{"id":35264,"date":"2024-12-20T13:00:02","date_gmt":"2024-12-20T13:00:02","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=35264"},"modified":"2025-12-11T17:06:47","modified_gmt":"2025-12-11T17:06:47","slug":"%e9%ad%8f%e5%b0%94%e6%96%af%e7%89%b9%e6%8b%89%e6%96%af%e6%9e%81%e5%80%bc%e5%ae%9a%e7%90%86","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/zh\/%e9%ad%8f%e5%b0%94%e6%96%af%e7%89%b9%e6%8b%89%e6%96%af%e6%9e%81%e5%80%bc%e5%ae%9a%e7%90%86\/","title":{"rendered":"\u9b4f\u5c14\u65af\u7279\u62c9\u65af\u6781\u503c\u5b9a\u7406"},"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>\u9b4f\u5c14\u65af\u7279\u62c9\u65af\u6781\u503c\u5b9a\u7406<\/h1>\n<p style=\"text-align:center;\"><em>\u4e3a\u4f55\u5728\u5982\u6b64\u591a\u7684\u6700\u4f18\u5316\u95ee\u9898\u4e2d\uff0c\u4eba\u4eec\u51e0\u4e4e\u9ed8\u8ba4\u201c\u6700\u5927\u503c\u5b58\u5728\u201d\u6216\u201c\u67d0\u533a\u95f4\u5185\u603b\u6709\u6700\u5c0f\u503c\u201d\uff0c\u800c\u5b9e\u9645\u4e0a\u5e76\u65e0\u4efb\u4f55\u5148\u9a8c\u7406\u7531\u4fdd\u8bc1\u8fd9\u4e00\u70b9\uff1f<strong>\u9b4f\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406<\/strong>\u6b63\u662f\u586b\u8865\u8fd9\u4e00\u8ba4\u77e5\u7a7a\u7f3a\u7684\u5173\u952e\uff1a\u5b83\u4fdd\u8bc1\u5b9a\u4e49\u5728\u95ed\u4e14\u6709\u754c\u533a\u95f4\u4e0a\u7684\u8fde\u7eed\u51fd\u6570\u4e0d\u4ec5\u662f\u6709\u754c\u7684\uff0c\u800c\u4e14\u786e\u5b9e\u80fd\u591f\u53d6\u5f97\u5176\u6781\u503c\u3002\u5728\u672c\u7bc7\u6587\u7ae0\u4e2d\uff0c\u6211\u4eec\u5c06\u56de\u987e\u5176\u8868\u8ff0\uff0c\u57fa\u4e8e\u70b9\u6001\u8fde\u7eed\u6027\u3001\u7d27\u81f4\u6027\u4e0e\u4e0a\u786e\u754c\u516c\u7406\uff0c\u8be6\u7ec6\u6784\u5efa\u4e00\u4efd\u4e25\u683c\u8bc1\u660e\uff0c\u5e76\u8fdb\u4e00\u6b65\u4ece\u8fde\u7eed\u51fd\u6570\u4f5c\u7528\u4e8e\u7d27\u96c6\u7684\u73b0\u4ee3\u89c6\u89d2\u4e88\u4ee5\u9610\u91ca\u3002\u76ee\u6807\u5728\u4e8e\uff0c\u4f7f\u8bfb\u8005\u5728\u7ed3\u675f\u9605\u8bfb\u65f6\uff0c\u4e0d\u4ec5\u8bb0\u4f4f\u5b9a\u7406\u7684\u5b57\u9762\u8868\u8ff0\uff0c\u66f4\u80fd\u591f\u7406\u89e3\u5176\u4e3a\u4f55\u6210\u7acb\uff0c\u4ee5\u53ca\u4e3a\u4f55\u5728\u5206\u6790\u5b66\u3001\u6700\u4f18\u5316\u4e0e\u5e94\u7528\u6a21\u578b\u4e2d\u4e0d\u65ad\u51fa\u73b0\u3002<\/em><\/p>\n<p style=\"text-align:center;\"><b>\u5b66\u4e60\u76ee\u6807<\/b><\/p>\n<ol>\n<li>\n    <strong>\u7406\u89e3\u9b4f\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\u7684\u8868\u8ff0\u3002<\/strong><br \/>\n    \u660e\u786e\u8fa8\u8bc6\u5b9a\u7406\u7684\u5047\u8bbe\uff08\u5728\u95ed\u4e14\u6709\u754c\u533a\u95f4 <span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span> \u4e0a\u7684\u8fde\u7eed\u51fd\u6570\uff09\u53ca\u5176\u4e3b\u8981\u7ed3\u8bba\uff1a\u6709\u754c\u6027\u4ee5\u53ca\u6700\u5927\u503c\u4e0e\u6700\u5c0f\u503c\u7684\u5b58\u5728\u6027\u3002\n  <\/li>\n<li>\n    <strong>\u4ece\u7d27\u81f4\u6027\u7684\u89d2\u5ea6\u89e3\u91ca\u9b4f\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\u3002<\/strong><br \/>\n    \u4ee5\u73b0\u4ee3\u8bed\u8a00\u8868\u8ff0\u8be5\u7ed3\u679c\uff1a\u8fde\u7eed\u51fd\u6570\u5c06\u7d27\u96c6\u6620\u5c04\u4e3a\u80fd\u53d6\u5f97\u6781\u503c\u7684\u96c6\u5408\uff0c\u4ece\u800c\u5c06 <span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span> \u7684\u60c5\u5f62\u4e0e\u5b9e\u5206\u6790\u7684\u4e00\u822c\u6846\u67b6\u8fde\u63a5\u8d77\u6765\u3002\n  <\/li>\n<li>\n    <strong>\u5c06\u9b4f\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\u4e0e\u6700\u4f18\u5316\u95ee\u9898\u8054\u7cfb\u8d77\u6765\u3002<\/strong><br \/>\n    \u8ba4\u8bc6\u8be5\u5b9a\u7406\u4f5c\u4e3a\u7406\u8bba\u57fa\u7840\u5728\u4f17\u591a\u4e00\u5143\u6700\u4f18\u5316\u95ee\u9898\uff08\u65e0\u8bba\u7406\u8bba\u6216\u5e94\u7528\u60c5\u5883\uff09\u4e2d\u5bf9\u6700\u5927\u503c\u4e0e\u6700\u5c0f\u503c\u5b58\u5728\u6027\u7684\u4fdd\u969c\u4f5c\u7528\u3002\n  <\/li>\n<\/ol>\n<p style=\"text-align:center;\"><b><u>\u5185\u5bb9\u7d22\u5f15<\/u>:<\/b><br \/>\n<a href=\"#1\"><b>\u5f15\u8a00<\/b><\/a><br \/>\n<a href=\"#2\"><b>\u9b4f\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\u7684\u8868\u8ff0<\/b><\/a><br \/>\n<a href=\"#3\">\u8bc1\u660e<\/a><br \/>\n<a href=\"#4\">\u6b65\u9aa4 1\uff1a<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u4e0a\u7684\u70b9\u6001\u8fde\u7eed\u6027<\/a><br \/>\n<a href=\"#5\">\u6b65\u9aa4 2\uff1a\u4e0e\u8fde\u7eed\u6027\u5bf9\u5e94\u7684\u5f00\u8986\u76d6<\/a><br \/>\n<a href=\"#6\">\u6b65\u9aa4 3\uff1a<span