{"id":13267,"date":"2025-01-11T22:42:20","date_gmt":"2025-01-11T14:42:20","guid":{"rendered":"http:\/\/www.aiersheng.cc\/?p=13267"},"modified":"2025-01-11T23:04:50","modified_gmt":"2025-01-11T15:04:50","slug":"13267","status":"publish","type":"post","link":"https:\/\/www.aiersheng.cc\/?p=13267","title":{"rendered":"\u6d59\u6c5f\u9ad8\u804c\u5355\u62db\u6570\u5b66\u5b66\u4e60\u65b9\u6cd5\u4e0e\u77e5\u8bc6\u70b9\u68b3\u7406"},"content":{"rendered":"<h1>\u6d59\u6c5f\u9ad8\u804c\u5355\u62db\u6570\u5b66\u5b66\u4e60\u65b9\u6cd5\u4e0e\u77e5\u8bc6\u70b9\u68b3\u7406<\/h1>\n<h2>\u4e00\u3001\u5b66\u4e60\u65b9\u6cd5<\/h2>\n<h3>\uff08\u4e00\uff09\u89e3\u540e\u53cd\u601d\uff0c\u63d0\u5347\u5206\u6790\u80fd\u529b<\/h3>\n<div class=\"paragraph\">\u5728\u5b8c\u6210\u6570\u5b66\u9898\u76ee\u540e\uff0c\u53ca\u65f6\u56de\u987e\u89e3\u9898\u8fc7\u7a0b\u81f3\u5173\u91cd\u8981\u3002\u601d\u8003\u4ee5\u4e0b\u51e0\u4e2a\u95ee\u9898\uff1a<\/div>\n<ul>\n<li>\n<div class=\"paragraph\"><strong>\u89e3\u9898\u601d\u8def<\/strong>\uff1a\u56de\u987e\u662f\u5982\u4f55\u901a\u8fc7\u5206\u6790\u9898\u76ee\u4fe1\u606f\uff0c\u8054\u60f3\u76f8\u5173\u77e5\u8bc6\u70b9\uff0c\u9010\u6b65\u63a2\u7d22\u51fa\u89e3\u9898\u9014\u5f84\u7684\u3002\u4f8b\u5982\uff0c\u5728\u89e3\u51b3\u4e00\u9053\u590d\u6742\u7684\u51fd\u6570\u95ee\u9898\u65f6\uff0c\u56de\u60f3\u662f\u5148\u786e\u5b9a\u51fd\u6570\u7c7b\u578b\uff0c\u8fd8\u662f\u5148\u5206\u6790\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u548c\u503c\u57df\uff0c\u6216\u662f\u5148\u8003\u8651\u51fd\u6570\u7684\u5355\u8c03\u6027\u7b49\u6027\u8d28\u6765\u5165\u624b\u7684\u3002<\/div>\n<\/li>\n<li>\n<div class=\"paragraph\"><strong>\u5173\u952e\u70b9<\/strong>\uff1a\u660e\u786e\u4f7f\u95ee\u9898\u5f97\u4ee5\u89e3\u51b3\u7684\u5173\u952e\u56e0\u7d20\u662f\u4ec0\u4e48\u3002\u53ef\u80fd\u662f\u4e00\u4e2a\u5173\u952e\u7684\u516c\u5f0f\u5e94\u7528\uff0c\u4e00\u4e2a\u5de7\u5999\u7684\u53d8\u91cf\u66ff\u6362\uff0c\u6216\u662f\u5bf9\u67d0\u4e2a\u6982\u5ff5\u7684\u51c6\u786e\u7406\u89e3\u3002\u6bd4\u5982\uff0c\u5728\u89e3\u51b3\u4e09\u89d2\u51fd\u6570\u95ee\u9898\u65f6\uff0c\u5173\u952e\u53ef\u80fd\u662f\u5229\u7528\u8bf1\u5bfc\u516c\u5f0f\u5c06\u590d\u6742\u7684\u89d2\u5ea6\u8f6c\u6362\u4e3a\u7279\u6b8a\u89d2\uff0c\u4ece\u800c\u7b80\u5316\u8ba1\u7b97\u3002<\/div>\n<\/li>\n<li>\n<div