{"id":27983,"date":"2024-08-17T13:00:47","date_gmt":"2024-08-17T13:00:47","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27983"},"modified":"2024-08-16T01:24:24","modified_gmt":"2024-08-16T01:24:24","slug":"%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\/","title":{"rendered":"\u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629: \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a\u060c \u0627\u0644\u062a\u0637\u0648\u064a\u0631 \u0648\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646"},"content":{"rendered":"<p><center><\/p>\n<h1>\u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629: \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a\u060c \u0627\u0644\u062a\u0637\u0648\u064a\u0631 \u0648\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646<\/h1>\n<p><em><strong>\u0627\u0644\u0645\u0644\u062e\u0635:<\/strong><br \/>\n\u064a\u0634\u0631\u062d \u0647\u0630\u0627 \u0627\u0644\u0645\u0642\u0627\u0644 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0648\u0627\u0644\u062b\u0646\u0627\u0626\u064a\u0629 \u0641\u064a \u062d\u0633\u0627\u0628 \u0627\u0644\u062a\u0641\u0627\u0636\u0644 \u0648\u0627\u0644\u062a\u0643\u0627\u0645\u0644\u060c \u0648\u064a\u0648\u0636\u062d \u0643\u064a\u0641\u064a\u0629 \u062a\u0639\u0631\u064a\u0641\u0647\u0627 \u0648\u062a\u0637\u0628\u064a\u0642\u0647\u0627 \u0628\u0634\u0643\u0644 \u0628\u062f\u064a\u0647\u064a \u0648\u0631\u0633\u0645\u064a. \u062a\u064f\u0639\u0631\u0636 \u0623\u0645\u062b\u0644\u0629 \u0628\u064a\u0627\u0646\u064a\u0629 \u0648\u062c\u0628\u0631\u064a\u0629\u060c \u0648\u062a\u064f\u0646\u0627\u0642\u0634 \u0627\u0644\u0634\u0631\u0648\u0637 \u0644\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062c\u0628\u0631 \u0627\u0644\u062d\u062f\u0648\u062f \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0627\u062a\u060c \u0643\u0645\u0627 \u062a\u064f\u062f\u0631\u062c \u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629 \u0644\u062a\u0639\u0632\u064a\u0632 \u0627\u0644\u0641\u0647\u0645. \u0627\u0644\u0647\u062f\u0641 \u0647\u0648 \u062a\u0642\u062f\u064a\u0645 \u0631\u0624\u064a\u0629 \u0648\u0627\u0636\u062d\u0629 \u0648\u0645\u0648\u062c\u0632\u0629 \u0644\u0647\u0630\u0647 \u0627\u0644\u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0641\u064a \u062f\u0631\u0627\u0633\u0629 \u062d\u0633\u0627\u0628 \u0627\u0644\u062a\u0641\u0627\u0636\u0644 \u0648\u0627\u0644\u062a\u0643\u0627\u0645\u0644.<\/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\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> \u0627\u0644\u0641\u0631\u0642 \u0628\u064a\u0646 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0648\u0627\u0644\u062b\u0646\u0627\u0626\u064a\u0629.<\/li>\n<li><strong>\u062a\u0639\u0631\u064a\u0641<\/strong> \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0645\u0646 \u0627\u0644\u0646\u0627\u062d\u064a\u0629 \u0627\u0644\u0631\u0633\u0645\u064a\u0629 \u0645\u0646 \u0627\u0644\u064a\u0645\u064a\u0646 \u0648\u0627\u0644\u064a\u0633\u0627\u0631.<\/li>\n<li><strong>\u062a\u0637\u0628\u064a\u0642<\/strong> \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0641\u064a \u0645\u0633\u0627\u0626\u0644 \u062d\u0633\u0627\u0628 \u0627\u0644\u062a\u0641\u0627\u0636\u0644 \u0648\u0627\u0644\u062a\u0643\u0627\u0645\u0644.<\/li>\n<li><strong>\u062a\u0641\u0633\u064a\u0631<\/strong> \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0648\u0627\u0644\u062b\u0646\u0627\u0626\u064a\u0629 \u0628\u0634\u0643\u0644 \u0628\u064a\u0627\u0646\u064a.<\/li>\n<li><strong>\u0627\u0644\u062a\u0639\u0631\u0641 \u0639\u0644\u0649<\/strong> \u0627\u0644\u0634\u0631\u0648\u0637 \u0627\u0644\u0644\u0627\u0632\u0645\u0629 \u0644\u0648\u062c\u0648\u062f \u062d\u062f \u062b\u0646\u0627\u0626\u064a.<\/li>\n<li><strong>\u0627\u0633\u062a\u062e\u062f\u0627\u0645<\/strong> \u062c\u0628\u0631 \u0627\u0644\u062d\u062f\u0648\u062f \u0641\u064a \u0633\u064a\u0627\u0642\u0627\u062a \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629.<\/li>\n<li><strong>\u062d\u0644<\/strong> \u062a\u0645\u0627\u0631\u064a\u0646 \u062d\u0633\u0627\u0628 \u0627\u0644\u062a\u0641\u0627\u0636\u0644 \u0648\u0627\u0644\u062a\u0643\u0627\u0645\u0644 \u0627\u0644\u0645\u062a\u0639\u0644\u0642\u0629 \u0628\u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629.