{"id":35268,"date":"2024-12-20T13:00:21","date_gmt":"2024-12-20T13:00:21","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=35268"},"modified":"2025-12-11T17:07:06","modified_gmt":"2025-12-11T17:07:06","slug":"%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/","title":{"rendered":"\u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0644\u0644\u0642\u064a\u0645 \u0627\u0644\u0642\u0635\u0648\u0649"},"content":{"rendered":"<style>\np, ul, ol{\ntext-align: justify;\n}\nh1{\ntext-align:center;\ntext-transform: uppercase;\n}\nh2{\ntext-align:center;\ntext-transform: uppercase;\nfont-size:24pt;\n}\nh3 { \n    text-align: center;\n    text-transform: uppercase;\n    font-size: 24px !important;\n}\n<\/style>\n<h1>\u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0644\u0644\u0642\u064a\u0645 \u0627\u0644\u0642\u0635\u0648\u0649<\/h1>\n<p style=\"text-align:center;\"><em>\u0644\u0645\u0627\u0630\u0627 \u064a\u064f\u0641\u062a\u0631\u0636 \u0641\u064a \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0623\u0646 \u00ab\u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u0639\u0638\u0645\u0649 \u0645\u0648\u062c\u0648\u062f\u0629\u00bb \u0623\u0648 \u0623\u0646 \u00ab\u0647\u0646\u0627\u0643 \u062f\u0627\u0626\u0645\u064b\u0627 \u0642\u064a\u0645\u0629 \u0635\u063a\u0631\u0649\u00bb \u0639\u0644\u0649 \u0641\u062a\u0631\u0629 \u0645\u0627\u060c \u0641\u064a \u062d\u064a\u0646 \u0623\u0646\u0651\u0647 \u0644\u0627 \u064a\u0648\u062c\u062f \u0645\u0627 \u064a\u0641\u0631\u0636 \u062d\u062f\u0648\u062b \u0630\u0644\u0643 \u0628\u0627\u0644\u0636\u0631\u0648\u0631\u0629\u061f \u062a\u064f\u0639\u062f <strong>\u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633<\/strong> \u0627\u0644\u0642\u0637\u0639\u0629 \u0627\u0644\u0645\u0641\u0642\u0648\u062f\u0629 \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0644\u063a\u0632\u060c \u0625\u0630 \u062a\u0636\u0645\u0646 \u0623\u0646\u0651 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u062a\u0635\u0644\u0629 \u0627\u0644\u0645\u0639\u0631\u0641\u0629 \u0639\u0644\u0649 \u0641\u062a\u0631\u0629 \u0645\u063a\u0644\u0642\u0629 \u0648\u0645\u062d\u062f\u0648\u062f\u0629 \u0644\u064a\u0633\u062a \u0645\u062d\u0635\u0648\u0631\u0629 \u0641\u062d\u0633\u0628\u060c \u0628\u0644 \u062a\u0628\u0644\u063a \u0641\u0639\u0644\u064a\u064b\u0627 \u0642\u064a\u0645\u0647\u0627 \u0627\u0644\u0642\u0635\u0648\u0649. \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062a\u062f\u0648\u064a\u0646\u0629 \u0646\u0633\u062a\u0639\u0631\u0636 \u0646\u0635 \u0627\u0644\u0645\u0628\u0631\u0647\u0646\u0629\u060c \u0648\u0646\u0628\u0646\u064a \u0628\u062a\u0641\u0635\u064a\u0644 \u0628\u0631\u0647\u0627\u0646\u064b\u0627 rigor\u064b\u0627 \u064a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0627\u0644\u0645\u0648\u0636\u0639\u064a\u0629\u060c \u0648\u0627\u0644\u0627\u062a\u0636\u0651\u0627\u0645\u060c \u0648\u0645\u0633\u0644\u0645\u0629 supremum\u060c \u0643\u0645\u0627 \u0646\u0639\u0644\u0651\u0642 \u0639\u0644\u0649 \u062a\u0641\u0633\u064a\u0631\u0647\u0627 \u0627\u0644\u062d\u062f\u064a\u062b \u0641\u064a \u0633\u064a\u0627\u0642 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u062a\u0635\u0644\u0629 \u0639\u0644\u0649 \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0627\u0644\u0645\u062f\u0645\u062c\u0629. \u0627\u0644\u0641\u0643\u0631\u0629 \u0647\u064a \u0623\u0646\u0651\u0643 \u0639\u0646\u062f \u0627\u0644\u0627\u0646\u062a\u0647\u0627\u0621 \u0644\u0646 \u062a\u062a\u0630\u0643\u0631 \u0627\u0644\u0645\u0628\u0631\u0647\u0646\u0629 \u0643\u062c\u0645\u0644\u0629 \u0641\u0642\u0637\u060c \u0628\u0644 \u0633\u062a\u0641\u0647\u0645 \u0644\u0645\u0627\u0630\u0627 \u0647\u064a \u0635\u062d\u064a\u062d\u0629 \u0648\u0644\u0645\u0627\u0630\u0627 \u062a\u0638\u0647\u0631 \u0645\u0631\u0627\u0631\u064b\u0627 \u0641\u064a \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u060c \u0648\u0641\u064a \u0627\u0644\u0623\u0645\u062b\u0644\u0629\u060c \u0648\u0641\u064a \u0627\u0644\u0646\u0645\u0627\u0630\u062c \u0627\u0644\u062a\u0637\u0628\u064a\u0642\u064a\u0629.<\/em><\/p>\n<p style=\"text-align:center;\"><b>\u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0645<\/b><\/p>\n<ol>\n<li>\n    <strong>\u0641\u0647\u0645 \u0646\u0635 \u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633.<\/strong><br \/>\n    \u062a\u062d\u062f\u064a\u062f \u0641\u0631\u0636\u064a\u0627\u062a \u0627\u0644\u0645\u0628\u0631\u0647\u0646\u0629 \u0628\u062f\u0642\u0629 (\u062f\u0627\u0644\u0629 \u0645\u062a\u0635\u0644\u0629 \u0639\u0644\u0649 \u0641\u062a\u0631\u0629 \u0645\u063a\u0644\u0642\u0629 \u0648\u0645\u062d\u062f\u0648\u062f\u0629 <span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span>) \u0648\u0627\u0633\u062a\u0646\u062a\u0627\u062c\u0627\u062a\u0647\u0627 \u0627\u0644\u0631\u0626\u064a\u0633\u0629: \u0627\u0644\u0627\u0646\u062d\u0635\u0627\u0631 \u0648\u0648\u062c\u0648\u062f \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0639\u0638\u0645\u0649 \u0648\u0627\u0644\u0635\u063a\u0631\u0649.\n  <\/li>\n<li>\n    <strong>\u062a\u0641\u0633\u064a\u0631 \u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0645\u0646 \u0645\u0646\u0638\u0648\u0631 \u0627\u0644\u0627\u062a\u0636\u0651\u0627\u0645.<\/strong><br \/>\n    \u0635\u064a\u0627\u063a\u0629 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0628\u0644\u063a\u0629 \u062d\u062f\u064a\u062b\u0629: \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u062a\u0635\u0644\u0629 \u062a\u0631\u0633\u0644 \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0627\u0644\u0645\u062f\u0645\u062c\u0629 \u0625\u0644\u0649 \u0645\u062c\u0645\u0648\u0639\u0627\u062a \u062a\u064f\u0628\u0644\u064e\u063a \u0641\u064a\u0647\u0627 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0642\u0635\u0648\u0649\u060c \u0628\u0645\u0627 \u064a\u0631\u0628\u0637 \u062d\u0627\u0644\u0629 <span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span> \u0628\u0627\u0644\u0625\u0637\u0627\u0631 \u0627\u0644\u0639\u0627\u0645 \u0644\u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u062d\u0642\u064a\u0642\u064a.\n  <\/li>\n<li>\n    <strong>\u0631\u0628\u0637 \u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0628\u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0623\u0645\u062b\u0644\u0629.<\/strong><br \/>\n    \u0627\u0644\u062a\u0639\u0631\u0641 \u0625\u0644\u0649 \u062f\u0648\u0631 \u0627\u0644\u0645\u0628\u0631\u0647\u0646\u0629 \u0643\u0623\u0633\u0627\u0633 \u0646\u0638\u0631\u064a \u0644\u0648\u062c\u0648\u062f \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0639\u0638\u0645\u0649 \u0648\u0627\u0644\u0635\u063a\u0631\u0649 \u0641\u064a \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0641\u064a \u0645\u062a\u063a\u064a\u0631 \u0648\u0627\u062d\u062f\u060c \u0633\u0648\u0627\u0621 \u0641\u064a \u0627\u0644\u0633\u064a\u0627\u0642\u0627\u062a \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0623\u0648 \u0627\u0644\u062a\u0637\u0628\u064a\u0642\u064a\u0629.\n  <\/li>\n<\/ol>\n<p style=\"text-align:center;\"><b><u>\u0641\u0647\u0631\u0633 \u0627\u0644\u0645\u062d\u062a\u0648\u064a\u0627\u062a<\/u>:<\/b><br \/>\n<a href=\"#1\"><b>\u0627\u0644\u0645\u0642\u062f\u0645\u0629<\/b><\/a><br \/>\n<a href=\"#2\"><b>\u0646\u0635 \u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633<\/b><\/a><br \/>\n<a href=\"#3\">\u0627\u0644\u0628\u0631\u0647\u0627\u0646<\/a><br \/>\n<a href=\"#4\">\u0627\u0644\u062e\u0637\u0648\u0629 1: \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0627\u0644\u0645\u0648\u0636\u0639\u064a\u0629 \u0639\u0644\u0649 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/a><br \/>\n<a href=\"#5\">\u0627\u0644\u062e\u0637\u0648\u0629 2: \u0627\u0644\u063a\u0637\u0627\u0621 \u0627\u0644\u0645\u0641\u062a\u0648\u062d \u0627\u0644\u0645\u0631\u062a\u0628\u0637 \u0628\u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629<\/a><br \/>\n<a href=\"#6\">\u0627\u0644\u062e\u0637\u0648\u0629 3: \u0627\u062a\u0636\u0651\u0627\u0645 <span dir=\"ltr\">[a,b]<\/span> \u0648\u0648\u062c\u0648\u062f \u063a\u0637\u0627\u0621 \u0641\u0631\u0639\u064a \u0645\u0646\u062a\u0647\u064d<\/a><br \/>\n<a href=\"#7\">\u0627\u0644\u062e\u0637\u0648\u0629 4: \u0628\u0646\u0627\u0621 <span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span> \u0644\u0627 \u064a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> (\u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0627\u0644\u0645\u0646\u062a\u0638\u0645\u0629)<\/a><br \/>\n<a href=\"#8\">\u0627\u0644\u062e\u0637\u0648\u0629 5: \u0645\u0646 \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0627\u0644\u0645\u0646\u062a\u0638\u0645\u0629 \u0625\u0644\u0649 \u0627\u0646\u062d\u0635\u0627\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u0639\u0644\u0649 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/a><br \/>\n<a href=\"#9\">\u0627\u0644\u062e\u0637\u0648\u0629 6: \u0648\u062c\u0648\u062f \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0639\u0638\u0645\u0649 \u0648\u0627\u0644\u0635\u063a\u0631\u0649<\/a><br \/>\n<a href=\"#10\"><b>\u062a\u0641\u0633\u064a\u0631 \u0645\u0646 \u0645\u0646\u0638\u0648\u0631 \u0627\u0644\u0627\u062a\u0636\u0651\u0627\u0645 \u0648\u062e\u0627\u062a\u0645\u0629<\/b><\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/N5mSrhJgCds\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><br \/>\n<a name=\"1\"><\/a><\/br><\/p>\n<h2>\u0627\u0644\u0645\u0642\u062f\u0645\u0629<\/h2>\n<p>\n\u062a\u064f\u0639\u062f <strong>\u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0644\u0644\u0642\u064a\u0645 \u0627\u0644\u0642\u0635\u0648\u0649<\/strong> \u0648\u0627\u062d\u062f\u0629 \u0645\u0646 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0627\u0644\u062a\u064a\u060c \u0639\u0644\u0649 \u0627\u0644\u0631\u063a\u0645 \u0645\u0646 \u0638\u0647\u0648\u0631\u0647\u0627 \u0639\u0627\u062f\u0629\u064b \u0641\u064a \u0627\u0644\u0648\u062d\u062f\u0627\u062a \u0627\u0644\u0623\u0648\u0644\u0649 \u0645\u0646 \u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u062d\u0642\u064a\u0642\u064a\u060c \u0641\u0625\u0646\u0647\u0627 \u062a\u062f\u0639\u0645 \u0628\u0635\u0645\u062a \u062c\u0632\u0621\u064b\u0627 \u0643\u0628\u064a\u0631\u064b\u0627 \u0645\u0646 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u062a\u0637\u0628\u064a\u0642\u064a\u0629. \u0641\u0641\u064a \u0643\u0644 \u0645\u0631\u0629 \u0646\u062a\u062d\u062f\u062b \u0641\u064a\u0647\u0627 \u0641\u064a \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 \u0623\u0648 \u0627\u0644\u0627\u0642\u062a\u0635\u0627\u062f \u0623\u0648 \u0627\u0644\u0625\u062d\u0635\u0627\u0621 \u0639\u0646 \u00ab\u062a\u0639\u0638\u064a\u0645\u00bb \u0623\u0648 \u00ab\u062a\u0635\u063a\u064a\u0631\u00bb \u0643\u0645\u064a\u0629 \u0645\u0627 \u062e\u0627\u0636\u0639\u0629 \u0644\u0642\u064a\u0648\u062f \u0645\u0639\u064a\u0646\u0629\u060c \u0646\u0643\u0648\u0646 \u0641\u064a \u0627\u0644\u062d\u0642\u064a\u0642\u0629 \u0646\u0633\u062a\u0639\u0645\u0644 \u0641\u0643\u0631\u0629 \u0642\u0631\u064a\u0628\u0629 \u062c\u062f\u064b\u0627 \u0645\u0646 \u0627\u0644\u0645\u0636\u0645\u0648\u0646 \u0627\u0644\u0630\u064a \u062a\u0636\u0645\u0646\u0647 \u0647\u0630\u0647 \u0627\u0644\u0645\u0628\u0631\u0647\u0646\u0629: \u0648\u0647\u064a \u0623\u0646\u0651 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u062a\u0635\u0644\u0629 \u0627\u0644\u0645\u0639\u0631\u0641\u0629 \u0639\u0644\u0649 \u0641\u062a\u0631\u0629 \u0645\u063a\u0644\u0642\u0629 \u0648\u0645\u062d\u062f\u0648\u062f\u0629 <strong>\u0644\u064a\u0633\u062a \u0645\u062d\u0635\u0648\u0631\u0629 \u0641\u062d\u0633\u0628\u060c \u0628\u0644 \u062a\u0628\u0644\u063a \u0641\u0639\u0644\u064a\u064b\u0627 \u0642\u064a\u0645\u0647\u0627 \u0627\u0644\u0642\u0635\u0648\u0649<\/strong>.\n<\/p>\n<p>\n\u0642\u062f \u064a\u0628\u062f\u0648 \u0645\u0646 \u0627\u0644\u0646\u0627\u062d\u064a\u0629 \u0627\u0644\u062d\u062f\u0633\u064a\u0629 \u00ab\u0628\u062f\u064a\u0647\u064a\u064b\u0627\u00bb \u0623\u0646\u0647 \u0625\u0630\u0627 \u0631\u0633\u0645\u0646\u0627 \u0645\u0646\u062d\u0646\u0649 \u0645\u062a\u0635\u0644\u064b\u0627 \u0639\u0644\u0649 \u0642\u0637\u0639\u0629 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong>\u060c \u0641\u0625\u0646\u0647 \u064a\u062c\u0628 \u0623\u0646 \u064a\u0648\u062c\u062f \u0646\u0642\u0637\u0629 \u0623\u0639\u0644\u0649 \u0648\u0623\u062e\u0631\u0649 \u0623\u062f\u0646\u0649. \u0648\u0645\u0639 \u0630\u0644\u0643\u060c \u064a\u0643\u0641\u064a \u0625\u062c\u0631\u0627\u0621 \u062a\u063a\u064a\u064a\u0631\u0627\u062a \u0637\u0641\u064a\u0641\u0629 \u0641\u064a \u0627\u0644\u0641\u0631\u0636\u064a\u0627\u062a \u062d\u062a\u0649 \u064a\u0646\u0647\u0627\u0631 \u0647\u0630\u0627 \u0627\u0644\u062d\u062f\u0633 \u0627\u0646\u0647\u064a\u0627\u0631\u064b\u0627 \u0643\u0627\u0645\u0644\u064b\u0627: \u0641\u0625\u0630\u0627 \u0641\u062a\u062d\u0646\u0627 \u0627\u0644\u0641\u062a\u0631\u0629\u060c \u0623\u0648 \u0641\u0642\u062f\u062a \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629\u060c \u0623\u0648 \u0644\u0645 \u064a\u0643\u0646 \u0627\u0644\u0645\u062c\u0627\u0644 \u0645\u062d\u062f\u0648\u062f\u064b\u0627\u060c \u064a\u0645\u0643\u0646 \u0644\u0644\u0642\u064a\u0645 \u0627\u0644\u0639\u0638\u0645\u0649 \u0648\u0627\u0644\u0635\u063a\u0631\u0649 \u0623\u0646 \u062a\u062e\u062a\u0641\u064a \u0628\u0628\u0633\u0627\u0637\u0629. \u062a\u0642\u0648\u0645 \u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0628\u062a\u0631\u062a\u064a\u0628 \u0647\u0630\u0627 \u0627\u0644\u062d\u062f\u0633 \u0648\u062a\u062e\u0628\u0631\u0646\u0627 \u0628\u062f\u0642\u0629 <em>\u0645\u062a\u0649<\/em> \u064a\u0645\u0643\u0646 \u0627\u0644\u0627\u0639\u062a\u0645\u0627\u062f \u0639\u0644\u064a\u0647 \u0648<em>\u0644\u0645\u0627\u0630\u0627<\/em>.\n<\/p>\n<p>\n\u0645\u0646 \u0645\u0646\u0638\u0648\u0631 \u0646\u0638\u0631\u064a\u060c \u062a\u064f\u0639\u062f \u0647\u0630\u0647 \u0627\u0644\u0645\u0628\u0631\u0647\u0646\u0629 \u0623\u0648\u0644 \u0645\u0648\u0627\u062c\u0647\u0629 \u062c\u062f\u064a\u0629 \u0645\u0639 \u0641\u0643\u0631\u0629 <strong>\u0627\u0644\u0627\u062a\u0636\u0651\u0627\u0645<\/strong>: \u0641\u0628\u0644\u063a\u0629 \u062d\u062f\u064a\u062b\u0629\u060c \u0645\u0627 \u062a\u0642\u0648\u0644\u0647 \u0647\u0648 \u0623\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u062a\u0635\u0644\u0629 \u062a\u062d\u0648\u0644 \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0627\u0644\u0645\u062f\u0645\u062c\u0629 \u0625\u0644\u0649 \u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0645\u062f\u0645\u062c\u0629. \u0648\u0645\u0646 \u0645\u0646\u0638\u0648\u0631 \u0639\u0645\u0644\u064a\u060c \u064a\u062a\u0631\u062c\u0645 \u0630\u0644\u0643 \u0625\u0644\u0649 \u0648\u062c\u0648\u062f \u062d\u0644\u0648\u0644 \u0644\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0641\u064a \u0628\u0639\u062f \u0648\u0627\u062d\u062f\u060c \u0643\u0645\u0627 \u0633\u062a\u0643\u0648\u0646 \u0639\u0646\u0635\u0631\u064b\u0627 \u0623\u0633\u0627\u0633\u064a\u064b\u0627 \u0641\u064a \u0646\u062a\u0627\u0626\u062c \u0644\u0627\u062d\u0642\u0629 \u0645\u062b\u0644 <b>\u0645\u0628\u0631\u0647\u0646\u0629 \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u0645\u062a\u0648\u0633\u0637\u0629<\/b>\u060c \u0648\u0641\u064a \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u0645\u0637\u0627\u0641 \u0644\u0641\u0647\u0645 \u0645\u062a\u0645\u0647\u0644 \u0644\u0640 \u00ab\u0627\u0644\u0645\u0628\u0631\u0647\u0646\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0641\u064a \u0627\u0644\u062d\u0633\u0627\u0628\u00bb.\n<\/p>\n<p>\n\u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0642\u0633\u0645 \u0633\u0646\u0639\u0631\u0636 \u0646\u0635 \u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0648\u0633\u0646\u0637\u0648\u0651\u0631 \u0628\u0631\u0647\u0627\u0646\u0647\u0627 \u0628\u062a\u0641\u0635\u064a\u0644\u060c \u0645\u0633\u062a\u0646\u062f\u064a\u0646 \u0625\u0644\u0649 \u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0639\u0644\u0649 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u0648\u0625\u0644\u0649 \u0645\u0633\u0644\u0645\u0629 supremum. \u0627\u0644\u0647\u062f\u0641 \u0647\u0648 \u0623\u0646 \u064a\u0643\u0648\u0646 \u0647\u0630\u0627 \u0627\u0644\u0646\u0635 \u0645\u0631\u062c\u0639\u064b\u0627 \u0631\u0627\u0633\u062e\u064b\u0627: \u0633\u0648\u0627\u0621 \u0644\u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0628\u062d\u062f \u0630\u0627\u062a\u0647\u0627\u060c \u0623\u0648 \u0644\u0644\u0639\u0648\u062f\u0629 \u0625\u0644\u064a\u0647\u0627 \u0643\u0644\u0645\u0627 \u0627\u062d\u062a\u062c\u062a \u0644\u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647\u0627 \u0639\u0646\u062f \u0628\u0631\u0647\u0646\u0629 \u0645\u0628\u0631\u0647\u0646\u0627\u062a \u0623\u062e\u0631\u0649 \u0623\u0648 \u0639\u0646\u062f \u062a\u0628\u0631\u064a\u0631 \u0648\u062c\u0648\u062f \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0639\u0638\u0645\u0649 \u0648\u0627\u0644\u0635\u063a\u0631\u0649 \u0641\u064a \u0645\u0633\u0627\u0626\u0644 \u0645\u062d\u062f\u062f\u0629.