dir=\"ltr\">[a,b]<\/span> \u7684\u7d27\u81f4\u6027\u4e0e\u6709\u9650\u5b50\u8986\u76d6<\/a><br \/>\n<a href=\"#7\">\u6b65\u9aa4 4\uff1a\u6784\u9020\u4e00\u4e2a\u4e0d\u4f9d\u8d56\u4e8e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u7684 <span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span>\uff08\u4e00\u81f4\u8fde\u7eed\u6027\uff09<\/a><br \/>\n<a href=\"#8\">\u6b65\u9aa4 5\uff1a\u7531\u4e00\u81f4\u8fde\u7eed\u6027\u63a8\u5bfc <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u5728 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u4e0a\u7684\u6709\u754c\u6027<\/a><br \/>\n<a href=\"#9\">\u6b65\u9aa4 6\uff1a\u6700\u5927\u503c\u4e0e\u6700\u5c0f\u503c\u7684\u5b58\u5728\u6027<\/a><br \/>\n<a href=\"#10\"><b>\u57fa\u4e8e\u7d27\u81f4\u6027\u7684\u89e3\u91ca\u4e0e\u7ed3\u8bba<\/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>\u5f15\u8a00<\/h2>\n<p>\n<strong>\u9b4f\u5c14\u65af\u7279\u62c9\u65af\u6781\u503c\u5b9a\u7406<\/strong>\u867d\u7136\u901a\u5e38\u51fa\u73b0\u5728\u5b9e\u5206\u6790\u7684\u6700\u521d\u7ae0\u8282\uff0c\u4f46\u4e8b\u5b9e\u4e0a\uff0c\u5b83\u5728\u5e94\u7528\u6570\u5b66\u7684\u5e7f\u5927\u9886\u57df\u4e2d\u53d1\u6325\u7740\u65e0\u58f0\u5374\u6838\u5fc3\u7684\u4f5c\u7528\u3002\u6bcf\u5f53\u6211\u4eec\u5728\u7269\u7406\u3001\u7ecf\u6d4e\u6216\u7edf\u8ba1\u4e2d\u8ba8\u8bba\u5728\u7279\u5b9a\u7ea6\u675f\u4e0b\u201c\u6700\u5927\u5316\u201d\u6216\u201c\u6700\u5c0f\u5316\u201d\u67d0\u4e00\u91cf\u65f6\uff0c\u672c\u8d28\u4e0a\u4f9d\u9760\u7684\u6b63\u662f\u8be5\u5b9a\u7406\u6240\u4fdd\u8bc1\u7684\u601d\u60f3\uff1a\u5b9a\u4e49\u5728\u95ed\u4e14\u6709\u754c\u533a\u95f4\u4e0a\u7684\u8fde\u7eed\u51fd\u6570<strong>\u4e0d\u4ec5\u662f\u6709\u754c\u7684\uff0c\u800c\u4e14\u5b9e\u9645\u80fd\u591f\u53d6\u5f97\u5176\u6781\u503c<\/strong>\u3002\n<\/p>\n<p>\n\u4ece\u76f4\u89c9\u4e0a\u770b\uff0c\u4f3c\u4e4e\u201c\u663e\u7136\u201d\u53ea\u8981\u5728\u533a\u95f4 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u4e0a\u753b\u51fa\u4e00\u6761\u8fde\u7eed\u66f2\u7ebf\uff0c\u5c31\u5fc5\u5b9a\u5b58\u5728\u6700\u9ad8\u70b9\u4e0e\u6700\u4f4e\u70b9\u3002\u7136\u800c\uff0c\u53ea\u9700\u5bf9\u5047\u8bbe\u7a0d\u4f5c\u6539\u53d8\uff0c\u8fd9\u79cd\u76f4\u89c9\u4fbf\u4f1a\u5f7b\u5e95\u5d29\u584c\uff1a\u82e5\u533a\u95f4\u4e0d\u662f\u95ed\u7684\u3001\u82e5\u51fd\u6570\u4e0d\u8fde\u7eed\u6216\u82e5\u5b9a\u4e49\u57df\u4e0d\u662f\u6709\u754c\u7684\uff0c\u6700\u5927\u503c\u4e0e\u6700\u5c0f\u503c\u4fbf\u53ef\u80fd\u5b8c\u5168\u4e0d\u5b58\u5728\u3002\u9b4f\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\u5bf9\u8fd9\u79cd\u76f4\u89c9\u52a0\u4ee5\u89c4\u8303\uff0c\u5e76\u7cbe\u786e\u6307\u51fa\u6211\u4eec\u5728\u4f55\u79cd\u60c5\u5f62\u4e0b\u53ef\u4ee5\u4f9d\u8d56\u5b83\uff0c\u4ee5\u53ca\u5176\u80cc\u540e\u7684\u7406\u8bba\u7406\u7531\u3002\n<\/p>\n<p>\n\u4ece\u7406\u8bba\u89d2\u5ea6\u6765\u770b\uff0c\u8be5\u5b9a\u7406\u662f\u6211\u4eec\u9996\u6b21\u4e25\u8083\u63a5\u89e6<strong>\u7d27\u81f4\u6027<\/strong>\u6982\u5ff5\u7684\u573a\u5408\uff1a\u7528\u73b0\u4ee3\u8bed\u8a00\u63cf\u8ff0\uff0c\u5373\u8fde\u7eed\u51fd\u6570\u5c06\u7d27\u96c6\u6620\u5c04\u4e3a\u7d27\u96c6\u3002\u4ece\u5b9e\u8df5\u89d2\u5ea6\u6765\u770b\uff0c\u8fd9\u610f\u5473\u7740\u8bb8\u591a\u4e00\u7ef4\u6700\u4f18\u5316\u95ee\u9898\u90fd\u5177\u6709\u89e3\uff0c\u5e76\u4e14\u5b83\u8fd8\u662f\u540e\u7eed\u7ed3\u679c\uff08\u5982<b>\u4e2d\u503c\u5b9a\u7406<\/b>\u4ee5\u53ca\u6700\u7ec8\u5bf9\u5fae\u79ef\u5206\u57fa\u672c\u5b9a\u7406\u7684\u7406\u89e3\uff09\u7684\u5173\u952e\u7ec4\u6210\u90e8\u5206\u3002\n<\/p>\n<p>\n\u5728\u672c\u8282\u4e2d\uff0c\u6211\u4eec\u5c06\u9648\u8ff0\u9b4f\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\uff0c\u5e76\u8be6\u7ec6\u5c55\u5f00\u5176\u8bc1\u660e\uff0c\u4f9d\u6258\u4e8e\u5728 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u4e0a\u7684\u8fde\u7eed\u6027\u6982\u5ff5\u4ee5\u53ca\u4e0a\u786e\u754c\u516c\u7406\u3002\u5e0c\u671b\u672c\u6587\u80fd\u591f\u4e3a\u4f60\u63d0\u4f9b\u4e00\u4efd\u53ef\u9760\u7684\u53c2\u8003\uff0c\u65e0\u8bba\u662f\u4e3a\u4e86\u5b66\u4e60\u8be5\u5b9a\u7406\u672c\u8eab\uff0c\u8fd8\u662f\u5728\u8bc1\u660e\u5176\u4ed6\u5b9a\u7406\u6216\u4e25\u683c\u8bba\u8bc1\u5177\u4f53\u95ee\u9898\u4e2d\u6700\u5927\u503c\u4e0e\u6700\u5c0f\u503c\u7684\u5b58\u5728\u6027\u65f6\u4f5c\u4e3a\u4f9d\u636e\u3002\n<\/p>\n<p><a name=\"2\"><\/a><\/br><\/p>\n<h2>\u9b4f\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\u7684\u8868\u8ff0<\/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;\">\u4efb\u610f\u5b9a\u4e49\u5728 <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u4e0a\u7684\u51fd\u6570<\/span><\/strong><\/a>\u4e14\u5728 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b],<\/span><\/span> \u4e0a\u8fde\u7eed\uff0c\u90fd\u5fc5\u5b9a\u662f\u6709\u754c\u7684\uff0c\u5e76\u5177\u6709\u6700\u5c0f\u503c\u4e0e\u6700\u5927\u503c <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u4e0e <span class=\"katex-eq\" data-katex-display=\"false\">M<\/span>\uff0c\u6ee1\u8db3\u82e5 <span class=\"katex-eq\" data-katex-display=\"false\">x\\in[a,b]<\/span>\uff0c\u5219 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)\\in[m,M]<\/span><\/span>\u3002<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"3\"><\/a><\/br><\/p>\n<h3>\u8bc1\u660e<\/h3>\n<p>\n\u6211\u4eec\u5c06\u8bc1\u660e\uff1a\u82e5 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f:[a,b]\\to\\mathbb{R}<\/span><\/span><\/strong> \u5728\u95ed\u4e14\u6709\u754c\u533a\u95f4 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u4e0a\u8fde\u7eed\uff0c\u5219 <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u662f\u6709\u754c\u7684\uff0c\u5e76\u4e14\u5728 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u4e0a\u53d6\u5f97\u6700\u5927\u503c\u4e0e\u6700\u5c0f\u503c\u3002\u6211\u4eec\u5c06\u628a\u8bc1\u660e\u5206\u4e3a\u4e24\u4e2a\u4e3b\u8981\u90e8\u5206\uff1a\n<\/p>\n<ul>\n<li>\u9996\u5148\u8bf4\u660e<strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u5728 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u4e0a\u7684\u8fde\u7eed\u6027\u8574\u542b\u5176\u4e3a<em>\u4e00\u81f4\u8fde\u7eed<\/em>\uff0c\u5e76\u636e\u6b64\u63a8\u5f97\u5176<strong>\u6709\u754c<\/strong>\u3002<\/li>\n<li>\u968f\u540e\u5229\u7528\u4e0a\u786e\u754c\u516c\u7406\u8bc1\u660e<strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u5728\u533a\u95f4\u5185\u80fd\u591f\u53d6\u5f97\u5176\u6700\u5927\u503c\u4e0e\u6700\u5c0f\u503c\u3002<\/li>\n<\/ul>\n<p><a name=\"4\"><\/a><\/br><\/p>\n<h4><b>\u6b65\u9aa4 1\uff1a<\/b> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u4e0a\u7684\u70b9\u6001\u8fde\u7eed\u6027<\/h4>\n<p>\n\u6839\u636e\u5047\u8bbe\uff0c<strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u5728\u6bcf\u4e00\u70b9 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in[a,b]<\/span><\/span><\/strong> \u5904\u90fd\u662f\u8fde\u7eed\u7684\u3002\u4f9d\u636e\u4ee5 <span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon<\/span> \u4e0e <span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span> \u4e3a\u57fa\u7840\u7684\u8fde\u7eed\u6027\u5b9a\u4e49\uff0c\u8fd9\u610f\u5473\u7740\uff1a\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\u5728\u6b64\u9636\u6bb5\uff0c<strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta(x_0)<\/span><\/span><\/strong> \u53ef\u80fd\u4f9d\u8d56\u4e8e\u70b9 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong>\u3002\u6211\u4eec\u5f53\u524d\u7684\u76ee\u6807\u662f\uff1a\u5728\u4e0a\u8ff0\u6bcf\u4e2a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta(x_0)<\/span><\/span><\/strong> \u7684\u57fa\u7840\u4e0a\uff0c\u6784\u9020\u51fa\u4e00\u4e2a<strong>\u4e0d\u4f9d\u8d56\u4e8e<\/strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u7684\u7edf\u4e00\u6570\u503c <strong><span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span><\/strong>\uff0c\u5e76\u4e14\u8be5\u6570\u503c\u5bf9\u6574\u4e2a\u533a\u95f4\u4e2d\u7684\u6240\u6709\u70b9\u90fd\u6709\u6548\u3002\n<\/p>\n<p><a name=\"5\"><\/a><\/br><\/p>\n<h4><b>\u6b65\u9aa4 2\uff1a<\/b> \u4e0e\u8fde\u7eed\u6027\u5bf9\u5e94\u7684\u5f00\u8986\u76d6<\/h4>\n<p>\n\u53d6\u4efb\u610f\u56fa\u5b9a\u7684 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon\\gt 0<\/span><\/span><\/strong>\u3002\u5bf9\u4e8e\u6bcf\u4e2a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in[a,b]<\/span><\/span><\/strong>\uff0c\u8fde\u7eed\u6027\u4fdd\u8bc1\u6211\u4eec\u80fd\u591f\u9009\u62e9\u67d0\u4e2a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta(x_0)\\gt 0<\/span><\/span><\/strong> \u4f7f\u5f97\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\u57fa\u4e8e\u8fd9\u4e9b\u6570\u503c\uff0c\u6211\u4eec\u5bf9\u6bcf\u4e2a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in[a,b]<\/span><\/span><\/strong> \u5b9a\u4e49\u4e00\u4e2a\u5f00\u533a\u95f4\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\u6bcf\u4e2a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{x_0}<\/span><\/span><\/strong> \u90fd\u662f <span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}<\/span> \u4e2d\u7684\u5f00\u96c6\uff0c\u5e76\u4e14\u65cf\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\u6784\u6210\u4e86 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u7684\u4e00\u4e2a<strong>\u5f00\u8986\u76d6<\/strong>\u3002\u4e8b\u5b9e\u4e0a\uff0c\u7ed9\u5b9a\u4efb\u610f\u4e00\u70b9 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y\\in[a,b]<\/span><\/span><\/strong>\uff0c\u53ea\u9700\u53d6 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0=y<\/span><\/span><\/strong>\uff1b\u7531\u6784\u9020\u53ef\u77e5 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y\\in I_y<\/span><\/span><\/strong>\u3002\u56e0\u6b64\uff0c\u533a\u95f4\u4e2d\u7684\u6bcf\u4e2a\u70b9\u81f3\u5c11\u5c5e\u4e8e\u67d0\u4e2a\u5f00\u533a\u95f4 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{x_0}<\/span><\/span><\/strong>\u3002\n<\/p>\n<p>\n\u4e00\u822c\u800c\u8a00\uff0c\u8fd9\u4e2a\u5f00\u96c6\u65cf\u662f<strong>\u65e0\u9650<\/strong>\u7684\uff08\u56e0\u4e3a\u5bf9\u6bcf\u4e2a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in[a,b]<\/span><\/span><\/strong> \u90fd\u6709\u4e00\u4e2a\u5bf9\u5e94\u7684\u5f00\u533a\u95f4\uff09\u3002\u6b64\u65f6\uff0c<strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u7684\u7d27\u81f4\u6027\u4fbf\u5f00\u59cb\u53d1\u6325\u4f5c\u7528\u3002\n<\/p>\n<p><a name=\"6\"><\/a><\/br><\/p>\n<h4><b>\u6b65\u9aa4 3\uff1a<\/b> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u7684\u7d27\u81f4\u6027\u4e0e\u6709\u9650\u5b50\u8986\u76d6<\/h4>\n<p>\n\u6839\u636e\u6d77\u6d85\u2013\u535a\u96f7\u5c14\u5b9a\u7406\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}<\/span><\/span> \u7684\u4e00\u4e2a\u5b50\u96c6\u5f53\u4e14\u4ec5\u5f53\u5176\u4e3a\u95ed\u4e14\u6709\u754c\u65f6\u662f\u7d27\u7684\u3002\u533a\u95f4 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u662f\u95ed\u4e14\u6709\u754c\u7684\uff0c\u56e0\u6b64\u5b83\u662f\u7d27\u96c6\u3002\u6839\u636e\u7d27\u81f4\u6027\u7684\u5b9a\u4e49\uff1a\n<\/p>\n<p>\n<strong>\u4efb\u4f55<\/strong>\u5bf9 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u7684\u5f00\u8986\u76d6\uff08\u5373\u4fbf\u5305\u542b\u65e0\u9650\u591a\u4e2a\u96c6\u5408\uff09\u90fd\u53ef\u4ee5\u62bd\u53d6\u51fa\u4e00\u4e2a<strong>\u6709\u9650\u5b50\u8986\u76d6<\/strong>\u3002\n<\/p>\n<p>\n\u5c06\u6b64\u6027\u8d28\u5e94\u7528\u4e8e\u5f00\u8986\u76d6 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{I_{x_0}\\}_{x_0\\in[a,b]}<\/span><\/span><\/strong>\uff0c\u53ef\u77e5\u5b58\u5728\u70b9 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_1,\\dots,x_N\\in[a,b]<\/span><\/span><\/strong> \u4f7f\u5f97\u5176\u5bf9\u5e94\u7684\u5f00\u533a\u95f4\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\u4ecd\u7136\u8986\u76d6\u6574\u4e2a\u533a\u95f4\uff1a\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\u5982\u6b64\u4e00\u6765\uff0c\u6211\u4eec\u4fbf\u5c06\u65e0\u9650\u65cf\u7684\u5f00\u533a\u95f4\u7f29\u51cf\u4e3a\u4ec5\u7531<strong>\u6709\u9650\u591a\u4e2a<\/strong>\u533a\u95f4\u7ec4\u6210\u7684\u5b50\u8986\u76d6\uff0c\u540c\u65f6\u4fdd\u6301\u4e86\u5bf9 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u7684\u8986\u76d6\u6027\u8d28\u3002\n<\/p>\n<p><a name=\"7\"><\/a><\/br><\/p>\n<h4><b>\u6b65\u9aa4 4\uff1a<\/b> \u6784\u9020\u4e00\u4e2a\u4e0d\u4f9d\u8d56\u4e8e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u7684 <span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span>\uff08\u4e00\u81f4\u8fde\u7eed\u6027\uff09<\/h4>\n<p>\n\u57fa\u4e8e\u6709\u9650\u5b50\u8986\u76d6\uff0c\u6211\u4eec\u5b9a\u4e49\u6570\u503c\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\u7531\u4e8e\u8fd9\u662f\u6709\u9650\u4e2a\u6b63\u6570\u7684\u6700\u5c0f\u503c\uff0c\u56e0\u6b64\u5fc5\u6709 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta\\gt 0<\/span><\/span><\/strong>\u3002\u6211\u4eec\u5c06\u8bc1\u660e\u6b64 <strong><span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span><\/strong> \u5bf9<strong>\u6240\u6709<\/strong>\u7684 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in[a,b]<\/span><\/span><\/strong> \u90fd\u6709\u6548\uff0c\u5373\u5b83\u4e0e\u5177\u4f53\u9009\u53d6\u7684 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong> \u65e0\u5173\u3002\n<\/p>\n<p>\n\u73b0\u5728\u53d6\uff1a\n<\/p>\n<ul>\n<li>\u4efb\u610f\u4e00\u70b9 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in[a,b]<\/span><\/span><\/strong>\uff0c\u4ee5\u53ca<\/li>\n<li>\u4e00\u70b9 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in[a,b]<\/span><\/span><\/strong>\uff0c\u6ee1\u8db3 