<\/li>\n<\/ul>\n<p><strong>\u062c\u062f\u0648\u0644 \u0627\u0644\u0645\u062d\u062a\u0648\u064a\u0627\u062a:<\/strong><br \/>\n<a href=\"#1\">\u0627\u0644\u0645\u0642\u062f\u0645\u0629<\/a><br \/>\n<a href=\"#2\">\u0627\u0644\u0641\u0643\u0631\u0629 \u0627\u0644\u0628\u062f\u064a\u0647\u064a\u0629 \u0644\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0648\u0627\u0644\u062b\u0646\u0627\u0626\u064a\u0629<\/a><br \/>\n<a href=\"#3\">\u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0631\u0633\u0645\u064a \u0644\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629<\/a><br \/>\n<a href=\"#4\">\u0634\u0631\u0648\u0637 \u062c\u0628\u0631 \u0627\u0644\u062d\u062f\u0648\u062f<\/a><br \/>\n<a href=\"#5\">\u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u0642\u062a\u0631\u062d\u0629 \u0648\u0645\u062d\u0644\u0648\u0644\u0629<\/a><\/p>\n<p><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/8lkvxEHsF6c\" title=\"\u0645\u0634\u063a\u0644 \u0641\u064a\u062f\u064a\u0648 \u064a\u0648\u062a\u064a\u0648\u0628\" 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>\u0627\u0644\u0645\u0642\u062f\u0645\u0629<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=8lkvxEHsF6c&amp;t=138s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u062a\u0638\u0647\u0631 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0639\u0646\u062f\u0645\u0627 \u0646\u0648\u0627\u062c\u0647 \u062d\u062f\u0648\u062f\u064b\u0627 \u0642\u062f \u062a\u0648\u062c\u062f \u0641\u0642\u0637 \u0645\u0646 \u0627\u0644\u064a\u0633\u0627\u0631 \u0623\u0648 \u0627\u0644\u064a\u0645\u064a\u0646\u060c<\/span><\/strong><\/a> \u0648\u0644\u0643\u0646 \u0644\u064a\u0633 \u0645\u0646 \u0643\u0644\u0627 \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0646. \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062a\u064a \u062f\u0631\u0633\u0646\u0627\u0647\u0627 \u062d\u062a\u0649 \u0627\u0644\u0622\u0646 \u0647\u064a \u0645\u0646 \u0627\u0644\u0646\u0648\u0639 \u0627\u0644\u0623\u062e\u064a\u0631 \u062a\u062d\u062f\u064a\u062f\u064b\u0627: \u0644\u0643\u064a \u064a\u0643\u0648\u0646 \u062d\u062f \u0627\u0644\u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u0639\u0646\u062f\u0645\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\to x_0<\/span><\/span> \u0645\u0648\u062c\u0648\u062f\u064b\u0627\u060c \u0645\u0646 \u0627\u0644\u0636\u0631\u0648\u0631\u064a \u0623\u0646 \u062a\u0643\u0648\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u0645\u0639\u0631\u0641\u0629 \u0628\u0634\u0643\u0644 \u062c\u064a\u062f \u0639\u0644\u0649 \u0643\u0644\u0627 \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0646 \u0645\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span>\u061b \u0625\u0630\u0627 \u0644\u0645 \u064a\u062d\u062f\u062b \u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u062d\u062f \u0644\u0646 \u064a\u0643\u0648\u0646 \u0641\u0639\u0627\u0644\u064b\u0627. \u0646\u0638\u0631\u064b\u0627 \u0644\u0623\u0646 \u0627\u0644\u062d\u0627\u0644\u0627\u062a \u0627\u0644\u062a\u064a \u064a\u062d\u062f\u062b \u0641\u064a\u0647\u0627 \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u062d\u062f\u0648\u062f \u0634\u0627\u0626\u0639\u0629\u060c \u0645\u0646 \u0627\u0644\u0636\u0631\u0648\u0631\u064a \u0625\u064a\u062c\u0627\u062f \u0637\u0631\u064a\u0642\u0629 \u0644\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639\u0647\u0627. \u064a\u062a\u0645 \u062d\u0644 \u0647\u0630\u0627 \u0645\u0646 \u062e\u0644\u0627\u0644 \u062a\u0639\u0631\u064a\u0641 \u0631\u0633\u0645\u064a.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u0627\u0644\u0641\u0643\u0631\u0629 \u0627\u0644\u0628\u062f\u064a\u0647\u064a\u0629 \u0644\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0648\u0627\u0644\u062b\u0646\u0627\u0626\u064a\u0629<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=8lkvxEHsF6c&amp;t=279s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0644\u0643\u064a \u064a\u0648\u062c\u062f \u062d\u062f \u0627\u0644\u062f\u0627\u0644\u0629<\/span><\/strong><\/a> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u0639\u0646\u062f\u0645\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\to x_0<\/span><\/span>\u060c \u0645\u0646 \u0627\u0644\u0636\u0631\u0648\u0631\u064a \u0623\u0646 \u062a\u0643\u0648\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0645\u0639\u0631\u0641\u0629 \u0628\u0634\u0643\u0644 \u062c\u064a\u062f \u0639\u0644\u0649 \u0643\u0644\u0627 \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0646 \u0645\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span>. \u0625\u0630\u0627 \u062d\u062f\u062b \u0630\u0644\u0643\u060c \u0641\u0625\u0646\u0646\u0627 \u0646\u062a\u062d\u062f\u062b \u0639\u0646 \u062d\u062f \u062b\u0646\u0627\u0626\u064a. \u0648\u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0647\u0630\u0647 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">L<\/span><\/span>\u060c \u0641\u0644\u0646 \u064a\u0643\u0648\u0646 \u0647\u0646\u0627\u0643 \u0645\u0634\u0643\u0644\u0629 \u0641\u064a \u0627\u0644\u0643\u062a\u0627\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) = L<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0627\u0644\u0622\u0646\u060c \u062a\u062e\u064a\u0644 \u0623\u0646\u0646\u0627 \u0646\u0639\u064a\u062f \u062a\u0639\u0631\u064a\u0641 \u0647\u0630\u0647 \u0627\u0644\u062f\u0627\u0644\u0629 \u0628\u062d\u064a\u062b \u064a\u0634\u0645\u0644 \u0645\u062c\u0627\u0644\u0647\u0627 \u0641\u0642\u0637 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0623\u0643\u0628\u0631 \u0645\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span>. \u0625\u0630\u0627 \u0641\u0639\u0644\u0646\u0627 \u0630\u0644\u0643\u060c \u0633\u0646\u0644\u0627\u062d\u0638 \u0623\u0646 \u0627\u0644\u062d\u062f \u0644\u0645 \u064a\u0639\u062f \u0645\u0648\u062c\u0648\u062f\u064b\u0627 (\u0644\u0623\u0646 \u0647\u0646\u0627\u0643 \u0642\u064a\u0645\u064b\u0627 \u0644\u0640<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/span> \u0644\u0646 \u064a\u0643\u0648\u0646 \u0644\u0647\u0627 \u0645\u0639\u0646\u0649)\u061b \u0648\u0645\u0639 \u0630\u0644\u0643\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0623\u0646 \u0646\u0642\u0648\u0644 \u0631\u0633\u0648\u0645\u064a\u064b\u0627 \u0623\u0646\u0647 \u0639\u0646\u062f\u0645\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\to x_0<\/span><\/span>\u060c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u0644\u0627 \u064a\u0632\u0627\u0644 \u064a\u0645\u064a\u0644 \u0625\u0644\u0649 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">L<\/span><\/span>. \u0627\u0644\u0641\u0643\u0631\u0629 \u0627\u0644\u0628\u062f\u064a\u0647\u064a\u0629 \u0627\u0644\u062a\u064a \u0646\u0646\u062a\u062c\u0647\u0627 \u0647\u0646\u0627 \u0647\u064a \u0627\u0644\u062d\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a \u0645\u0646 \u0627\u0644\u064a\u0645\u064a\u0646\u060c \u0648\u0647\u0648 \u0645\u0627 \u0646\u0645\u062b\u0644\u0647 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0643\u062a\u0627\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) = L<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0648\u0628\u0637\u0631\u064a\u0642\u0629 \u0645\u0645\u0627\u062b\u0644\u0629 \u062a\u0645\u0627\u0645\u064b\u0627 \u0633\u064a\u0643\u0648\u0646 \u0644\u062f\u064a\u0646\u0627 \u0627\u0644\u062d\u062f \u0645\u0646 \u0627\u0644\u064a\u0633\u0627\u0631<\/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;\">\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0633\u064a\u0638\u0644 \u0627\u0644\u062d\u062f \u0627\u0644\u062b\u0646\u0627\u0626\u064a \u0645\u0648\u062c\u0648\u062f\u064b\u0627 \u0643\u0644\u0645\u0627 \u0648\u062c\u062f\u062a \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0648\u0643\u0627\u0646\u062a \u0645\u062a\u0633\u0627\u0648\u064a\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) = \\lim_{x\\to x_0}f(x) = \\lim_{x\\to x_0^-}f(x)<\/span><\/span><\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0631\u0633\u0645\u064a \u0644\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=8lkvxEHsF6c&amp;t=438s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0631\u0633\u0645\u064a\u064b\u0627\u060c \u064a\u0643\u0641\u064a<\/span> <\/strong><\/a>\u062a\u0637\u0628\u064a\u0642 \u062a\u0639\u062f\u064a\u0644 \u0635\u063a\u064a\u0631 \u0639\u0644\u0649 \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u0635\u0644\u064a.<\/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 := \\left(\\forall \\epsilon\\gt 0 \\right)<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\exist \\delta \\gt 0 \\right)<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\right.<\/span><\/span> <span style=\"background-color: #88ff88;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\lt|x-x_0|\\lt\\delta <\/span><\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left.\\rightarrow |f(x)-L|\\lt\\epsilon \\right)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0645\u0646 \u0627\u0644\u064a\u0645\u064a\u0646\u060c \u064a\u0643\u0648\u0646 \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0643\u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\forall \\epsilon\\gt 0 \\right)<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\exist \\delta \\gt 0 \\right)<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\right.<\/span><\/span> <span style=\"background-color: #88ff88;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0 \\lt x \\lt x_0 + \\delta <\/span><\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left.