\n<\/p>\n<p><a name=\"2\"><\/a><\/br><\/p>\n<h2>\u0646\u0635 \u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633<\/h2>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: justify; background-color: #e0e0ff;\">\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=N5mSrhJgCds&amp;t=439s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0643\u0644 \u062f\u0627\u0644\u0629 <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u0645\u0639\u0631\u0641\u0629<\/span><\/strong><\/a> \u0648\u0645\u062a\u0635\u0644\u0629 \u0639\u0644\u0649 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b],<\/span><\/span> \u0647\u064a \u062f\u0627\u0644\u0629 \u0645\u062d\u0635\u0648\u0631\u0629 \u0648\u0644\u0647\u0627 \u0642\u064a\u0645\u062a\u0627 \u0635\u063a\u0631\u0649 \u0648\u0639\u0638\u0645\u0649\u060c <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u0648<span class=\"katex-eq\" data-katex-display=\"false\">M<\/span>\u060c \u0628\u062d\u064a\u062b \u0625\u0630\u0627 \u0643\u0627\u0646\u062a <span class=\"katex-eq\" data-katex-display=\"false\">x\\in[a,b]<\/span>\u060c \u0641\u0625\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)\\in[m,M]<\/span><\/span>.<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"3\"><\/a><\/br><\/p>\n<h3>\u0627\u0644\u0628\u0631\u0647\u0627\u0646<\/h3>\n<p>\n\u0644\u0646\u0628\u0631\u0647\u0646 \u0623\u0646\u0647 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f:[a,b]\\to\\mathbb{R}<\/span><\/span><\/strong> \u062f\u0627\u0644\u0629 \u0645\u062a\u0635\u0644\u0629 \u0639\u0644\u0649 \u0627\u0644\u0641\u062a\u0631\u0629 \u0627\u0644\u0645\u063a\u0644\u0642\u0629 \u0648\u0627\u0644\u0645\u062d\u062f\u0648\u062f\u0629 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong>\u060c \u0641\u0625\u0646 <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u062f\u0627\u0644\u0629 \u0645\u062d\u0635\u0648\u0631\u0629 \u0648\u062a\u0628\u0644\u063a \u0642\u064a\u0645\u0629 \u0639\u0638\u0645\u0649 \u0648\u0642\u064a\u0645\u0629 \u0635\u063a\u0631\u0649 \u0639\u0644\u0649 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong>. \u0633\u0646\u0642\u0633\u0645 \u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u0625\u0644\u0649 \u062c\u0632\u0623\u064a\u0646 \u0643\u0628\u064a\u0631\u064a\u0646:\n<\/p>\n<ul>\n<li>\u0623\u0648\u0644\u064b\u0627\u060c \u0633\u0646\u0628\u064a\u0651\u0646 \u0623\u0646 \u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u0639\u0644\u0649 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u062a\u0633\u062a\u0644\u0632\u0645 \u0623\u0646 \u062a\u0643\u0648\u0646 <em>\u0645\u0633\u062a\u0645\u0631\u0629 \u0628\u0627\u0646\u062a\u0638\u0627\u0645<\/em>\u060c \u0648\u0645\u0646 \u0630\u0644\u0643 \u0633\u0646\u0633\u062a\u0646\u062a\u062c \u0623\u0646\u0647\u0627 <strong>\u0645\u062d\u0635\u0648\u0631\u0629<\/strong>.<\/li>\n<li>\u062b\u0645\u060c \u0648\u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0633\u0644\u0645\u0629 supremum\u060c \u0633\u0646\u0628\u0631\u0647\u0646 \u0623\u0646 <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u062a\u0628\u0644\u063a \u0642\u064a\u0645\u0647\u0627 \u0627\u0644\u0639\u0638\u0645\u0649 \u0648\u0627\u0644\u0635\u063a\u0631\u0649 \u0639\u0644\u0649 \u0627\u0644\u0641\u062a\u0631\u0629.<\/li>\n<\/ul>\n<p><a name=\"4\"><\/a><\/br><\/p>\n<h4><b>\u0627\u0644\u062e\u0637\u0648\u0629 1:<\/b> \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0627\u0644\u0645\u0648\u0636\u0639\u064a\u0629 \u0639\u0644\u0649 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/h4>\n<p>\n\u0648\u0641\u0642\u064b\u0627 \u0644\u0644\u0641\u0631\u0636\u060c \u0641\u0625\u0646 <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u0645\u062a\u0635\u0644\u0629 \u0639\u0646\u062f \u0643\u0644 \u0646\u0642\u0637\u0629 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in[a,b]<\/span><\/span><\/strong>. \u0648\u062a\u0639\u0646\u064a \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0628\u062d\u0633\u0628 \u062a\u0639\u0631\u064a\u0641 <span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon<\/span> \u0648<span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span> \u0645\u0627 \u064a\u0644\u064a:\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n(\\forall x_0\\in[a,b])(\\forall \\epsilon\\gt 0)(\\exists \\delta(x_0)\\gt 0)\n\n\\big(|x-x_0|\\lt\\delta(x_0)\\Rightarrow |f(x)-f(x_0)|\\lt\\epsilon\\big).\n\n<\/span>\n<\/p>\n<p>\n\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0645\u0631\u062d\u0644\u0629\u060c \u0642\u062f \u064a\u0639\u062a\u0645\u062f \u0627\u0644\u0639\u062f\u062f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta(x_0)<\/span><\/span><\/strong> \u0639\u0644\u0649 \u0627\u0644\u0646\u0642\u0637\u0629 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong>. \u0647\u062f\u0641\u0646\u0627 \u0627\u0644\u0645\u0628\u0627\u0634\u0631 \u0647\u0648 \u0623\u0646 \u0646\u0628\u0646\u064a\u060c \u0627\u0646\u0637\u0644\u0627\u0642\u064b\u0627 \u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u0645\u0642\u0627\u062f\u064a\u0631 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta(x_0)<\/span><\/span><\/strong>\u060c \u0639\u062f\u062f\u064b\u0627 \u0648\u0627\u062d\u062f\u064b\u0627 <strong><span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span><\/strong> \u0644\u0627 \u064a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong> \u0648\u064a\u0635\u0644\u062d \u0644\u062c\u0645\u064a\u0639 \u0646\u0642\u0627\u0637 \u0627\u0644\u0641\u062a\u0631\u0629 \u0641\u064a \u0622\u0646 \u0648\u0627\u062d\u062f.\n<\/p>\n<p><a name=\"5\"><\/a><\/br><\/p>\n<h4><b>\u0627\u0644\u062e\u0637\u0648\u0629 2:<\/b> \u0627\u0644\u063a\u0637\u0627\u0621 \u0627\u0644\u0645\u0641\u062a\u0648\u062d \u0627\u0644\u0645\u0631\u062a\u0628\u0637 \u0628\u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629<\/h4>\n<p>\n\u0644\u0646\u062b\u0628\u062a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon\\gt 0<\/span><\/span><\/strong> \u0643\u064a\u0641\u0645\u0627 \u0643\u0627\u0646. \u0648\u0644\u0643\u0644 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in[a,b]<\/span><\/span><\/strong>\u060c \u062a\u0633\u0645\u062d \u0644\u0646\u0627 \u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u0628\u0627\u062e\u062a\u064a\u0627\u0631 \u0639\u062f\u062f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta(x_0)\\gt 0<\/span><\/span><\/strong> \u0628\u062d\u064a\u062b\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|x-x_0|\\lt\\delta(x_0)\\Rightarrow |f(x)-f(x_0)|\\lt\\frac{\\epsilon}{2}.\n\n<\/span>\n<\/p>\n<p>\n\u0627\u0646\u0637\u0644\u0627\u0642\u064b\u0627 \u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u0642\u064a\u0645 \u0646\u0639\u0631\u0651\u0641\u060c \u0644\u0643\u0644 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in[a,b]<\/span><\/span><\/strong>\u060c \u0641\u062a\u0631\u0629 \u0645\u0641\u062a\u0648\u062d\u0629\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nI_{x_0}=\\left(x_0-\\frac{\\delta(x_0)}{2},\\,x_0+\\frac{\\delta(x_0)}{2}\\right).\n\n<\/span>\n<\/p>\n<p>\n\u0643\u0644 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{x_0}<\/span><\/span><\/strong> \u0647\u0648 \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0641\u062a\u0648\u062d\u0629 \u0641\u064a <span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}<\/span>\u060c \u0643\u0645\u0627 \u0623\u0646 \u0627\u0644\u0639\u0627\u0626\u0644\u0629\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n\\{I_{x_0}\\}_{x_0\\in[a,b]}\n\n<\/span>\n<\/p>\n<p>\n\u062a\u0634\u0643\u0644 <strong>\u063a\u0637\u0627\u0621\u064b \u0645\u0641\u062a\u0648\u062d\u064b\u0627<\/strong> \u0644\u0644\u0641\u062a\u0631\u0629 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong>. \u0641\u0628\u0645\u062c\u0631\u062f \u0627\u062e\u062a\u064a\u0627\u0631 \u0623\u064a \u0646\u0642\u0637\u0629 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y\\in[a,b]<\/span><\/span><\/strong>\u060c \u064a\u0643\u0641\u064a \u0623\u062e\u0630 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0=y<\/span><\/span><\/strong>\u061b \u0648\u0628\u0645\u0642\u062a\u0636\u0649 \u0627\u0644\u0628\u0646\u0627\u0621\u060c \u064a\u0643\u0648\u0646 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y\\in I_y<\/span><\/span><\/strong>. \u0648\u0647\u0643\u0630\u0627\u060c \u0641\u0625\u0646 \u0643\u0644 \u0646\u0642\u0637\u0629 \u0645\u0646 \u0627\u0644\u0641\u062a\u0631\u0629 \u062a\u0646\u062a\u0645\u064a \u0625\u0644\u0649 \u0648\u0627\u062d\u062f \u0639\u0644\u0649 \u0627\u0644\u0623\u0642\u0644 \u0645\u0646 \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0627\u0644\u0645\u0641\u062a\u0648\u062d\u0629 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{x_0}<\/span><\/span><\/strong>.