{"id":29094,"date":"2021-08-19T13:00:33","date_gmt":"2021-08-19T13:00:33","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=29094"},"modified":"2024-09-22T09:29:37","modified_gmt":"2024-09-22T09:29:37","slug":"%e5%ae%9a%e4%b9%89%e5%9f%9f%e3%80%81%e5%80%bc%e5%9f%9f%e5%92%8c%e5%9b%be%e5%83%8f-%e6%8f%90%e8%ae%ae%e4%b8%8e%e8%a7%a3%e7%ad%94","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/zh\/%e5%ae%9a%e4%b9%89%e5%9f%9f%e3%80%81%e5%80%bc%e5%9f%9f%e5%92%8c%e5%9b%be%e5%83%8f-%e6%8f%90%e8%ae%ae%e4%b8%8e%e8%a7%a3%e7%ad%94\/","title":{"rendered":"\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf &#8211; \u63d0\u8bae\u4e0e\u89e3\u7b54"},"content":{"rendered":"<p><center><\/p>\n<h1>\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf &#8211; \u63d0\u8bae\u4e0e\u89e3\u7b54<\/h1>\n<p><em><strong>\u6458\u8981\uff1a<\/strong><br \/>\n   \u5728\u8fd9\u8282\u8bfe\u4e2d\uff0c\u6211\u4eec\u901a\u8fc7\u7ec3\u4e60\u548c\u89e3\u7b54\u793a\u4f8b\uff0c\u7ec3\u4e60\u5982\u4f55\u786e\u5b9a\u4ee3\u6570\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf\uff0c\u5f3a\u8c03\u5b9e\u8df5\u5bf9\u4e8e\u638c\u63e1\u8fd9\u4e9b\u6280\u5de7\u7684\u91cd\u8981\u6027\u3002<br \/>\n   <\/em><\/p>\n<p>   <strong>\u5b66\u4e60\u76ee\u6807\uff1a<\/strong><br \/>\n   \u5728\u8fd9\u8282\u8bfe\u7ed3\u675f\u65f6\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a<\/p>\n<ol style=\"text-align:left;\">\n<li><strong>\u7406\u89e3<\/strong>\u5982\u4f55\u786e\u5b9a\u4ee3\u6570\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u3002<\/li>\n<li><strong>\u8bc6\u522b<\/strong>\u4e0d\u540c\u7c7b\u578b\u51fd\u6570\u7684\u503c\u57df\u3002<\/li>\n<li><strong>\u8868\u793a<\/strong>\u4ee3\u6570\u51fd\u6570\u5728\u76f4\u89d2\u5750\u6807\u7cfb\u4e2d\u7684\u56fe\u50cf\u3002<\/li>\n<li><strong>\u5e94\u7528<\/strong>\u7b80\u5316\u6280\u5de7\u6765\u89e3\u51b3\u66f4\u590d\u6742\u7684\u51fd\u6570\u3002<\/li>\n<\/ol>\n<p>   <\/center><\/p>\n<h2>\u5982\u4f55\u638c\u63e1\u8fd9\u4e9b\u6280\u5de7<\/h2>\n<p style=\"text-align: justify;\">\u8981\u638c\u63e1\u786e\u5b9a\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf\u7684\u6280\u5de7\uff0c\u81f3\u5c11\u5728\u8fd9\u4e2a\u5c42\u6b21\u4e0a\uff0c\u6ca1\u5fc5\u8981\u590d\u4e60\u6211\u4eec\u5df2\u7ecf\u6db5\u76d6\u7684\u66f4\u591a\u7406\u8bba\u3002\u6b64\u65f6\uff0c\u6700\u597d\u662f\u591a\u505a\u7ec3\u4e60\uff0c\u800c\u6700\u597d\u7684\u7ec3\u4e60\u65b9\u5f0f\u5c31\u662f\u968f\u673a\u53d1\u660e\u7ec3\u4e60\u9898\u3002\u53ea\u6709\u8fd9\u6837\uff0c\u4f60\u624d\u80fd\u771f\u6b63\u4e86\u89e3\u6211\u4eec\u76ee\u524d\u5b66\u4e60\u7684\u6280\u5de7\u7684\u6781\u9650\uff0c\u5e76\u57f9\u517b\u51fa\u80fd\u591f\u7075\u6d3b\u8fd0\u7528\u7684\u76f4\u89c9\u3002<\/p>\n<p