8x + 6}<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">d(x) = \\displaystyle \\frac{4x^2 - 4x - 9}{\\sqrt{-3x^2 + 7}}<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">e(x) = \\displaystyle \\sqrt{\\frac{9x^4 + 2x^2 + 7}{(-8x^2 + 4)\\sqrt{-6x^2 + 9x + 5}}}<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\displaystyle \\frac{(7x^2 + 6x - 1)\\sqrt{9x^8 + 3x^4 + 9}}{5x\\sqrt{3x^2 + 8x - 3}}<\/span><\/span><\/li>\n<\/ol>\n<p style=\"text-align: justify;\">\u0645\u0646 \u0647\u0646\u0627\u060c \u0625\u0630\u0627 \u0643\u0646\u062a \u062a\u0631\u063a\u0628 \u0641\u064a \u0627\u0644\u0645\u0632\u064a\u062f \u0645\u0646 \u0627\u0644\u062a\u062f\u0631\u064a\u0628\u060c \u0641\u0645\u0646 \u0627\u0644\u0623\u0641\u0636\u0644 \u0623\u0646 \u062a\u062e\u062a\u0631\u0639 \u062f\u0648\u0627\u0644\u0643 \u0627\u0644\u062e\u0627\u0635\u0629 \u0648\u062a\u062d\u0627\u0648\u0644 \u062d\u0644\u0647\u0627.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0645\u062c\u0627\u0644 \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u060c \u0645\u062c\u0627\u0644 \u0627\u0644\u0642\u064a\u0645 \u0648\u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a &#8211; \u0627\u0644\u0645\u0642\u062a\u0631\u062d\u0629 \u0648\u0627\u0644\u0645\u062d\u0644\u0629 \u0627\u0644\u0645\u0644\u062e\u0635: \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u062f\u0631\u0633\u060c \u0646\u062a\u062f\u0631\u0628 \u0639\u0644\u0649 \u0643\u064a\u0641\u064a\u0629 \u062a\u062d\u062f\u064a\u062f \u0645\u062c\u0627\u0644 \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u060c \u0645\u062c\u0627\u0644 \u0627\u0644\u0642\u064a\u0645 \u0648\u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a \u0644\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u062c\u0628\u0631\u064a\u0629 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0648\u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0627\u0644\u0645\u062d\u0644\u0648\u0644\u0629\u060c \u0645\u0639 \u0627\u0644\u062a\u0623\u0643\u064a\u062f \u0639\u0644\u0649 \u0623\u0647\u0645\u064a\u0629 \u0627\u0644\u0645\u0645\u0627\u0631\u0633\u0629 \u0644\u0625\u062a\u0642\u0627\u0646 \u0647\u0630\u0647 \u0627\u0644\u062a\u0642\u0646\u064a\u0627\u062a. \u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0645: \u0628\u0646\u0647\u0627\u064a\u0629 \u0647\u0630\u0627 \u0627\u0644\u062f\u0631\u0633 \u0633\u064a\u0643\u0648\u0646 \u0627\u0644\u0637\u0627\u0644\u0628 \u0642\u0627\u062f\u0631\u0627\u064b \u0639\u0644\u0649: \u0641\u0647\u0645 \u0643\u064a\u0641\u064a\u0629 \u062a\u062d\u062f\u064a\u062f \u0645\u062c\u0627\u0644 \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0644\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u062c\u0628\u0631\u064a\u0629. \u062a\u062d\u062f\u064a\u062f 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