\\rightarrow |f(x)-L|\\lt\\epsilon \\right)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0623\u0645\u0627 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0645\u0646 \u0627\u0644\u064a\u0633\u0627\u0631 \u0641\u0633\u064a\u0643\u0648\u0646 \u0643\u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\forall \\epsilon\\gt 0 \\right)<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\exist \\delta \\gt 0 \\right)<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\right.<\/span><\/span> <span style=\"background-color: #88ff88;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0 - \\delta \\lt x \\lt x_0<\/span><\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left.\\rightarrow |f(x)-L|\\lt\\epsilon \\right)<\/span><\/span><\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u0634\u0631\u0648\u0637 \u062c\u0628\u0631 \u0627\u0644\u062d\u062f\u0648\u062f<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=8lkvxEHsF6c&amp;t=801s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0627\u0644\u0623\u0645\u0631 \u0627\u0644\u0645\u062b\u064a\u0631 \u0644\u0644\u0627\u0647\u062a\u0645\u0627\u0645 \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a \u0647\u0648 \u0623\u0646\u0647\u0627 \u0645\u062f\u0645\u062c\u0629<\/span><\/strong><\/a> \u0641\u064a \u0646\u0641\u0633 \u0627\u0644\u0648\u0642\u062a \u0641\u064a \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u062a\u0642\u0644\u064a\u062f\u064a \u0644\u0644\u062d\u062f\u0648\u062f\u060c \u0648\u0647\u0630\u0627 \u0645\u0647\u0645 \u0644\u0623\u0646\u0647 \u064a\u0639\u0641\u064a\u0646\u0627 \u0645\u0646 \u0625\u0639\u0627\u062f\u0629 \u0625\u062b\u0628\u0627\u062a \u062c\u0645\u064a\u0639 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u062a\u064a \u0623\u062b\u0628\u062a\u0646\u0627\u0647\u0627 \u0628\u0627\u0644\u0641\u0639\u0644 \u0644\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062b\u0646\u0627\u0626\u064a\u0629. \u0633\u064a\u0639\u0645\u0644 \u0643\u0644 \u062c\u0628\u0631 \u0627\u0644\u062d\u062f\u0648\u062f \u062a\u0645\u0627\u0645\u064b\u0627 \u0643\u0645\u0627 \u0631\u0623\u064a\u0646\u0627 \u0641\u064a \u0627\u0644\u062f\u0631\u0648\u0633 \u0627\u0644\u0633\u0627\u0628\u0642\u0629 \u0637\u0627\u0644\u0645\u0627 \u0643\u0627\u0646\u062a \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0645\u0639\u0646\u064a\u0629 \u0645\u0646 \u0646\u0641\u0633 \u0627\u0644\u0646\u0648\u0639 (\u0643\u0644\u0647\u0627 \u0645\u0646 \u0627\u0644\u064a\u0633\u0627\u0631\u060c \u0623\u0648 \u0643\u0644\u0647\u0627 \u0645\u0646 \u0627\u0644\u064a\u0645\u064a\u0646\u060c \u0628\u062f\u0648\u0646 \u062e\u0644\u0637)\u060c \u0645\u0648\u062c\u0647\u0629 \u0625\u0644\u0649 \u0646\u0641\u0633 \u0627\u0644\u0646\u0642\u0637\u0629 \u0648\u062a\u0648\u062c\u062f \u0641\u064a \u062a\u0644\u0643 \u0627\u0644\u0646\u0642\u0637\u0629.<\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u0642\u062a\u0631\u062d\u0629 \u0648\u0645\u062d\u0644\u0648\u0644\u0629<\/h2>\n<ol style=\"text-align: justify; color: #000000;\">\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to {\\frac{1}{2}}^- } \\sqrt{\\dfrac{x+2}{x+1}} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=8lkvxEHsF6c&amp;t=994s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u0627\u0644\u062d\u0644]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 1^+} \\sqrt{\\dfrac{x-1}{x+2}} <\/span><\/span><a href=\"https:\/\/www.youtube.com\/watch?v=8lkvxEHsF6c&amp;t=1058s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"> <strong>[\u0627\u0644\u062d\u0644]<\/strong><\/span><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 2^+} \\left(\\dfrac{x}{x+1} \\right) \\left(\\dfrac{2x+5}{x^2+x} \\right)<\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=8lkvxEHsF6c&amp;t=1058s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><strong>[\u0627\u0644\u062d\u0644]<\/strong><\/span><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 1^-} \\left(\\dfrac{1}{x+1} \\right) \\left(\\dfrac{x+6}{x} \\right) \\left(\\\u062ffrac{3-x}{x} \\right) <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=8lkvxEHsF6c&amp;t=1102s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><strong>[\u0627\u0644\u062d\u0644]<\/strong><\/span><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{h\\to 0^+ } \\dfrac{\\sqrt{h^2 + 4h +5} - \\sqrt{5}}{h} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=8lkvxEHsF6c&amp;t=1168s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><strong>[\u0627\u0644\u062d\u0644]<\/strong><\/span><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{h\\to 0^-} \\\u062ffrac{\\sqrt{6} - \\\u062ffrac{5h^2 + 11h +6}}{h}<\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=8lkvxEHsF6c&amp;t=1276s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u0627\u0644\u062d\u0644]<\/span><\/strong><\/a><\/li>\n<li>\n<table>\n<tbody>\n<tr style=\"text-align: justify;\">\n<td>a. <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to -2^+} (x+3)\\\u062ffrac{|x+2|}{x+2}\n\n<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td>b. <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to -2^-} (x+3)\\\u062ffrac{|x+2|}{x+2}\n\n<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=8lkvxEHsF6c&amp;t=1378s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u0627\u0644\u062d\u0644]<\/span><\/strong><\/a><\/li>\n<li>\n<table>\n<tbody>\n<tr style=\"text-align: justify;\">\n<td>a. <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 1^+} \\\u062ffrac{\\sqrt{2x}(x-1)}{|x-1|}\n\n<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td>b. <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 1^-}\\\u062ffrac{\\sqrt{2x}(x-1)}{|x-1|}\n\n<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=8lkvxEHsF6c&amp;t=1655s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u0627\u0644\u062d\u0644]<\/span><\/strong><\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629: \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a\u060c \u0627\u0644\u062a\u0637\u0648\u064a\u0631 \u0648\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u0645\u0644\u062e\u0635: \u064a\u0634\u0631\u062d \u0647\u0630\u0627 \u0627\u0644\u0645\u0642\u0627\u0644 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0648\u0627\u0644\u062b\u0646\u0627\u0626\u064a\u0629 \u0641\u064a \u062d\u0633\u0627\u0628 \u0627\u0644\u062a\u0641\u0627\u0636\u0644 \u0648\u0627\u0644\u062a\u0643\u0627\u0645\u0644\u060c \u0648\u064a\u0648\u0636\u062d \u0643\u064a\u0641\u064a\u0629 \u062a\u0639\u0631\u064a\u0641\u0647\u0627 \u0648\u062a\u0637\u0628\u064a\u0642\u0647\u0627 \u0628\u0634\u0643\u0644 \u0628\u062f\u064a\u0647\u064a \u0648\u0631\u0633\u0645\u064a. \u062a\u064f\u0639\u0631\u0636 \u0623\u0645\u062b\u0644\u0629 \u0628\u064a\u0627\u0646\u064a\u0629 \u0648\u062c\u0628\u0631\u064a\u0629\u060c \u0648\u062a\u064f\u0646\u0627\u0642\u0634 \u0627\u0644\u0634\u0631\u0648\u0637 \u0644\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062c\u0628\u0631 \u0627\u0644\u062d\u062f\u0648\u062f \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0627\u062a\u060c \u0643\u0645\u0627 \u062a\u064f\u062f\u0631\u062c \u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629 \u0644\u062a\u0639\u0632\u064a\u0632 \u0627\u0644\u0641\u0647\u0645. \u0627\u0644\u0647\u062f\u0641 \u0647\u0648 \u062a\u0642\u062f\u064a\u0645 \u0631\u0624\u064a\u0629 \u0648\u0627\u0636\u062d\u0629 \u0648\u0645\u0648\u062c\u0632\u0629 \u0644\u0647\u0630\u0647 \u0627\u0644\u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0641\u064a \u062f\u0631\u0627\u0633\u0629 \u062d\u0633\u0627\u0628 \u0627\u0644\u062a\u0641\u0627\u0636\u0644 \u0648\u0627\u0644\u062a\u0643\u0627\u0645\u0644. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":27972,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":8,"footnotes":""},"categories":[860,565],"tags":[],"class_list":["post-27983","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 v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629: \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a\u060c \u0627\u0644\u062a\u0637\u0648\u064a\u0631 \u0648\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u0627\u0633\u062a\u0643\u0634\u0641 \u0634\u0631\u062d\u0627\u064b \u0645\u0641\u0635\u0644\u0627\u064b \u0644\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0648\u0627\u0644\u062b\u0646\u0627\u0626\u064a\u0629 \u0645\u0639 \u062a\u0639\u0631\u064a\u0641\u0627\u062a \u0631\u0633\u0645\u064a\u0629\u060c \u0623\u0645\u062b\u0644\u0629 \u0639\u0645\u0644\u064a\u0629 \u0648\u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/toposuranos.com\/material\/ar\/\u0627\u0644\u062d\u062f\u0648\u062f-\u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629-\u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a\u060c-\u0627\u0644\u062a\u0637\u0648\u064a\u0631-\u0648\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629: \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a\u060c \u0627\u0644\u062a\u0637\u0648\u064a\u0631 \u0648\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646\" \/>\n<meta property=\"og:description\" content=\"\u0627\u0633\u062a\u0643\u0634\u0641 \u0634\u0631\u062d\u0627\u064b \u0645\u0641\u0635\u0644\u0627\u064b \u0644\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0648\u0627\u0644\u062b\u0646\u0627\u0626\u064a\u0629 \u0645\u0639 \u062a\u0639\u0631\u064a\u0641\u0627\u062a \u0631\u0633\u0645\u064a\u0629\u060c \u0623\u0645\u062b\u0644\u0629 \u0639\u0645\u0644\u064a\u0629 \u0648\u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629\" \/>\n<meta property=\"og:url\" content=\"https:\/\/toposuranos.com\/material\/ar\/\u0627\u0644\u062d\u062f\u0648\u062f-\u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629-\u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a\u060c-\u0627\u0644\u062a\u0637\u0648\u064a\u0631-\u0648\/\" \/>\n<meta property=\"og:site_name\" content=\"toposuranos.com\/material\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/groups\/toposuranos\" \/>\n<meta property=\"article:published_time\" content=\"2024-08-17T13:00:47+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/limiteslaterales.