\n<\/p>\n<p>\n\u0647\u0630\u0647 \u0627\u0644\u0639\u0627\u0626\u0644\u0629 \u0645\u0646 \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0627\u0644\u0645\u0641\u062a\u0648\u062d\u0629 \u0647\u064a\u060c \u0641\u064a \u0627\u0644\u0639\u0645\u0648\u0645\u060c <strong>\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629<\/strong> (\u0644\u0643\u0648\u0646 \u0647\u0646\u0627\u0643 \u0645\u062c\u0645\u0648\u0639\u0629 \u0644\u0643\u0644 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in[a,b]<\/span><\/span><\/strong>). \u0648\u0647\u0646\u0627 \u064a\u0638\u0647\u0631 \u062f\u0648\u0631 \u0627\u062a\u0636\u0651\u0627\u0645 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong>.\n<\/p>\n<p><a name=\"6\"><\/a><\/br><\/p>\n<h4><b>\u0627\u0644\u062e\u0637\u0648\u0629 3:<\/b> \u0627\u062a\u0636\u0651\u0627\u0645 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u0648\u0648\u062c\u0648\u062f \u063a\u0637\u0627\u0621 \u0641\u0631\u0639\u064a \u0645\u0646\u062a\u0647\u064d<\/h4>\n<p>\n\u0646\u0639\u0644\u0645 \u0645\u0646 \u0645\u0628\u0631\u0647\u0646\u0629 \u0647\u0627\u064a\u0646\u0647\u2013\u0628\u0648\u0631\u064a\u0644 \u0623\u0646 \u0623\u064a \u0645\u062c\u0645\u0648\u0639\u0629 \u062c\u0632\u0626\u064a\u0629 \u0645\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}<\/span><\/span> \u062a\u0643\u0648\u0646 \u0645\u062f\u0645\u062c\u0629 \u0625\u0630\u0627 \u0648\u0641\u0642\u0637 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0645\u063a\u0644\u0642\u0629 \u0648\u0645\u062d\u062f\u0648\u062f\u0629. \u0648\u0628\u0645\u0627 \u0623\u0646 \u0627\u0644\u0641\u062a\u0631\u0629 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u0645\u063a\u0644\u0642\u0629 \u0648\u0645\u062d\u062f\u0648\u062f\u0629\u060c \u0641\u0647\u064a \u0625\u0630\u0646 \u0645\u062f\u0645\u062c\u0629. \u0648\u0628\u062d\u0633\u0628 \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0627\u062a\u0636\u0651\u0627\u0645\u060c \u064a\u0639\u0646\u064a \u0630\u0644\u0643:\n<\/p>\n<p>\n\u0625\u0646\u0647 \u0645\u0646 <strong>\u0643\u0644<\/strong> \u063a\u0637\u0627\u0621 \u0645\u0641\u062a\u0648\u062d \u0644\u0644\u0641\u062a\u0631\u0629 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> (\u062d\u062a\u0649 \u0648\u0625\u0646 \u0643\u0627\u0646 \u064a\u0636\u0645 \u0639\u062f\u062f\u064b\u0627 \u063a\u064a\u0631 \u0645\u0646\u062a\u0647\u064d \u0645\u0646 \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0627\u062a) \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u0631\u0627\u062c <strong>\u063a\u0637\u0627\u0621 \u0641\u0631\u0639\u064a \u0645\u0646\u062a\u0647\u064d<\/strong>.\n<\/p>\n<p>\n\u0648\u0639\u0646\u062f \u062a\u0637\u0628\u064a\u0642 \u0647\u0630\u0647 \u0627\u0644\u062e\u0627\u0635\u064a\u0629 \u0639\u0644\u0649 \u0627\u0644\u063a\u0637\u0627\u0621 \u0627\u0644\u0645\u0641\u062a\u0648\u062d <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{I_{x_0}\\}_{x_0\\in[a,b]}<\/span><\/span><\/strong>\u060c \u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u0648\u062c\u0648\u062f \u0646\u0642\u0627\u0637 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_1,\\dots,x_N\\in[a,b]<\/span><\/span><\/strong> \u0628\u062d\u064a\u062b \u0627\u0644\u0641\u062a\u0631\u0627\u062a \u0627\u0644\u0645\u0642\u0627\u0628\u0644\u0629\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nI_{x_1},\\, I_{x_2},\\,\\dots,\\,I_{x_N}\n\n<\/span>\n<\/p>\n<p>\n\u0644\u0627 \u062a\u0632\u0627\u0644 \u062a\u063a\u0637\u064a \u0643\u0627\u0645\u0644 \u0627\u0644\u0641\u062a\u0631\u0629:\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n[a,b]\\subset I_{x_1}\\cup I_{x_2}\\cup\\cdots\\cup I_{x_N}.\n\n<\/span>\n<\/p>\n<p>\n\u0648\u0628\u0630\u0644\u0643 \u0646\u0643\u0648\u0646 \u0642\u062f \u0627\u0646\u062a\u0642\u0644\u0646\u0627 \u0645\u0646 \u0639\u0627\u0626\u0644\u0629 \u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629 \u0645\u0646 \u0627\u0644\u0641\u062a\u0631\u0627\u062a \u0627\u0644\u0645\u0641\u062a\u0648\u062d\u0629 \u0625\u0644\u0649 \u063a\u0637\u0627\u0621 \u0641\u0631\u0639\u064a \u064a\u062a\u0643\u0648\u0646 \u0645\u0646 <strong>\u0639\u062f\u062f \u0645\u0646\u062a\u0647\u064d<\/strong> \u0645\u0646 \u0627\u0644\u0641\u062a\u0631\u0627\u062a\u060c \u0645\u0646 \u062f\u0648\u0646 \u0623\u0646 \u0646\u0641\u0642\u062f \u062e\u0627\u0635\u064a\u0629 \u062a\u063a\u0637\u064a\u0629 \u0627\u0644\u0641\u062a\u0631\u0629 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong>.\n<\/p>\n<p><a name=\"7\"><\/a><\/br><\/p>\n<h4><b>\u0627\u0644\u062e\u0637\u0648\u0629 4:<\/b> \u0628\u0646\u0627\u0621 <span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span> \u0644\u0627 \u064a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> (\u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0627\u0644\u0645\u0646\u062a\u0638\u0645\u0629)<\/h4>\n<p>\n\u0627\u0646\u0637\u0644\u0627\u0642\u064b\u0627 \u0645\u0646 \u0627\u0644\u063a\u0637\u0627\u0621 \u0627\u0644\u0641\u0631\u0639\u064a \u0627\u0644\u0645\u0646\u062a\u0647\u064a \u0646\u0639\u0631\u0651\u0641 \u0627\u0644\u0639\u062f\u062f\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n\\delta=\\min\\left\\{\\frac{\\delta(x_1)}{2},\\frac{\\delta(x_2)}{2},\\dots,\\frac{\\delta(x_N)}{2}\\right\\}.\n\n<\/span>\n<\/p>\n<p>\n\u0648\u0628\u0645\u0627 \u0623\u0646 \u0647\u0630\u0627 \u0627\u0644\u062d\u062f\u0651 \u0627\u0644\u0623\u062f\u0646\u0649 \u0645\u0623\u062e\u0648\u0630 \u0645\u0646 \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0646\u062a\u0647\u064a\u0629 \u0645\u0646 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0645\u0648\u062c\u0628\u0629\u060c \u0641\u0625\u0646\u0647 \u064a\u062a\u062d\u0642\u0642 \u0623\u0646 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta\\gt 0<\/span><\/span><\/strong>. \u0648\u0633\u0646\u0631\u0649 \u0623\u0646 \u0647\u0630\u0627 \u0627\u0644\u0639\u062f\u062f <strong><span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span><\/strong> \u064a\u0635\u0644\u062d \u0644\u0640<strong>\u0643\u0644<\/strong> \u0646\u0642\u0637\u0629 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in[a,b]<\/span><\/span><\/strong>\u060c \u0623\u064a \u0625\u0646\u0647 \u0644\u0627 \u064a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0627\u062e\u062a\u064a\u0627\u0631 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong>.\n<\/p>\n<p>\n\u0644\u0646\u0623\u062e\u0630 \u0627\u0644\u0622\u0646:\n<\/p>\n<ul>\n<li>\u0646\u0642\u0637\u0629 \u0643\u064a\u0641\u0645\u0627 \u0643\u0627\u0646\u062a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in[a,b]<\/span><\/span><\/strong>\u060c<\/li>\n<li>\u0648\u0646\u0642\u0637\u0629 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in[a,b]<\/span><\/span><\/strong> \u062a\u062d\u0642\u0642 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|x-x_0|\\lt\\delta<\/span><\/span><\/strong>.<\/li>\n<\/ul>\n<p>\n\u0648\u0628\u0645\u0627 \u0623\u0646 \u0627\u0644\u0641\u062a\u0631\u0627\u062a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{x_1},\\dots,I_{x_N}<\/span><\/span><\/strong> \u062a\u063a\u0637\u064a \u0627\u0644\u0641\u062a\u0631\u0629 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong>\u060c \u0641\u0625\u0646 \u0627\u0644\u0646\u0642\u0637\u0629 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong> \u062a\u0646\u062a\u0645\u064a \u0625\u0644\u0649 \u0648\u0627\u062d\u062f\u0629 \u0645\u0646\u0647\u0627 \u0639\u0644\u0649 \u0627\u0644\u0623\u0642\u0644\u060c \u0644\u0646\u0642\u0644 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{x_j}<\/span><\/span><\/strong> \u0645\u0646 \u0623\u062c\u0644 \u0628\u0639\u0636 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">j\\in\\{1,\\dots,N\\}<\/span><\/span><\/strong>. \u0648\u0628\u062d\u0633\u0628 \u062a\u0639\u0631\u064a\u0641 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{x_j}<\/span><\/span><\/strong>\u060c \u064a\u0639\u0646\u064a \u0630\u0644\u0643 \u0623\u0646\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|x_0-x_j|\\lt\\frac{\\delta(x_j)}{2}.\n\n<\/span>\n<\/p>\n<p>\n\u0648\u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0648\u0628\u062d\u0633\u0628 \u062a\u0639\u0631\u064a\u0641 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span><\/span><\/strong> \u0644\u062f\u064a\u0646\u0627 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta\\le\\frac{\\delta(x_j)}{2}<\/span><\/span><\/strong>\u060c \u0648\u0645\u0646 \u062b\u0645\u0651 \u0641\u0625\u0646 \u0645\u0646 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|x-x_0|\\lt\\delta<\/span><\/span><\/strong> \u0646\u0633\u062a\u0646\u062a\u062c\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|x-x_0|\\lt\\frac{\\delta(x_j)}{2}.