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|x-x_0|\\lt\\delta<\/span><\/span><\/strong>\u3002<\/li>\n<\/ul>\n<p>\n\u7531\u4e8e\u533a\u95f4 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{x_1},\\dots,I_{x_N}<\/span><\/span><\/strong> \u8986\u76d6\u4e86 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong>\uff0c\u70b9 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong> \u81f3\u5c11\u5c5e\u4e8e\u5176\u4e2d\u4e00\u4e2a\uff0c\u4f8b\u5982\u5c5e\u4e8e\u67d0\u4e2a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{x_j}<\/span><\/span><\/strong>\uff0c\u5176\u4e2d <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">j\\in\\{1,\\dots,N\\}<\/span><\/span><\/strong>\u3002\u6839\u636e <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{x_j}<\/span><\/span><\/strong> \u7684\u5b9a\u4e49\uff0c\u8fd9\u610f\u5473\u7740\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\u6b64\u5916\uff0c\u7531 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span><\/span><\/strong> \u7684\u5b9a\u4e49\u53ef\u77e5 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta\\le\\frac{\\delta(x_j)}{2}<\/span><\/span><\/strong>\uff0c\u56e0\u6b64\u7531 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|x-x_0|\\lt\\delta<\/span><\/span><\/strong> \u53ef\u63a8\u51fa\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\u5229\u7528\u4e09\u89d2\u4e0d\u7b49\u5f0f\uff0c\u5f97\u5230\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\u7531\u4e8e\u6839\u636e <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta(x_j)<\/span><\/span><\/strong> \u7684\u5b9a\u4e49\uff08\u5373 <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u5728 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_j<\/span><\/span><\/strong> \u5904\u5bf9 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon\/2<\/span><\/span><\/strong> \u7684\u8fde\u7eed\u6027\uff09\uff0c\u4e0d\u7b49\u5f0f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|x_0-x_j|\\lt\\delta(x_j)<\/span><\/span><\/strong> \u4e0e <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|x-x_j|\\lt\\delta(x_j)<\/span><\/span><\/strong> \u8574\u542b\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{\u4e14}\\quad\n\n|f(x)-f(x_j)|\\lt\\frac{\\epsilon}{2}.\n\n<\/span>\n<\/p>\n<p>\n\u518d\u6b21\u4f7f\u7528\u4e09\u89d2\u4e0d\u7b49\u5f0f\uff0c\u53ef\u5f97\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\u7531\u4e8e <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong> \u4e0e <strong><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/strong> \u5747\u4e3a\u4efb\u610f\u53d6\u5b9a\uff0c\u56e0\u6b64\u6211\u4eec\u5df2\u8bc1\u660e\uff1a\u5bf9\u5f00\u5934\u6240\u53d6\u7684 <strong><span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon<\/span><\/strong>\uff0c\u5b58\u5728\u67d0\u4e2a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta\\gt 0<\/span><\/span><\/strong>\uff0c\u5e76\u4e14\u6b64\u6570\u4e0e <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong> <strong>\u65e0\u5173<\/strong>\uff0c\u4f7f\u5f97\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\u82e5\u5c06 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong> \u6539\u8bb0\u4f5c <strong><span class=\"katex-eq\" data-katex-display=\"false\">y<\/span><\/strong>\uff0c\u5219\u53ef\u5199\u4e3a\uff1a\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\u8fd9\u6b63\u662f <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u5728 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u4e0a<strong>\u4e00\u81f4\u8fde\u7eed<\/strong>\u7684\u5b9a\u4e49\u3002\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u53ea\u9700\u5c06\u6b64\u7ed3\u679c\u5e94\u7528\u4e8e\u60c5\u5f62 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon=1<\/span><\/span><\/strong>\u3002\n<\/p>\n<p><a name=\"8\"><\/a><\/br><\/p>\n<h4><b>\u6b65\u9aa4 5\uff1a<\/b> \u7531\u4e00\u81f4\u8fde\u7eed\u6027\u63a8\u5f97 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u5728 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u4e0a\u7684\u6709\u754c\u6027<\/h4>\n<p>\n\u73b0\u5728\u5e94\u7528\u4e00\u81f4\u8fde\u7eed\u6027\u53d6 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon=1<\/span><\/span><\/strong>\u3002\u5b58\u5728\u67d0\u4e2a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta_1\\gt 0<\/span><\/span><\/strong>\uff0c\u4f7f\u5f97\u5bf9\u6240\u6709 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x,y\\in[a,b]<\/span><\/span><\/strong> \u90fd\u6210\u7acb\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\u6211\u4eec\u5c06\u533a\u95f4 