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"\u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629: \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a\u060c \u0627\u0644\u062a\u0637\u0648\u064a\u0631 \u0648\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646\" \/>\n<meta name=\"twitter:description\" content=\"\u0627\u0633\u062a\u0643\u0634\u0641 \u0634\u0631\u062d\u0627\u064b \u0645\u0641\u0635\u0644\u0627\u064b \u0644\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0648\u0627\u0644\u062b\u0646\u0627\u0626\u064a\u0629 \u0645\u0639 \u062a\u0639\u0631\u064a\u0641\u0627\u062a \u0631\u0633\u0645\u064a\u0629\u060c \u0623\u0645\u062b\u0644\u0629 \u0639\u0645\u0644\u064a\u0629 \u0648\u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629\" \/>\n<meta name=\"twitter:image\" content=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/limiteslaterales.jpg\" \/>\n<meta name=\"twitter:creator\" content=\"@topuranos\" \/>\n<meta name=\"twitter:site\" content=\"@topuranos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"giorgio.reveco\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tiempo de lectura\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\\\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"\u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629: \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a\u060c \u0627\u0644\u062a\u0637\u0648\u064a\u0631 \u0648\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646\",\"datePublished\":\"2024-08-17T13:00:47+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\\\/\"},\"wordCount\":352,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/08\\\/limiteslaterales.jpg\",\"articleSection\":[\"\u062d\u0633\u0627\u0628 \u0627\u0644\u062a\u0641\u0627\u0636\u0644\",\"\u0631\u064a\u0627\u0636\u064a\u0627\u062a\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\\\/\",\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\\\/\",\"name\":\"\u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629: \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a\u060c \u0627\u0644\u062a\u0637\u0648\u064a\u0631 \u0648\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 - toposuranos.com\\\/material\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/08\\\/limiteslaterales.jpg\",\"datePublished\":\"2024-08-17T13:00:47+00:00\",\"description\":\"\u0627\u0633\u062a\u0643\u0634\u0641 \u0634\u0631\u062d\u0627\u064b \u0645\u0641\u0635\u0644\u0627\u064b \u0644\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0648\u0627\u0644\u062b\u0646\u0627\u0626\u064a\u0629 \u0645\u0639 \u062a\u0639\u0631\u064a\u0641\u0627\u062a \u0631\u0633\u0645\u064a\u0629\u060c \u0623\u0645\u062b\u0644\u0629 \u0639\u0645\u0644\u064a\u0629 \u0648\u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\\\/#breadcrumb\"},\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\\\/#primaryimage\",\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/08\\\/limiteslaterales.jpg\",\"contentUrl\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/08\\\/limiteslaterales.jpg\",\"width\":1024,\"height\":347},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/ar\\\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/es\\\/cursos-de-matematica-y-fisica\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629: \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a\u060c \u0627\u0644\u062a\u0637\u0648\u064a\u0631 \u0648\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#website\",\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/\",\"name\":\"toposuranos.com\\\/material\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"es\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#organization\",\"name\":\"toposuranos.com\\\/material\",\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/logo.png\",\"contentUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/logo.png\",\"width\":2400,\"height\":2059,\"caption\":\"toposuranos.com\\\/material\"},\"image\":{\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/www.facebook.com\\\/groups\\\/toposuranos\",\"https:\\\/\\\/x.com\\\/topuranos\",\"https:\\\/\\\/www.youtube.com\\\/channel\\\/UC16yDm12cPcrwsE0fAM7X1g\",\"https:\\\/\\\/www.linkedin.com\\\/company\\\/69429190\"]},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\",\"name\":\"giorgio.reveco\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/1694478625378-96x96.jpeg\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/1694478625378-96x96.jpeg\",\"contentUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/1694478625378-96x96.jpeg\",\"caption\":\"giorgio.reveco\"},\"description\":\"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.