\n\n<\/span>\n<\/p>\n<p>\n\u0648\u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0639\u062f\u0645 \u0627\u0644\u0645\u0633\u0627\u0648\u0627\u0629 \u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629\u060c \u0646\u062d\u0635\u0644 \u0639\u0644\u0649\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|x-x_j|\\le |x-x_0|+|x_0-x_j|\n\n\\lt \\frac{\\delta(x_j)}{2}+\\frac{\\delta(x_j)}{2}\n\n=\\delta(x_j).\n\n<\/span>\n<\/p>\n<p>\n\u0648\u0628\u0633\u0628\u0628 \u0627\u062e\u062a\u064a\u0627\u0631 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta(x_j)<\/span><\/span><\/strong> (\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u0639\u0646\u062f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_j<\/span><\/span><\/strong> \u0644\u0644\u0642\u064a\u0645\u0629 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon\/2<\/span><\/span><\/strong>)\u060c \u0641\u0625\u0646 \u0627\u0644\u0645\u062a\u0628\u0627\u064a\u0646\u062a\u064a\u0646 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|x_0-x_j|\\lt\\delta(x_j)<\/span><\/span><\/strong> \u0648<strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|x-x_j|\\lt\\delta(x_j)<\/span><\/span><\/strong> \u062a\u0636\u0645\u0646\u0627\u0646\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|f(x_0)-f(x_j)|\\lt\\frac{\\epsilon}{2}\n\n\\quad\\text{\u0648}\\quad\n\n|f(x)-f(x_j)|\\lt\\frac{\\epsilon}{2}.\n\n<\/span>\n<\/p>\n<p>\n\u0648\u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0639\u062f\u0645 \u0627\u0644\u0645\u0633\u0627\u0648\u0627\u0629 \u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629 \u0645\u0631\u0629 \u0623\u062e\u0631\u0649\u060c \u0646\u062d\u0635\u0644 \u0639\u0644\u0649\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|f(x)-f(x_0)|\n\n\\le |f(x)-f(x_j)| + |f(x_j)-f(x_0)|\n\n\\lt \\frac{\\epsilon}{2}+\\frac{\\epsilon}{2}\n\n=\\epsilon.\n\n<\/span>\n<\/p>\n<p>\n\u0648\u0628\u0645\u0627 \u0623\u0646 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong> \u0648<strong><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/strong> \u0643\u0627\u0646\u0627 \u0627\u062e\u062a\u064a\u0627\u0631\u064a\u064a\u0646\u060c \u0646\u0643\u0648\u0646 \u0642\u062f \u0628\u0631\u0647\u0646\u0627 \u0623\u0646\u0647 \u0645\u0646 \u0623\u062c\u0644 <strong><span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon<\/span><\/strong> \u0627\u0644\u0645\u062b\u0628\u062a \u0641\u064a \u0627\u0644\u0628\u062f\u0627\u064a\u0629 \u064a\u0648\u062c\u062f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta\\gt 0<\/span><\/span><\/strong> \u0645\u0633\u062a\u0642\u0644 \u0639\u0646 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong> \u0628\u062d\u064a\u062b\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n(\\forall x_0\\in[a,b])(\\forall x\\in[a,b])\n\n\\big(|x-x_0|\\lt\\delta\\Rightarrow |f(x)-f(x_0)|\\lt\\epsilon\\big).\n\n<\/span>\n<\/p>\n<p>\n\u0648\u0625\u0630\u0627 \u0623\u0639\u062f\u0646\u0627 \u062a\u0633\u0645\u064a\u0629 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong> \u0628\u0640<strong><span class=\"katex-eq\" data-katex-display=\"false\">y<\/span><\/strong>\u060c \u064a\u0645\u0643\u0646 \u0643\u062a\u0627\u0628\u0629 \u0630\u0644\u0643 \u0639\u0644\u0649 \u0627\u0644\u0646\u062d\u0648 \u0627\u0644\u062a\u0627\u0644\u064a:\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n(\\forall \\epsilon\\gt 0)(\\exists \\delta\\gt 0)(\\forall x,y\\in[a,b])\n\n\\big(|x-y|\\lt\\delta\\Rightarrow |f(x)-f(y)|\\lt\\epsilon\\big),\n\n<\/span>\n<\/p>\n<p>\n\u0648\u0647\u0630\u0627 \u0647\u0648 \u0628\u0627\u0644\u0636\u0628\u0637 \u062a\u0639\u0631\u064a\u0641 <strong>\u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0627\u0644\u0645\u0646\u062a\u0638\u0645\u0629<\/strong> \u0644\u0644\u062f\u0627\u0644\u0629 <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u0639\u0644\u0649 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong>. \u0648\u0641\u064a\u0645\u0627 \u064a\u0644\u064a\u060c \u0633\u0646\u062d\u062a\u0627\u062c \u0641\u0642\u0637 \u0625\u0644\u0649 \u062a\u0637\u0628\u064a\u0642 \u0647\u0630\u0647 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0641\u064a \u062d\u0627\u0644\u0629 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon=1<\/span><\/span><\/strong>.\n<\/p>\n<p><a name=\"8\"><\/a><\/br><\/p>\n<h4><b>\u0627\u0644\u062e\u0637\u0648\u0629 5:<\/b> \u0645\u0646 \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0627\u0644\u0645\u0646\u062a\u0638\u0645\u0629 \u0625\u0644\u0649 \u0627\u0646\u062d\u0635\u0627\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u0639\u0644\u0649 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/h4>\n<p>\n\u0644\u0646\u0637\u0628\u0651\u0642 \u0627\u0644\u0622\u0646 \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0627\u0644\u0645\u0646\u062a\u0638\u0645\u0629 \u0645\u0639 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon=1<\/span><\/span><\/strong>. \u064a\u0648\u062c\u062f \u0639\u062f\u062f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta_1\\gt 0<\/span><\/span><\/strong> \u0628\u062d\u064a\u062b \u0644\u0643\u0644 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x,y\\in[a,b]<\/span><\/span><\/strong> \u064a\u062a\u062d\u0642\u0642\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|x-y|\\lt\\delta_1\\Rightarrow |f(x)-f(y)|\\lt 1.\n\n<\/span>\n<\/p>\n<p>\n\u0646\u0642\u0633\u0651\u0645 \u0627\u0644\u0622\u0646 \u0627\u0644\u0641\u062a\u0631\u0629 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u0625\u0644\u0649 \u0639\u062f\u062f \u0645\u0646\u062a\u0647\u064d \u0645\u0646 \u0627\u0644\u0641\u062a\u0631\u0627\u062a \u0627\u0644\u062c\u0632\u0626\u064a\u0629 \u0627\u0644\u062a\u064a \u0637\u0648\u0644 \u0643\u0644 \u0645\u0646\u0647\u0627 \u0623\u0635\u063a\u0631 \u0645\u0646 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta_1<\/span><\/span><\/strong>. \u0623\u064a \u0646\u062e\u062a\u0627\u0631 \u0639\u062f\u062f\u064b\u0627 \u0635\u062d\u064a\u062d\u064b\u0627 <strong><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/strong> \u0648\u0646\u0642\u0627\u0637\u064b\u0627\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\na = x_0 \\lt x_1 \\lt \\cdots \\lt x_n = b\n\n<\/span>\n<\/p>\n<p>\n\u0628\u062d\u064a\u062b \u0644\u0643\u0644 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k=0,1,\\dots,n-1<\/span><\/span><\/strong> \u064a\u0643\u0648\u0646\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nx_{k+1}-x_k\\lt\\delta_1.\n\n<\/span>\n<\/p>\n<p>\n\u0646\u0646\u0638\u0631 \u0627\u0644\u0622\u0646 \u0641\u064a \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0629 \u0627\u0644\u0645\u0646\u062a\u0647\u064a\u0629 \u0645\u0646 \u0627\u0644\u0642\u064a\u0645\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n\\{f(x_0),f(x_1),\\dots,f(x_{n-1})\\}.\n\n<\/span>\n<\/p>\n<p>\n\u0648\u0628\u0645\u0627 \u0623\u0646\u0647\u0627 \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0646\u062a\u0647\u064a\u0629 \u0645\u0646 \u0623\u0639\u062f\u0627\u062f \u062d\u0642\u064a\u0642\u064a\u0629\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u062a\u0639\u0631\u064a\u0641\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nC = \\max\\{|f(x_k)| \\;|\\; k=0,1,\\dots,n-1\\}.\n\n<\/span>\n<\/p>\n<p>\n\u0633\u0646\u0628\u0631\u0647\u0646 \u0623\u0646 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C+1<\/span><\/span><\/strong> \u0647\u0648 \u062d\u062f \u0639\u0644\u0648\u064a \u0628\u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u0645\u0637\u0644\u0642\u0629 \u0644\u0644\u062f\u0627\u0644\u0629 <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u0639\u0644\u0649 \u0643\u0627\u0645\u0644 \u0627\u0644\u0641\u062a\u0631\u0629 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong>. \u0641\u0644\u064a\u0643\u0646 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in[a,b]<\/span><\/span><\/strong> \u0646\u0642\u0637\u0629 \u0643\u064a\u0641\u0645\u0627 \u0643\u0627\u0646\u062a. \u0639\u0646\u062f\u0626\u0630 \u064a\u0648\u062c\u062f \u0645\u0624\u0634\u0631 <strong><span class=\"katex-eq\" data-katex-display=\"false\">k<\/span><\/strong> \u0628\u062d\u064a\u062b <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in[x_k,x_{k+1}]<\/span><\/span><\/strong>. \u0648\u0639\u0644\u0649 \u0648\u062c\u0647 \u0627\u0644\u062e\u0635\u0648\u0635\u060c \u064a\u062a\u062d\u0642\u0642\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|x-x_k|\\le x_{k+1}-x_k\\lt\\delta_1.