style=\"text-align: justify;\">\u63a5\u4e0b\u6765\u6211\u4eec\u8981\u505a\u7684\u6b63\u662f\u8fd9\u4e00\u70b9\uff1a\u6211\u5c06\u968f\u673a\u53d1\u660e\u4e00\u4e9b\u7ec3\u4e60\u9898\uff0c\u5e76\u5728\u590d\u4e60\u7684\u6280\u5de7\u5141\u8bb8\u7684\u8303\u56f4\u5185\u89e3\u7b54\uff1b\u5982\u679c\u65e0\u6cd5\u7528\u8fd9\u4e9b\u6280\u5de7\u89e3\u7b54\uff0c\u6211\u5c06\u89e3\u91ca\u5b83\u4eec\u5728\u54ea\u4e9b\u65b9\u9762\u5931\u8d25\u4ee5\u53ca\u539f\u56e0\u3002<\/p>\n<h3>\u7ec3\u4e60\u9898\uff1a<\/h3>\n<p style=\"text-align: justify;\">\u786e\u5b9a\u4ee5\u4e0b\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf\uff1a<\/p>\n<ol style=\"text-align: justify;\">\n<li><span class=\"katex-eq\" data-katex-display=\"false\">a(x) = \\displaystyle \\frac{x^3 - 3x^2 + 5x - 1}{x^2 + 2x - 1}<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">b(x) = \\displaystyle \\frac{4x^4 + 2x^3 - 5x^2 - 2x - 2}{2x^2 - x - 1}<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">c(x) = \\displaystyle \\frac{x^5 + x^3 - x - 1}{x^2 - x - 1}<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">d(x) = \\displaystyle \\frac{3x^2 - 3x - 2}{\\sqrt{x^2 - 1}}<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">e(x) = \\displaystyle \\sqrt{\\frac{x^4 - x^2 - 11}{(x^2 - 1)\\sqrt{x^2 - x - 1}}}<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\displaystyle \\frac{(x^2 - 2x - 2)\\sqrt{7x^8 - 5x^4 - 2}}{x\\sqrt{5x^2 - 3x + 2}}<\/span><\/li>\n<\/ol>\n<h3>\u7ec3\u4e60\u9898\u89e3\u7b54\uff1a<\/h3>\n<p>   <center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/f2g4MVSvfSI\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n<p>   <center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/8nF10hKDbz4\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n<p>   <center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/MA9mvrEohpc\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n<h3>\u5efa\u8bae\u7684\u7ec3\u4e60\u9898\uff1a<\/h3>\n<p style=\"text-align: justify;\">\u4ee5\u4e0b\u5efa\u8bae\u7684\u7ec3\u4e60\u9898\u4e0e\u4e4b\u524d\u89e3\u7b54\u7684\u7c7b\u4f3c\uff1b\u6211\u53ea\u66f4\u6539\u4e86\u6570\u5b57\u3002\u7ed3\u6784\u662f\u4e00\u6837\u7684\uff0c\u56e0\u6b64\u4e4b\u524d\u7684\u89e3\u7b54\u53ef\u80fd\u4f1a\u6709\u5e2e\u52a9\u3002\u5982\u679c\u4f60\u5bf9\u8fd9\u4e9b\u6280\u5de7\u8fd8\u4e0d\u591f\u719f\u7ec3\uff0c\u4f60\u53ef\u4ee5\u4f7f\u7528\u50cf <a href=\"https:\/\/www.wolframalpha.com\/\" rel=\"nofollow, noreferrer, noopener\" target=\"_blank\">WolframAlpha<\/a> \u548c <a href=\"https:\/\/www.geogebra.org\/\" rel=\"nofollow, noreferrer, noopener\" target=\"_blank\">GeoGebra<\/a> \u8fd9\u6837\u7684\u5728\u7ebf\u5de5\u5177\u3002\u5982\u679c\u4f60\u5728\u4ee3\u6570\u65b9\u9762\u6709\u56f0\u96be\uff0c\u590d\u4e60\u4ee5\u4e0b\u8bfe\u7a0b\u4f1a\u5bf9\u4f60\u6709\u5e2e\u52a9\uff1a<\/p>\n<p style=\"text-align: justify;\">\u548c\u4e4b\u524d\u7684\u7ec3\u4e60\u9898\u4e00\u6837\uff0c\u4f60\u9700\u8981\u8ba1\u7b97\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf\u3002<\/p>\n<ol style=\"text-align: justify;\">\n<li><span class=\"katex-eq\" data-katex-display=\"false\">a(x) = \\displaystyle \\frac{-5x^3 + 9x^2 - 7x - 2}{5x^2 + 3x + 9}<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">b(x) = \\displaystyle \\frac{-8x^4 + 2x^3 + 4x^2 + 4x + 1}{3x^2 - 9x + 3}<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">c(x) = \\displaystyle \\frac{-7x^5 + 9x^3 + 7x + 5}{-2x^2 - 8x + 6}<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">d(x) = \\displaystyle \\frac{4x^2 - 4x - 9}{\\sqrt{-3x^2 + 7}}<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">e(x) = \\displaystyle \\sqrt{\\frac{9x^4 + 2x^2 + 7}{(-8x^2 + 4)\\sqrt{-6x^2 + 9x + 5}}}<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\displaystyle \\frac{(7x^2 + 6x - 1)\\sqrt{9x^8 + 3x^4 + 9}}{5x\\sqrt{3x^2 + 8x - 3}}<\/span><\/li>\n<\/ol>\n<p style=\"text-align: justify;\">\u4ece\u8fd9\u91cc\u5f00\u59cb\uff0c\u5982\u679c\u4f60\u60f3\u7ec3\u4e60\u66f4\u591a\uff0c\u6700\u597d\u81ea\u5df1\u53d1\u660e\u4e00\u4e9b\u51fd\u6570\u5e76\u52a0\u4ee5\u5c1d\u8bd5\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf &#8211; \u63d0\u8bae\u4e0e\u89e3\u7b54 \u6458\u8981\uff1a \u5728\u8fd9\u8282\u8bfe\u4e2d\uff0c\u6211\u4eec\u901a\u8fc7\u7ec3\u4e60\u548c\u89e3\u7b54\u793a\u4f8b\uff0c\u7ec3\u4e60\u5982\u4f55\u786e\u5b9a\u4ee3\u6570\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf\uff0c\u5f3a\u8c03\u5b9e\u8df5\u5bf9\u4e8e\u638c\u63e1\u8fd9\u4e9b\u6280\u5de7\u7684\u91cd\u8981\u6027\u3002 \u5b66\u4e60\u76ee\u6807\uff1a \u5728\u8fd9\u8282\u8bfe\u7ed3\u675f\u65f6\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a \u7406\u89e3\u5982\u4f55\u786e\u5b9a\u4ee3\u6570\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u3002 \u8bc6\u522b\u4e0d\u540c\u7c7b\u578b\u51fd\u6570\u7684\u503c\u57df\u3002 \u8868\u793a\u4ee3\u6570\u51fd\u6570\u5728\u76f4\u89d2\u5750\u6807\u7cfb\u4e2d\u7684\u56fe\u50cf\u3002 \u5e94\u7528\u7b80\u5316\u6280\u5de7\u6765\u89e3\u51b3\u66f4\u590d\u6742\u7684\u51fd\u6570\u3002 \u5982\u4f55\u638c\u63e1\u8fd9\u4e9b\u6280\u5de7 \u8981\u638c\u63e1\u786e\u5b9a\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf\u7684\u6280\u5de7\uff0c\u81f3\u5c11\u5728\u8fd9\u4e2a\u5c42\u6b21\u4e0a\uff0c\u6ca1\u5fc5\u8981\u590d\u4e60\u6211\u4eec\u5df2\u7ecf\u6db5\u76d6\u7684\u66f4\u591a\u7406\u8bba\u3002\u6b64\u65f6\uff0c\u6700\u597d\u662f\u591a\u505a\u7ec3\u4e60\uff0c\u800c\u6700\u597d\u7684\u7ec3\u4e60\u65b9\u5f0f\u5c31\u662f\u968f\u673a\u53d1\u660e\u7ec3\u4e60\u9898\u3002\u53ea\u6709\u8fd9\u6837\uff0c\u4f60\u624d\u80fd\u771f\u6b63\u4e86\u89e3\u6211\u4eec\u76ee\u524d\u5b66\u4e60\u7684\u6280\u5de7\u7684\u6781\u9650\uff0c\u5e76\u57f9\u517b\u51fa\u80fd\u591f\u7075\u6d3b\u8fd0\u7528\u7684\u76f4\u89c9\u3002 \u63a5\u4e0b\u6765\u6211\u4eec\u8981\u505a\u7684\u6b63\u662f\u8fd9\u4e00\u70b9\uff1a\u6211\u5c06\u968f\u673a\u53d1\u660e\u4e00\u4e9b\u7ec3\u4e60\u9898\uff0c\u5e76\u5728\u590d\u4e60\u7684\u6280\u5de7\u5141\u8bb8\u7684\u8303\u56f4\u5185\u89e3\u7b54\uff1b\u5982\u679c\u65e0\u6cd5\u7528\u8fd9\u4e9b\u6280\u5de7\u89e3\u7b54\uff0c\u6211\u5c06\u89e3\u91ca\u5b83\u4eec\u5728\u54ea\u4e9b\u65b9\u9762\u5931\u8d25\u4ee5\u53ca\u539f\u56e0\u3002 \u7ec3\u4e60\u9898\uff1a \u786e\u5b9a\u4ee5\u4e0b\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf\uff1a \u7ec3\u4e60\u9898\u89e3\u7b54\uff1a \u5efa\u8bae\u7684\u7ec3\u4e60\u9898\uff1a \u4ee5\u4e0b\u5efa\u8bae\u7684\u7ec3\u4e60\u9898\u4e0e\u4e4b\u524d\u89e3\u7b54\u7684\u7c7b\u4f3c\uff1b\u6211\u53ea\u66f4\u6539\u4e86\u6570\u5b57\u3002\u7ed3\u6784\u662f\u4e00\u6837\u7684\uff0c\u56e0\u6b64\u4e4b\u524d\u7684\u89e3\u7b54\u53ef\u80fd\u4f1a\u6709\u5e2e\u52a9\u3002\u5982\u679c\u4f60\u5bf9\u8fd9\u4e9b\u6280\u5de7\u8fd8\u4e0d\u591f\u719f\u7ec3\uff0c\u4f60\u53ef\u4ee5\u4f7f\u7528\u50cf WolframAlpha \u548c GeoGebra \u8fd9\u6837\u7684\u5728\u7ebf\u5de5\u5177\u3002\u5982\u679c\u4f60\u5728\u4ee3\u6570\u65b9\u9762\u6709\u56f0\u96be\uff0c\u590d\u4e60\u4ee5\u4e0b\u8bfe\u7a0b\u4f1a\u5bf9\u4f60\u6709\u5e2e\u52a9\uff1a \u548c\u4e4b\u524d\u7684\u7ec3\u4e60\u9898\u4e00\u6837\uff0c\u4f60\u9700\u8981\u8ba1\u7b97\u5b9a\u4e49\u57df\u3001\u503c\u57df\u548c\u56fe\u50cf\u3002 \u4ece\u8fd9\u91cc\u5f00\u59cb\uff0c\u5982\u679c\u4f60\u60f3\u7ec3\u4e60\u66f4\u591a\uff0c\u6700\u597d\u81ea\u5df1\u53d1\u660e\u4e00\u4e9b\u51fd\u6570\u5e76\u52a0\u4ee5\u5c1d\u8bd5\u3002<\/p>\n","protected":false},"author":1,"featured_media":29088,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":3,"footnotes":""},"categories":[591,575],"tags":[],"class_list":["post-29094","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-591","category-575"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - 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