\",\"sameAs\":[\"http:\\\/\\\/toposuranos.com\\\/material\"],\"url\":\"https:\\\/\\\/toposuranos.com\\\/material\\\/author\\\/giorgio-reveco\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629: \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a\u060c \u0627\u0644\u062a\u0637\u0648\u064a\u0631 \u0648\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 - toposuranos.com\/material","description":"\u0627\u0633\u062a\u0643\u0634\u0641 \u0634\u0631\u062d\u0627\u064b \u0645\u0641\u0635\u0644\u0627\u064b \u0644\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0648\u0627\u0644\u062b\u0646\u0627\u0626\u064a\u0629 \u0645\u0639 \u062a\u0639\u0631\u064a\u0641\u0627\u062a \u0631\u0633\u0645\u064a\u0629\u060c \u0623\u0645\u062b\u0644\u0629 \u0639\u0645\u0644\u064a\u0629 \u0648\u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/toposuranos.com\/material\/ar\/\u0627\u0644\u062d\u062f\u0648\u062f-\u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629-\u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a\u060c-\u0627\u0644\u062a\u0637\u0648\u064a\u0631-\u0648\/","og_locale":"es_ES","og_type":"article","og_title":"\u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629: \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a\u060c \u0627\u0644\u062a\u0637\u0648\u064a\u0631 \u0648\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646","og_description":"\u0627\u0633\u062a\u0643\u0634\u0641 \u0634\u0631\u062d\u0627\u064b \u0645\u0641\u0635\u0644\u0627\u064b \u0644\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0648\u0627\u0644\u062b\u0646\u0627\u0626\u064a\u0629 \u0645\u0639 \u062a\u0639\u0631\u064a\u0641\u0627\u062a \u0631\u0633\u0645\u064a\u0629\u060c \u0623\u0645\u062b\u0644\u0629 \u0639\u0645\u0644\u064a\u0629 \u0648\u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629","og_url":"https:\/\/toposuranos.com\/material\/ar\/\u0627\u0644\u062d\u062f\u0648\u062f-\u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629-\u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a\u060c-\u0627\u0644\u062a\u0637\u0648\u064a\u0631-\u0648\/","og_site_name":"toposuranos.com\/material","article_publisher":"https:\/\/www.facebook.com\/groups\/toposuranos","article_published_time":"2024-08-17T13:00:47+00:00","og_image":[{"url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/limiteslaterales.jpg","type":"","width":"","height":""}],"author":"giorgio.reveco","twitter_card":"summary_large_image","twitter_title":"\u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629: \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a\u060c \u0627\u0644\u062a\u0637\u0648\u064a\u0631 \u0648\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646","twitter_description":"\u0627\u0633\u062a\u0643\u0634\u0641 \u0634\u0631\u062d\u0627\u064b \u0645\u0641\u0635\u0644\u0627\u064b \u0644\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0648\u0627\u0644\u062b\u0646\u0627\u0626\u064a\u0629 \u0645\u0639 \u062a\u0639\u0631\u064a\u0641\u0627\u062a \u0631\u0633\u0645\u064a\u0629\u060c \u0623\u0645\u062b\u0644\u0629 \u0639\u0645\u0644\u064a\u0629 \u0648\u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629","twitter_image":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/limiteslaterales.jpg","twitter_creator":"@topuranos","twitter_site":"@topuranos","twitter_misc":{"Escrito por":"giorgio.reveco","Tiempo de lectura":"3 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\/#article","isPartOf":{"@id":"https:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\/"},"author":{"name":"giorgio.reveco","@id":"https:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1"},"headline":"\u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629: \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a\u060c \u0627\u0644\u062a\u0637\u0648\u064a\u0631 \u0648\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646","datePublished":"2024-08-17T13:00:47+00:00","mainEntityOfPage":{"@id":"https:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\/"},"wordCount":352,"commentCount":0,"publisher":{"@id":"https:\/\/toposuranos.com\/material\/#organization"},"image":{"@id":"https:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\/#primaryimage"},"thumbnailUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/limiteslaterales.jpg","articleSection":["\u062d\u0633\u0627\u0628 \u0627\u0644\u062a\u0641\u0627\u0636\u0644","\u0631\u064a\u0627\u0636\u064a\u0627\u062a"],"inLanguage":"es","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\/","url":"https:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\/","name":"\u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629: \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a\u060c \u0627\u0644\u062a\u0637\u0648\u064a\u0631 \u0648\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 - toposuranos.com\/material","isPartOf":{"@id":"https:\/\/toposuranos.com\/material\/#website"},"primaryImageOfPage":{"@id":"https:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\/#primaryimage"},"image":{"@id":"https:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\/#primaryimage"},"thumbnailUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/limiteslaterales.jpg","datePublished":"2024-08-17T13:00:47+00:00","description":"\u0627\u0633\u062a\u0643\u0634\u0641 \u0634\u0631\u062d\u0627\u064b \u0645\u0641\u0635\u0644\u0627\u064b \u0644\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0648\u0627\u0644\u062b\u0646\u0627\u0626\u064a\u0629 \u0645\u0639 \u062a\u0639\u0631\u064a\u0641\u0627\u062a \u0631\u0633\u0645\u064a\u0629\u060c \u0623\u0645\u062b\u0644\u0629 \u0639\u0645\u0644\u064a\u0629 \u0648\u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629","breadcrumb":{"@id":"https:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\/#breadcrumb"},"inLanguage":"es","potentialAction":[{"@type":"ReadAction","target":["https:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\/"]}]},{"@type":"ImageObject","inLanguage":"es","@id":"https:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\/#primaryimage","url":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/limiteslaterales.jpg","contentUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/limiteslaterales.jpg","width":1024,"height":347},{"@type":"BreadcrumbList","@id":"https:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d8%a7%d9%84%d8%ac%d8%a7%d9%86%d8%a8%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa%d8%8c-%d8%a7%d9%84%d8%aa%d8%b7%d9%88%d9%8a%d8%b1-%d9%88\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"http:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/"},{"@type":"ListItem","position":2,"name":"\u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629: \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a\u060c \u0627\u0644\u062a\u0637\u0648\u064a\u0631 \u0648\u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646"}]},{"@type":"WebSite","@id":"https:\/\/toposuranos.com\/material\/#website","url":"https:\/\/toposuranos.com\/material\/","name":"toposuranos.com\/material","description":"","publisher":{"@id":"https:\/\/toposuranos.com\/material\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/toposuranos.com\/material\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"es"},{"@type":"Organization","@id":"https:\/\/toposuranos.com\/material\/#organization","name":"toposuranos.com\/material","url":"https:\/\/toposuranos.com\/material\/","logo":{"@type":"ImageObject","inLanguage":"es","@id":"https:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","width":2400,"height":2059,"caption":"toposuranos.com\/material"},"image":{"@id":"https:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/groups\/toposuranos","https:\/\/x.com\/topuranos","https:\/\/www.youtube.com\/channel\/UC16yDm12cPcrwsE0fAM7X1g","https:\/\/www.linkedin.com\/company\/69429190"]},{"@type":"Person","@id":"https:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1","name":"giorgio.reveco","image":{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","caption":"giorgio.reveco"},"description":"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.","sameAs":["http:\/\/toposuranos.com\/material"],"url":"https:\/\/toposuranos.com\/material\/author\/giorgio-reveco\/"}]}},"_links":{"self":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/27983","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/comments?post=27983"}],"version-history":[{"count":0,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/27983\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media\/27972"}],"wp:attachment":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media?parent=27983"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/categories?post=27983"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/tags?post=27983"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}