\n\n<\/span>\n<\/p>\n<p>\n\u0648\u0628\u062d\u0633\u0628 \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0627\u0644\u0645\u0646\u062a\u0638\u0645\u0629 \u0645\u0639 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon=1<\/span><\/span><\/strong>\u060c \u0641\u0625\u0646 \u0645\u0646 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|x-x_k|\\lt\\delta_1<\/span><\/span><\/strong> \u0646\u0633\u062a\u0646\u062a\u062c \u0623\u0646\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|f(x)-f(x_k)|\\lt 1.\n\n<\/span>\n<\/p>\n<p>\n\u0648\u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0639\u062f\u0645 \u0627\u0644\u0645\u0633\u0627\u0648\u0627\u0629 \u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629:\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|f(x)|\\le |f(x)-f(x_k)| + |f(x_k)| \\lt 1 + |f(x_k)| \\le 1 + C.\n\n<\/span>\n<\/p>\n<p>\n\u0648\u0628\u0645\u0627 \u0623\u0646 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in[a,b]<\/span><\/span><\/strong> \u0643\u0627\u0646 \u0627\u062e\u062a\u064a\u0627\u0631\u064a\u064b\u0627\u060c \u0646\u0633\u062a\u0646\u062a\u062c \u0623\u0646\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|f(x)|\\le C+1 \\quad \\text{\u0644\u0643\u0644 } x\\in[a,b],\n\n<\/span>\n<\/p>\n<p>\n\u0623\u064a \u0625\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> <strong>\u0645\u062d\u0635\u0648\u0631\u0629<\/strong> \u0639\u0644\u0649 \u0627\u0644\u0641\u062a\u0631\u0629 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong>.\n<\/p>\n<p><a name=\"9\"><\/a><\/br><\/p>\n<h4><b>\u0627\u0644\u062e\u0637\u0648\u0629 6:<\/b> \u0648\u062c\u0648\u062f \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0639\u0638\u0645\u0649 \u0648\u0627\u0644\u0635\u063a\u0631\u0649<\/h4>\n<p>\n\u0646\u0639\u0631\u0651\u0641 \u0645\u062c\u0645\u0648\u0639\u0629 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u062a\u064a \u062a\u0623\u062e\u0630\u0647\u0627 \u0627\u0644\u062f\u0627\u0644\u0629 \u0639\u0644\u0649 \u0627\u0644\u0641\u062a\u0631\u0629:\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nH=\\{f(x)\\;|\\;x\\in[a,b]\\}\\subset\\mathbb{R}.\n\n<\/span>\n<\/p>\n<p>\n\u0646\u0639\u0644\u0645 \u0627\u0644\u0622\u0646 \u0623\u0646 <strong><span class=\"katex-eq\" data-katex-display=\"false\">H<\/span><\/strong> \u063a\u064a\u0631 \u062e\u0627\u0644\u064a\u0629 (\u0644\u0623\u0646 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u0644\u064a\u0633\u062a \u0643\u0630\u0644\u0643) \u0648\u0645\u062d\u0635\u0648\u0631\u0629\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0628\u062d\u0633\u0628 \u0645\u0633\u0644\u0645\u0629 supremum \u064a\u0648\u062c\u062f \u0639\u062f\u062f\u0627\u0646 \u062d\u0642\u064a\u0642\u064a\u0627\u0646\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nM=\\sup H,\\qquad m=\\inf H.\n\n<\/span>\n<\/p>\n<p>\n\u0644\u0646\u0628\u0631\u0647\u0646 \u0623\u0646 <strong><span class=\"katex-eq\" data-katex-display=\"false\">M<\/span><\/strong> \u064a\u062a\u062d\u0642\u0642 \u0643\u0642\u064a\u0645\u0629 \u0644\u0644\u062f\u0627\u0644\u0629\u060c \u0623\u064a \u0625\u0646\u0647 \u064a\u0648\u062c\u062f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_1\\in[a,b]<\/span><\/span><\/strong> \u0628\u062d\u064a\u062b <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x_1)=M<\/span><\/span><\/strong>. \u0648\u0633\u0646\u0633\u064a\u0631 \u0648\u0641\u0642 \u0628\u0631\u0647\u0627\u0646 \u0628\u0627\u0644\u062e\u0644\u0641.\n<\/p>\n<p>\n\u0644\u0646\u0641\u062a\u0631\u0636 \u0623\u0646 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span><\/strong> \u0644\u0627 \u064a\u0628\u0644\u063a \u0627\u0644\u0642\u064a\u0645\u0629 <strong><span class=\"katex-eq\" data-katex-display=\"false\">M<\/span><\/strong> \u0623\u0628\u062f\u064b\u0627\u060c \u0623\u064a:\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n(\\forall x\\in[a,b])\\big(f(x)\\lt M\\big).\n\n<\/span>\n<\/p>\n<p>\n\u062a\u062d\u062a \u0647\u0630\u0627 \u0627\u0644\u0627\u0641\u062a\u0631\u0627\u0636\u060c \u062a\u0643\u0648\u0646 \u0627\u0644\u062f\u0627\u0644\u0629\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\ng(x)=\\frac{1}{M-f(x)}\n\n<\/span>\n<\/p>\n<p>\n\u0645\u064f\u0639\u0631\u0651\u0641\u0629 \u062c\u064a\u062f\u064b\u0627 \u0648\u0645\u0648\u062c\u0628\u0629 \u0644\u0643\u0644 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in[a,b]<\/span><\/span><\/strong>\u060c \u0625\u0630 \u0625\u0646 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">M-f(x)\\gt 0<\/span><\/span><\/strong> \u0648\u0641\u0642 \u0627\u0644\u0641\u0631\u0636. \u0648\u0628\u0645\u0627 \u0623\u0646 <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u0645\u062a\u0635\u0644\u0629 \u0648<strong><span class=\"katex-eq\" data-katex-display=\"false\">M<\/span><\/strong> \u062b\u0627\u0628\u062a\u060c \u0641\u0625\u0646 <strong><span class=\"katex-eq\" data-katex-display=\"false\">g<\/span><\/strong> \u0623\u064a\u0636\u064b\u0627 \u0645\u062a\u0635\u0644\u0629. \u0648\u0628\u062d\u0633\u0628 \u0627\u0644\u062c\u0632\u0621 \u0627\u0644\u0623\u0648\u0644 \u0645\u0646 \u0627\u0644\u0628\u0631\u0647\u0627\u0646\u060c \u0643\u0644 \u062f\u0627\u0644\u0629 \u0645\u062a\u0635\u0644\u0629 \u0639\u0644\u0649 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u0645\u062d\u0635\u0648\u0631\u0629\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u064a\u0648\u062c\u062f \u0639\u062f\u062f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">N\\gt 0<\/span><\/span><\/strong> \u0628\u062d\u064a\u062b\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n(\\forall x\\in[a,b])\\big(g(x)\\le N\\big).\n\n<\/span>\n<\/p>\n<p>\n\u0648\u0639\u0644\u0649 \u0648\u062c\u0647 \u0627\u0644\u062e\u0635\u0648\u0635\u060c \u0644\u0643\u0644 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in[a,b]<\/span><\/span><\/strong> \u064a\u062a\u062d\u0642\u0642\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n\\frac{1}{M-f(x)} = g(x)\\le N,\n\n<\/span>\n<\/p>\n<p>\n\u0648\u0647\u0648 \u0645\u0627 \u064a\u0639\u0627\u062f\u0644\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nM-f(x)\\ge \\frac{1}{N}\n\n\\quad\\Rightarrow\\quad\n\nf(x)\\le M-\\frac{1}{N}.\n\n<\/span>\n<\/p>\n<p>\n\u0648\u064a\u0639\u0646\u064a \u0630\u0644\u0643 \u0623\u0646 \u0643\u0644 \u0642\u064a\u0645 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span><\/strong> \u0639\u0644\u0649 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u0647\u064a \u0623\u0635\u063a\u0631 \u0623\u0648 \u062a\u0633\u0627\u0648\u064a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">M-\\frac{1}{N}<\/span><\/span><\/strong>. \u0648\u0639\u0644\u0649 \u0648\u062c\u0647 \u0627\u0644\u062e\u0635\u0648\u0635\u060c \u0641\u0625\u0646 supremum \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0629 <strong><span class=\"katex-eq\" data-katex-display=\"false\">H<\/span><\/strong> \u064a\u062d\u0642\u0642\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n\\sup H\\le M-\\frac{1}{N}\\lt M,\n\n<\/span>\n<\/p>\n<p>\n\u0648\u0647\u0648 \u0645\u0627 \u064a\u0646\u0627\u0642\u0636 \u062a\u0639\u0631\u064a\u0641 <strong><span class=\"katex-eq\" data-katex-display=\"false\">M<\/span><\/strong> \u0628\u0648\u0635\u0641\u0647 supremum \u0644\u0640<strong><span class=\"katex-eq\" data-katex-display=\"false\">H<\/span><\/strong>. \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0643\u0627\u0646 \u0627\u0641\u062a\u0631\u0627\u0636\u0646\u0627 \u0627\u0644\u0623\u0648\u0644 \u062e\u0627\u0637\u0626\u064b\u0627\u060c \u0648\u064a\u062c\u0628 \u0623\u0646 \u062a\u0648\u062c\u062f \u0646\u0642\u0637\u0629 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_1\\in[a,b]<\/span><\/span><\/strong> \u062a\u062d\u0642\u0642\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nf(x_1)=M.\n\n<\/span>\n<\/p>\n<p>\n\u0648\u064a\u0645\u0643\u0646 \u0628\u0648\u0627\u0633\u0637\u0629 \u062d\u062c\u0629 \u0645\u0645\u0627\u062b\u0644\u0629 \u062a\u0645\u0627\u0645\u064b\u0627\u060c \u0639\u0646\u062f \u062a\u0637\u0628\u064a\u0642\u0647\u0627 \u0639\u0644\u0649 \u0627\u0644\u0625infimum <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m=\\inf H<\/span><\/span><\/strong> (\u0645\u062b\u0644\u064b\u0627 \u0639\u0628\u0631 \u0627\u0644\u0646\u0638\u0631 \u0641\u064a \u0627\u0644\u062f\u0627\u0644\u0629 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h(x)=-f(x)<\/span><\/span><\/strong>)\u060c \u0623\u0646 \u0646\u0628\u0631\u0647\u0646 \u0639\u0644\u0649 \u0648\u062c\u0648\u062f \u0646\u0642\u0637\u0629 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_2\\in[a,b]<\/span><\/span><\/strong> \u0628\u062d\u064a\u062b\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nf(x_2)=m.