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u5212\u5206\u4e3a\u6709\u9650\u4e2a\u5b50\u533a\u95f4\uff0c\u4f7f\u5f97\u6bcf\u6bb5\u7684\u957f\u5ea6\u5747\u5c0f\u4e8e <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta_1<\/span><\/span><\/strong>\u3002\u5373\u53d6\u4e00\u4e2a\u6574\u6570 <strong><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/strong> \u4e0e\u70b9\u5217\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\u4f7f\u5f97\u5bf9\u6bcf\u4e2a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k=0,1,\\dots,n-1]<\/span><\/span><\/strong> \u90fd\u6709\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\u8003\u8651\u6709\u9650\u96c6\u5408\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\u7531\u4e8e\u8fd9\u662f\u6709\u9650\u4e2a\u5b9e\u6570\u7684\u96c6\u5408\uff0c\u6211\u4eec\u53ef\u4ee5\u65e0\u56f0\u96be\u5730\u5b9a\u4e49\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\u6211\u4eec\u5c06\u8bc1\u660e <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C+1<\/span><\/span><\/strong> \u662f <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u5728\u6574\u4e2a\u533a\u95f4 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u7684\u7edd\u5bf9\u503c\u4e0a\u754c\u3002\u4efb\u53d6 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in[a,b]<\/span><\/span><\/strong>\uff0c\u5fc5\u5b58\u5728\u67d0\u4e2a\u6307\u6807 <strong><span class=\"katex-eq\" data-katex-display=\"false\">k<\/span><\/strong> \u4f7f\u5f97 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in[x_k,x_{k+1}]<\/span><\/span><\/strong>\u3002\u7279\u522b\u5730\uff0c\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\u7531\u4e8e\u4e00\u81f4\u8fde\u7eed\u6027\u5728 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon=1<\/span><\/span><\/strong> \u7684\u60c5\u5f62\u4e0b\u6210\u7acb\uff0c\u53ef\u7531 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|x-x_k|\\lt\\delta_1<\/span><\/span><\/strong> \u63a8\u51fa\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\u5229\u7528\u4e09\u89d2\u4e0d\u7b49\u5f0f\uff1a\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\u7531\u4e8e <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in[a,b]<\/span><\/span><\/strong> \u662f\u4efb\u610f\u7684\uff0c\u6545\u53ef\u5f97\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{\u5bf9\u6240\u6709 } x\\in[a,b].\n\n<\/span>\n<\/p>\n<p>\n\u4e5f\u5c31\u662f\u8bf4\uff0c\u51fd\u6570 <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u5728 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u4e0a\u662f<strong>\u6709\u754c<\/strong>\u7684\u3002\n<\/p>\n<p><a name=\"9\"><\/a><\/br><\/p>\n<h4><b>\u6b65\u9aa4 6\uff1a<\/b> \u6700\u5927\u503c\u4e0e\u6700\u5c0f\u503c\u7684\u5b58\u5728\u6027<\/h4>\n<p>\n\u6211\u4eec\u5b9a\u4e49\u51fd\u6570\u5728\u8be5\u533a\u95f4\u4e0a\u53d6\u503c\u7684\u96c6\u5408\uff1a\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\u6211\u4eec\u5df2\u7ecf\u77e5\u9053 <strong><span class=\"katex-eq\" data-katex-display=\"false\">H<\/span><\/strong> \u975e\u7a7a\uff08\u56e0\u4e3a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u975e\u7a7a\uff09\uff0c\u5e76\u4e14\u6709\u754c\uff0c\u56e0\u6b64\u6839\u636e\u4e0a\u786e\u754c\u516c\u7406\u5b58\u5728\u5b9e\u6570\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\u63a5\u4e0b\u6765\u8bc1\u660e <strong><span class=\"katex-eq\" data-katex-display=\"false\">M<\/span><\/strong> \u80fd\u4f5c\u4e3a\u51fd\u6570\u7684\u53d6\u503c\u88ab\u8fbe\u5230\uff0c\u5373\u5b58\u5728\u67d0\u4e2a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_1\\in[a,b]<\/span><\/span><\/strong> \u4f7f\u5f97 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x_1)=M<\/span><\/span><\/strong>\u3002\u6211\u4eec\u5c06\u4f7f\u7528\u53cd\u8bc1\u6cd5\u3002\n<\/p>\n<p>\n\u5047\u8bbe <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span><\/strong> \u4ece\u4e0d\u53d6\u503c <strong><span class=\"katex-eq\" data-katex-display=\"false\">M<\/span><\/strong>\uff0c\u5373\uff1a\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\u5728\u8be5\u5047\u8bbe\u4e0b\uff0c\u51fd\u6570\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\u5728\u6574\u4e2a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u4e0a\u5747\u6709\u5b9a\u4e49\u4e14\u4e3a\u6b63\uff0c\u56e0\u4e3a\u6839\u636e\u5047\u8bbe <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">M-f(x)\\gt 0<\/span><\/span><\/strong>\u3002\u6b64\u5916\uff0c\u7531\u4e8e <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u8fde\u7eed\u4e14 <strong><span class=\"katex-eq\" data-katex-display=\"false\">M<\/span><\/strong> \u4e3a\u5e38\u6570\uff0c\u6545 <strong><span class=\"katex-eq\" data-katex-display=\"false\">g<\/span><\/strong> \u4e5f\u662f\u8fde\u7eed\u7684\u3002\u6839\u636e\u8bc1\u660e\u7684\u7b2c\u4e00\u90e8\u5206\uff0c\u4efb\u4f55\u5728 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u4e0a\u7684\u8fde\u7eed\u51fd\u6570\u90fd\u662f\u6709\u754c\u7684\uff0c\u56e0\u6b64\u5b58\u5728\u67d0\u4e2a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">N\\gt 0<\/span><\/span><\/strong> \u4f7f\u5f97\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\u7279\u522b\u5730\uff0c\u5bf9\u6240\u6709 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in[a,b]<\/span><\/span><\/strong> \u90fd\u6709\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\u8fd9\u7b49\u4ef7\u4e8e\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\u8fd9\u610f\u5473\u7740 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span><\/strong> \u5728\u6574\u4e2a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u4e0a\u7684\u6240\u6709\u503c\u90fd\u5c0f\u4e8e\u6216\u7b49\u4e8e <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">M-\\frac{1}{N}<\/span><\/span><\/strong>\u3002\u7279\u522b\u662f\uff0c<strong><span class=\"katex-eq\" data-katex-display=\"false\">H<\/span><\/strong> \u7684\u4e0a\u786e\u754c\u6ee1\u8db3\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\u8fd9\u4e0e <strong><span class=\"katex-eq\" data-katex-display=\"false\">M<\/span><\/strong> \u4f5c\u4e3a <strong><span class=\"katex-eq\" data-katex-display=\"false\">H<\/span><\/strong> \u7684\u4e0a\u786e\u754c\u7684\u5b9a\u4e49\u76f8\u77db\u76fe\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u7684\u5047\u8bbe\u5fc5\u4e3a\u9519\u8bef\uff0c\u5373\u5fc5\u5b58\u5728\u67d0\u4e2a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_1\\in[a,b]<\/span><\/span><\/strong> \u4f7f\u5f97\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\u7528\u5b8c\u5168\u7c7b\u4f3c\u7684\u63a8\u7406\u5904\u7406\u4e0b\u786e\u754c <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m=\\inf H<\/span><\/span><\/strong>\uff08\u4f8b\u5982\u8003\u8651\u51fd\u6570 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h(x)=-f(x)<\/span><\/span><\/strong>\uff09\uff0c\u53ef\u8bc1\u660e\u5b58\u5728\u67d0\u4e2a <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_2\\in[a,b]<\/span><\/span><\/strong> \u4f7f\u5f97\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>\u4ece\u7d27\u81f4\u6027\u7684\u89d2\u5ea6\u89e3\u8bfb\u4e0e\u7ed3\u8bba<\/h2>\n<p>\n\u6211\u4eec\u5df2\u7ecf\u8bc1\u660e\uff0c\u4efb\u610f\u8fde\u7eed\u51fd\u6570 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f:[a,b]\\to\\mathbb{R}<\/span><\/span><\/strong> \u5728\u533a\u95f4 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u4e0a\u90fd\u662f\u6709\u754c\u7684\uff0c\u5e76\u4e14\u80fd\u591f\u53d6\u5f97\u5176\u6700\u5927\u503c\u4e0e\u6700\u5c0f\u503c\u3002\u7528\u73b0\u4ee3\u5206\u6790\u8bed\u8a00\u6765\u8bf4\uff0c\u8fd9\u53ef\u89e3\u91ca\u4e3a\uff1a\u5728 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}<\/span><\/span><\/strong> \u4e2d\uff0c\u50cf <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u8fd9\u6837\u7684\u95ed\u4e14\u6709\u754c\u533a\u95f4\u662f\u7d27\u96c6\uff0c\u800c\u8fde\u7eed\u51fd\u6570\u4f1a\u5c06\u7d27\u96c6\u6620\u5c04\u4e3a\u7d27\u96c6\u3002\n<\/p>\n<p>\n\u7279\u522b\u5730\uff0c\u5982\u679c <strong><span class=\"katex-eq\" data-katex-display=\"false\">I<\/span><\/strong> \u662f\u7d27\u96c6\u4e14 <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u5728 <strong><span class=\"katex-eq\" data-katex-display=\"false\">I<\/span><\/strong> \u4e0a\u8fde\u7eed\uff0c\u5219\u5176\u50cf <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(I)<\/span><\/span><\/strong> \u662f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}<\/span><\/span><\/strong> \u4e2d\u7684\u4e00\u4e2a\u7d27\u5b50\u96c6\u3002\u8fd9\u4fdd\u8bc1\u4e86 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(I)<\/span><\/span><\/strong> \u662f\u6709\u754c\u7684\uff0c\u5e76\u4e14\u5176\u4e2d\u7684\u6700\u5927\u503c\u4e0e\u6700\u5c0f\u503c\u5747\u80fd\u88ab\u5b9e\u9645\u53d6\u5f97\uff0c\u8fd9\u6b63\u662f\u9b4f\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\u7684\u5185\u5bb9\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u9b4f\u5c14\u65af\u7279\u62c9\u65af\u6781\u503c\u5b9a\u7406 \u4e3a\u4f55\u5728\u5982\u6b64\u591a\u7684\u6700\u4f18\u5316\u95ee\u9898\u4e2d\uff0c\u4eba\u4eec\u51e0\u4e4e\u9ed8\u8ba4\u201c\u6700\u5927\u503c\u5b58\u5728\u201d\u6216\u201c\u67d0\u533a\u95f4\u5185\u603b\u6709\u6700\u5c0f\u503c\u201d\uff0c\u800c\u5b9e\u9645\u4e0a\u5e76\u65e0\u4efb\u4f55\u5148\u9a8c\u7406\u7531\u4fdd\u8bc1\u8fd9\u4e00\u70b9\uff1f\u9b4f\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\u6b63\u662f\u586b\u8865\u8fd9\u4e00\u8ba4\u77e5\u7a7a\u7f3a\u7684\u5173\u952e\uff1a\u5b83\u4fdd\u8bc1\u5b9a\u4e49\u5728\u95ed\u4e14\u6709\u754c\u533a\u95f4\u4e0a\u7684\u8fde\u7eed\u51fd\u6570\u4e0d\u4ec5\u662f\u6709\u754c\u7684\uff0c\u800c\u4e14\u786e\u5b9e\u80fd\u591f\u53d6\u5f97\u5176\u6781\u503c\u3002\u5728\u672c\u7bc7\u6587\u7ae0\u4e2d\uff0c\u6211\u4eec\u5c06\u56de\u987e\u5176\u8868\u8ff0\uff0c\u57fa\u4e8e\u70b9\u6001\u8fde\u7eed\u6027\u3001\u7d27\u81f4\u6027\u4e0e\u4e0a\u786e\u754c\u516c\u7406\uff0c\u8be6\u7ec6\u6784\u5efa\u4e00\u4efd\u4e25\u683c\u8bc1\u660e\uff0c\u5e76\u8fdb\u4e00\u6b65\u4ece\u8fde\u7eed\u51fd\u6570\u4f5c\u7528\u4e8e\u7d27\u96c6\u7684\u73b0\u4ee3\u89c6\u89d2\u4e88\u4ee5\u9610\u91ca\u3002\u76ee\u6807\u5728\u4e8e\uff0c\u4f7f\u8bfb\u8005\u5728\u7ed3\u675f\u9605\u8bfb\u65f6\uff0c\u4e0d\u4ec5\u8bb0\u4f4f\u5b9a\u7406\u7684\u5b57\u9762\u8868\u8ff0\uff0c\u66f4\u80fd\u591f\u7406\u89e3\u5176\u4e3a\u4f55\u6210\u7acb\uff0c\u4ee5\u53ca\u4e3a\u4f55\u5728\u5206\u6790\u5b66\u3001\u6700\u4f18\u5316\u4e0e\u5e94\u7528\u6a21\u578b\u4e2d\u4e0d\u65ad\u51fa\u73b0\u3002 \u5b66\u4e60\u76ee\u6807 \u7406\u89e3\u9b4f\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\u7684\u8868\u8ff0\u3002 \u660e\u786e\u8fa8\u8bc6\u5b9a\u7406\u7684\u5047\u8bbe\uff08\u5728\u95ed\u4e14\u6709\u754c\u533a\u95f4 \u4e0a\u7684\u8fde\u7eed\u51fd\u6570\uff09\u53ca\u5176\u4e3b\u8981\u7ed3\u8bba\uff1a\u6709\u754c\u6027\u4ee5\u53ca\u6700\u5927\u503c\u4e0e\u6700\u5c0f\u503c\u7684\u5b58\u5728\u6027\u3002 \u4ece\u7d27\u81f4\u6027\u7684\u89d2\u5ea6\u89e3\u91ca\u9b4f\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\u3002 \u4ee5\u73b0\u4ee3\u8bed\u8a00\u8868\u8ff0\u8be5\u7ed3\u679c\uff1a\u8fde\u7eed\u51fd\u6570\u5c06\u7d27\u96c6\u6620\u5c04\u4e3a\u80fd\u53d6\u5f97\u6781\u503c\u7684\u96c6\u5408\uff0c\u4ece\u800c\u5c06 \u7684\u60c5\u5f62\u4e0e\u5b9e\u5206\u6790\u7684\u4e00\u822c\u6846\u67b6\u8fde\u63a5\u8d77\u6765\u3002 \u5c06\u9b4f\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\u4e0e\u6700\u4f18\u5316\u95ee\u9898\u8054\u7cfb\u8d77\u6765\u3002 \u8ba4\u8bc6\u8be5\u5b9a\u7406\u4f5c\u4e3a\u7406\u8bba\u57fa\u7840\u5728\u4f17\u591a\u4e00\u5143\u6700\u4f18\u5316\u95ee\u9898\uff08\u65e0\u8bba\u7406\u8bba\u6216\u5e94\u7528\u60c5\u5883\uff09\u4e2d\u5bf9\u6700\u5927\u503c\u4e0e\u6700\u5c0f\u503c\u5b58\u5728\u6027\u7684\u4fdd\u969c\u4f5c\u7528\u3002 \u5185\u5bb9\u7d22\u5f15: \u5f15\u8a00 \u9b4f\u5c14\u65af\u7279\u62c9\u65af\u5b9a\u7406\u7684\u8868\u8ff0 \u8bc1\u660e \u6b65\u9aa4 1\uff1a \u4e0a\u7684\u70b9\u6001\u8fde\u7eed\u6027 \u6b65\u9aa4 2\uff1a\u4e0e\u8fde\u7eed\u6027\u5bf9\u5e94\u7684\u5f00\u8986\u76d6 \u6b65\u9aa4 3\uff1a[a,b] \u7684\u7d27\u81f4\u6027\u4e0e\u6709\u9650\u5b50\u8986\u76d6 \u6b65\u9aa4 4\uff1a\u6784\u9020\u4e00\u4e2a\u4e0d\u4f9d\u8d56\u4e8e \u7684 \uff08\u4e00\u81f4\u8fde\u7eed\u6027\uff09 \u6b65\u9aa4 5\uff1a\u7531\u4e00\u81f4\u8fde\u7eed\u6027\u63a8\u5bfc \u5728 \u4e0a\u7684\u6709\u754c\u6027 \u6b65\u9aa4 6\uff1a\u6700\u5927\u503c\u4e0e\u6700\u5c0f\u503c\u7684\u5b58\u5728\u6027 \u57fa\u4e8e\u7d27\u81f4\u6027\u7684\u89e3\u91ca\u4e0e\u7ed3\u8bba \u5f15\u8a00 \u9b4f\u5c14\u65af\u7279\u62c9\u65af\u6781\u503c\u5b9a\u7406\u867d\u7136\u901a\u5e38\u51fa\u73b0\u5728\u5b9e\u5206\u6790\u7684\u6700\u521d\u7ae0\u8282\uff0c\u4f46\u4e8b\u5b9e\u4e0a\uff0c\u5b83\u5728\u5e94\u7528\u6570\u5b66\u7684\u5e7f\u5927\u9886\u57df\u4e2d\u53d1\u6325\u7740\u65e0\u58f0\u5374\u6838\u5fc3\u7684\u4f5c\u7528\u3002\u6bcf\u5f53\u6211\u4eec\u5728\u7269\u7406\u3001\u7ecf\u6d4e\u6216\u7edf\u8ba1\u4e2d\u8ba8\u8bba\u5728\u7279\u5b9a\u7ea6\u675f\u4e0b\u201c\u6700\u5927\u5316\u201d\u6216\u201c\u6700\u5c0f\u5316\u201d\u67d0\u4e00\u91cf\u65f6\uff0c\u672c\u8d28\u4e0a\u4f9d\u9760\u7684\u6b63\u662f\u8be5\u5b9a\u7406\u6240\u4fdd\u8bc1\u7684\u601d\u60f3\uff1a\u5b9a\u4e49\u5728\u95ed\u4e14\u6709\u754c\u533a\u95f4\u4e0a\u7684\u8fde\u7eed\u51fd\u6570\u4e0d\u4ec5\u662f\u6709\u754c\u7684\uff0c\u800c\u4e14\u5b9e\u9645\u80fd\u591f\u53d6\u5f97\u5176\u6781\u503c\u3002 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