\n\n<\/span>\n<\/p>\n<p><a name=\"10\"><\/a><\/br><\/p>\n<h2>\u062a\u0641\u0633\u064a\u0631 \u0645\u0646 \u0645\u0646\u0638\u0648\u0631 \u0627\u0644\u0627\u062a\u0636\u0651\u0627\u0645 \u0648\u062e\u0627\u062a\u0645\u0629<\/h2>\n<p>\n\u0644\u0642\u062f \u0628\u0631\u0647\u0646\u0627 \u0623\u0646 \u0643\u0644 \u062f\u0627\u0644\u0629 \u0645\u062a\u0635\u0644\u0629 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f:[a,b]\\to\\mathbb{R}<\/span><\/span><\/strong> \u0647\u064a \u062f\u0627\u0644\u0629 \u0645\u062d\u0635\u0648\u0631\u0629 \u0648\u062a\u0628\u0644\u063a \u0642\u064a\u0645\u0647\u0627 \u0627\u0644\u0639\u0638\u0645\u0649 \u0648\u0627\u0644\u0635\u063a\u0631\u0649 \u0639\u0644\u0649 \u0627\u0644\u0641\u062a\u0631\u0629 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong>. \u0648\u0641\u064a \u0644\u063a\u0629 \u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u062d\u062f\u064a\u062b\u0629\u060c \u064a\u064f\u0641\u0647\u0645 \u0647\u0630\u0627 \u0628\u0623\u0646 \u0627\u0644\u0641\u062a\u0631\u0627\u062a \u0627\u0644\u0645\u063a\u0644\u0642\u0629 \u0648\u0627\u0644\u0645\u062d\u062f\u0648\u062f\u0629 \u0645\u062b\u0644 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u0647\u064a \u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0645\u062f\u0645\u062c\u0629\u060c \u0648\u0623\u0646 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u062a\u0635\u0644\u0629 \u062a\u0631\u0633\u0644 \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0627\u0644\u0645\u062f\u0645\u062c\u0629 \u0625\u0644\u0649 \u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0645\u062f\u0645\u062c\u0629.\n<\/p>\n<p>\n\u0648\u0639\u0644\u0649 \u0648\u062c\u0647 \u0627\u0644\u062e\u0635\u0648\u0635\u060c \u0625\u0630\u0627 \u0643\u0627\u0646 <strong><span class=\"katex-eq\" data-katex-display=\"false\">I<\/span><\/strong> \u0645\u062f\u0645\u062c\u064b\u0627 \u0648\u0643\u0627\u0646\u062a <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u062f\u0627\u0644\u0629 \u0645\u062a\u0635\u0644\u0629 \u0639\u0644\u0649 <strong><span class=\"katex-eq\" data-katex-display=\"false\">I<\/span><\/strong>\u060c \u0641\u0625\u0646 \u0627\u0644\u0635\u0648\u0631\u0629 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(I)<\/span><\/span><\/strong> \u062a\u0643\u0648\u0646 \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u062f\u0645\u062c\u0629 \u0636\u0645\u0646 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}<\/span><\/span><\/strong>. \u0648\u0647\u0630\u0627 \u064a\u0636\u0645\u0646 \u0623\u0646 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(I)<\/span><\/span><\/strong> \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u062d\u0635\u0648\u0631\u0629\u060c \u0648\u0623\u0646 \u0642\u064a\u0645\u0629 \u0639\u0638\u0645\u0649 \u0648\u0642\u064a\u0645\u0629 \u0635\u063a\u0631\u0649 \u062a\u062a\u062d\u0642\u0642\u0627\u0646 \u0641\u064a\u0647\u0627 \u0641\u0639\u0644\u064a\u064b\u0627\u060c \u0648\u0647\u0648 \u0628\u0627\u0644\u0636\u0628\u0637 \u0645\u0636\u0645\u0648\u0646 \u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0644\u0644\u0642\u064a\u0645 \u0627\u0644\u0642\u0635\u0648\u0649 \u0644\u0645\u0627\u0630\u0627 \u064a\u064f\u0641\u062a\u0631\u0636 \u0641\u064a \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0623\u0646 \u00ab\u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u0639\u0638\u0645\u0649 \u0645\u0648\u062c\u0648\u062f\u0629\u00bb \u0623\u0648 \u0623\u0646 \u00ab\u0647\u0646\u0627\u0643 \u062f\u0627\u0626\u0645\u064b\u0627 \u0642\u064a\u0645\u0629 \u0635\u063a\u0631\u0649\u00bb \u0639\u0644\u0649 \u0641\u062a\u0631\u0629 \u0645\u0627\u060c \u0641\u064a \u062d\u064a\u0646 \u0623\u0646\u0651\u0647 \u0644\u0627 \u064a\u0648\u062c\u062f \u0645\u0627 \u064a\u0641\u0631\u0636 \u062d\u062f\u0648\u062b \u0630\u0644\u0643 \u0628\u0627\u0644\u0636\u0631\u0648\u0631\u0629\u061f \u062a\u064f\u0639\u062f \u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0627\u0644\u0642\u0637\u0639\u0629 \u0627\u0644\u0645\u0641\u0642\u0648\u062f\u0629 \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0644\u063a\u0632\u060c \u0625\u0630 \u062a\u0636\u0645\u0646 \u0623\u0646\u0651 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u062a\u0635\u0644\u0629 \u0627\u0644\u0645\u0639\u0631\u0641\u0629 \u0639\u0644\u0649 \u0641\u062a\u0631\u0629 \u0645\u063a\u0644\u0642\u0629 \u0648\u0645\u062d\u062f\u0648\u062f\u0629 \u0644\u064a\u0633\u062a \u0645\u062d\u0635\u0648\u0631\u0629 \u0641\u062d\u0633\u0628\u060c [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":35255,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":2,"footnotes":""},"categories":[860,565],"tags":[],"class_list":["post-35268","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>\u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0644\u0644\u0642\u064a\u0645 \u0627\u0644\u0642\u0635\u0648\u0649 - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u0627\u0641\u0647\u0645 \u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0645\u0646 \u0627\u0644\u0623\u0633\u0627\u0633: \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629\u060c \u0648\u0627\u0644\u0627\u062a\u0636\u0651\u0627\u0645\u060c \u0648\u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0627\u0644\u0645\u0637\u0628\u0642 \u0639\u0644\u0649 \u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0639\u0638\u0645\u0649 \u0648\u0627\u0644\u0635\u063a\u0631\u0649.\" \/>\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\/\u0645\u0628\u0631\u0647\u0646\u0629-\u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633-\u0644\u0644\u0642\u064a\u0645-\u0627\u0644\u0642\u0635\u0648\u0649\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0644\u0644\u0642\u064a\u0645 \u0627\u0644\u0642\u0635\u0648\u0649\" \/>\n<meta property=\"og:description\" content=\"\u0627\u0641\u0647\u0645 \u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0645\u0646 \u0627\u0644\u0623\u0633\u0627\u0633: \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629\u060c \u0648\u0627\u0644\u0627\u062a\u0636\u0651\u0627\u0645\u060c \u0648\u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0627\u0644\u0645\u0637\u0628\u0642 \u0639\u0644\u0649 \u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0639\u0638\u0645\u0649 \u0648\u0627\u0644\u0635\u063a\u0631\u0649.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/toposuranos.com\/material\/ar\/\u0645\u0628\u0631\u0647\u0646\u0629-\u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633-\u0644\u0644\u0642\u064a\u0645-\u0627\u0644\u0642\u0635\u0648\u0649\/\" \/>\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=\"2024-12-20T13:00:21+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-12-11T17:07:06+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/06\/Weierstrass-1-1024x683.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"\u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0644\u0644\u0642\u064a\u0645 \u0627\u0644\u0642\u0635\u0648\u0649\" \/>\n<meta name=\"twitter:description\" content=\"\u0627\u0641\u0647\u0645 \u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0645\u0646 \u0627\u0644\u0623\u0633\u0627\u0633: \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629\u060c \u0648\u0627\u0644\u0627\u062a\u0636\u0651\u0627\u0645\u060c \u0648\u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0627\u0644\u0645\u0637\u0628\u0642 \u0639\u0644\u0649 \u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0639\u0638\u0645\u0649 \u0648\u0627\u0644\u0635\u063a\u0631\u0649.\" \/>\n<meta name=\"twitter:image\" content=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/06\/Weierstrass-1.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=\"8 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"https:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"\u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0644\u0644\u0642\u064a\u0645 \u0627\u0644\u0642\u0635\u0648\u0649\",\"datePublished\":\"2024-12-20T13:00:21+00:00\",\"dateModified\":\"2025-12-11T17:07:06+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/\"},\"wordCount\":1089,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/toposuranos.com\/material\/#organization\"},\"image\":{\"@id\":\"https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/06\/Weierstrass-1.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\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/\",\"url\":\"https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/\",\"name\":\"\u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0644\u0644\u0642\u064a\u0645 \u0627\u0644\u0642\u0635\u0648\u0649 - toposuranos.com\/material\",\"isPartOf\":{\"@id\":\"https:\/\/toposuranos.com\/material\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/06\/Weierstrass-1.jpg\",\"datePublished\":\"2024-12-20T13:00:21+00:00\",\"dateModified\":\"2025-12-11T17:07:06+00:00\",\"description\":\"\u0627\u0641\u0647\u0645 \u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0645\u0646 \u0627\u0644\u0623\u0633\u0627\u0633: \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629\u060c \u0648\u0627\u0644\u0627\u062a\u0636\u0651\u0627\u0645\u060c \u0648\u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0627\u0644\u0645\u0637\u0628\u0642 \u0639\u0644\u0649 \u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0639\u0638\u0645\u0649 \u0648\u0627\u0644\u0635\u063a\u0631\u0649.\",\"breadcrumb\":{\"@id\":\"https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/#breadcrumb\"},\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/#primaryimage\",\"url\":\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/06\/Weierstrass-1.jpg\",\"contentUrl\":\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/06\/Weierstrass-1.jpg\",\"width\":1536,\"height\":1024},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"https:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0644\u0644\u0642\u064a\u0645 \u0627\u0644\u0642\u0635\u0648\u0649\"}]},{\"@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\":\"https:\/\/toposuranos.com\/material\/#\/schema\/person\/image\/\",\"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":"\u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0644\u0644\u0642\u064a\u0645 \u0627\u0644\u0642\u0635\u0648\u0649 - toposuranos.com\/material","description":"\u0627\u0641\u0647\u0645 \u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0645\u0646 \u0627\u0644\u0623\u0633\u0627\u0633: \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629\u060c \u0648\u0627\u0644\u0627\u062a\u0636\u0651\u0627\u0645\u060c \u0648\u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0627\u0644\u0645\u0637\u0628\u0642 \u0639\u0644\u0649 \u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0639\u0638\u0645\u0649 \u0648\u0627\u0644\u0635\u063a\u0631\u0649.","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\/\u0645\u0628\u0631\u0647\u0646\u0629-\u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633-\u0644\u0644\u0642\u064a\u0645-\u0627\u0644\u0642\u0635\u0648\u0649\/","og_locale":"es_ES","og_type":"article","og_title":"\u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0644\u0644\u0642\u064a\u0645 \u0627\u0644\u0642\u0635\u0648\u0649","og_description":"\u0627\u0641\u0647\u0645 \u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0645\u0646 \u0627\u0644\u0623\u0633\u0627\u0633: \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629\u060c \u0648\u0627\u0644\u0627\u062a\u0636\u0651\u0627\u0645\u060c \u0648\u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0627\u0644\u0645\u0637\u0628\u0642 \u0639\u0644\u0649 \u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0639\u0638\u0645\u0649 \u0648\u0627\u0644\u0635\u063a\u0631\u0649.","og_url":"https:\/\/toposuranos.com\/material\/ar\/\u0645\u0628\u0631\u0647\u0646\u0629-\u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633-\u0644\u0644\u0642\u064a\u0645-\u0627\u0644\u0642\u0635\u0648\u0649\/","og_site_name":"toposuranos.com\/material","article_publisher":"https:\/\/www.facebook.com\/groups\/toposuranos","article_published_time":"2024-12-20T13:00:21+00:00","article_modified_time":"2025-12-11T17:07:06+00:00","og_image":[{"url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/06\/Weierstrass-1-1024x683.jpg","type":"","width":"","height":""}],"author":"giorgio.reveco","twitter_card":"summary_large_image","twitter_title":"\u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0644\u0644\u0642\u064a\u0645 \u0627\u0644\u0642\u0635\u0648\u0649","twitter_description":"\u0627\u0641\u0647\u0645 \u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0645\u0646 \u0627\u0644\u0623\u0633\u0627\u0633: \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629\u060c \u0648\u0627\u0644\u0627\u062a\u0636\u0651\u0627\u0645\u060c \u0648\u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0627\u0644\u0645\u0637\u0628\u0642 \u0639\u0644\u0649 \u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0639\u0638\u0645\u0649 \u0648\u0627\u0644\u0635\u063a\u0631\u0649.","twitter_image":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/06\/Weierstrass-1.jpg","twitter_creator":"@topuranos","twitter_site":"@topuranos","twitter_misc":{"Escrito por":"giorgio.reveco","Tiempo de lectura":"8 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/#article","isPartOf":{"@id":"https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/"},"author":{"name":"giorgio.reveco","@id":"https:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1"},"headline":"\u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0644\u0644\u0642\u064a\u0645 \u0627\u0644\u0642\u0635\u0648\u0649","datePublished":"2024-12-20T13:00:21+00:00","dateModified":"2025-12-11T17:07:06+00:00","mainEntityOfPage":{"@id":"https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/"},"wordCount":1089,"commentCount":0,"publisher":{"@id":"https:\/\/toposuranos.com\/material\/#organization"},"image":{"@id":"https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/#primaryimage"},"thumbnailUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/06\/Weierstrass-1.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\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/","url":"https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/","name":"\u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0644\u0644\u0642\u064a\u0645 \u0627\u0644\u0642\u0635\u0648\u0649 - toposuranos.com\/material","isPartOf":{"@id":"https:\/\/toposuranos.com\/material\/#website"},"primaryImageOfPage":{"@id":"https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/#primaryimage"},"image":{"@id":"https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/#primaryimage"},"thumbnailUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/06\/Weierstrass-1.jpg","datePublished":"2024-12-20T13:00:21+00:00","dateModified":"2025-12-11T17:07:06+00:00","description":"\u0627\u0641\u0647\u0645 \u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0645\u0646 \u0627\u0644\u0623\u0633\u0627\u0633: \u0627\u0644\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629\u060c \u0648\u0627\u0644\u0627\u062a\u0636\u0651\u0627\u0645\u060c \u0648\u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0627\u0644\u0645\u0637\u0628\u0642 \u0639\u0644\u0649 \u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0639\u0638\u0645\u0649 \u0648\u0627\u0644\u0635\u063a\u0631\u0649.","breadcrumb":{"@id":"https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/#breadcrumb"},"inLanguage":"es","potentialAction":[{"@type":"ReadAction","target":["https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/"]}]},{"@type":"ImageObject","inLanguage":"es","@id":"https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/#primaryimage","url":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/06\/Weierstrass-1.jpg","contentUrl":"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/06\/Weierstrass-1.jpg","width":1536,"height":1024},{"@type":"BreadcrumbList","@id":"https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%a8%d8%b1%d9%87%d9%86%d8%a9-%d9%81%d8%a7%d9%8a%d8%b1%d8%b4%d8%aa%d8%b1%d8%a7%d8%b3-%d9%84%d9%84%d9%82%d9%8a%d9%85-%d8%a7%d9%84%d9%82%d8%b5%d9%88%d9%89\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"https:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/"},{"@type":"ListItem","position":2,"name":"\u0645\u0628\u0631\u0647\u0646\u0629 \u0641\u0627\u064a\u0631\u0634\u062a\u0631\u0627\u0633 \u0644\u0644\u0642\u064a\u0645 \u0627\u0644\u0642\u0635\u0648\u0649"}]},{"@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":"https:\/\/toposuranos.com\/material\/#\/schema\/person\/image\/","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\/35268","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=35268"}],"version-history":[{"count":0,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/35268\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media\/35255"}],"wp:attachment":[{"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media?parent=35268"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/categories?post=35268"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/tags?post=35268"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}