class=\"paragraph\"><strong>\u56f0\u96be\u4e0e\u514b\u670d<\/strong>\uff1a\u53cd\u601d\u5728\u89e3\u9898\u8fc7\u7a0b\u4e2d\u9047\u5230\u7684\u56f0\u96be\uff0c\u4ee5\u53ca\u662f\u5982\u4f55\u514b\u670d\u8fd9\u4e9b\u56f0\u96be\u7684\u3002\u662f\u901a\u8fc7\u67e5\u9605\u8d44\u6599\uff0c\u8fd8\u662f\u5411\u8001\u5e08\u6216\u540c\u5b66\u8bf7\u6559\uff0c\u6216\u662f\u81ea\u5df1\u53cd\u590d\u601d\u8003\u540e\u7a81\u7136\u987f\u609f\u3002\u603b\u7ed3\u514b\u670d\u56f0\u96be\u7684\u65b9\u6cd5\uff0c\u6709\u52a9\u4e8e\u5728\u4eca\u540e\u9047\u5230\u7c7b\u4f3c\u95ee\u9898\u65f6\u80fd\u591f\u66f4\u5feb\u5730\u627e\u5230\u89e3\u51b3\u529e\u6cd5\u3002<\/div>\n<\/li>\n<\/ul>\n<div class=\"paragraph\">\u901a\u8fc7\u8fd9\u6837\u7684\u53cd\u601d\uff0c\u53ef\u4ee5\u53d1\u73b0\u89e3\u9898\u7684\u5173\u952e\u6240\u5728\uff0c\u5e76\u4ece\u4e2d\u63d0\u70bc\u51fa\u6570\u5b66\u601d\u60f3\u548c\u65b9\u6cd5\u3002\u4f8b\u5982\uff0c\u5728\u89e3\u51b3\u6570\u5217\u95ee\u9898\u65f6\uff0c\u53ef\u80fd\u4f1a\u53d1\u73b0\u7d2f\u52a0\u6cd5\u6216\u7d2f\u4e58\u6cd5\u662f\u89e3\u51b3\u67d0\u4e9b\u7279\u5b9a\u7c7b\u578b\u6570\u5217\u95ee\u9898\u7684\u5173\u952e\u65b9\u6cd5\u3002\u5982\u679c\u4e0d\u8fdb\u884c\u53cd\u601d\uff0c\u53ea\u662f\u76f2\u76ee\u5730\u505a\u9898\uff0c\u89e3\u9898\u80fd\u529b\u5f88\u96be\u5f97\u5230\u5b9e\u8d28\u6027\u7684\u63d0\u9ad8\u3002\u56e0\u6b64\uff0c\u89e3\u9898\u540e\u8981\u52e4\u4e8e\u53cd\u601d\uff0c\u7ad9\u5728\u66f4\u9ad8\u7684\u89d2\u5ea6\u5ba1\u89c6\u9898\u76ee\u548c\u89e3\u6cd5\uff0c\u4ece\u800c\u201c\u7ad9\u5f97\u9ad8\uff0c\u770b\u5f97\u8fdc\uff0c\u9a7e\u9a6d\u5168\u5c40\u201d\uff0c\u63d0\u5347\u5206\u6790\u95ee\u9898\u7684\u80fd\u529b\u3002<\/div>\n<h3>\uff08\u4e8c\uff09\u592f\u5b9e\u57fa\u7840\uff0c\u7262\u8bb0\u6982\u5ff5<\/h3>\n<div class=\"paragraph\">\u6570\u5b66\u5e76\u975e\u4ec5\u4ec5\u662f\u505a\u9898\uff0c\u6700\u57fa\u672c\u7684\u6982\u5ff5\u3001\u516c\u7406\u3001\u5b9a\u7406\u548c\u516c\u5f0f\u662f\u5b66\u4e60\u6570\u5b66\u7684\u57fa\u77f3\u3002\u5728\u9ad8\u804c\u5355\u62db\u8003\u8bd5\u4e2d\uff0c\u5c24\u5176\u662f\u201c\u4e0d\u5b9a\u9879\u9009\u62e9\u9898\u201d\uff0c\u6e05\u6670\u7684\u6982\u5ff5\u7406\u89e3\u81f3\u5173\u91cd\u8981\u3002\u5982\u679c\u6982\u5ff5\u6a21\u7cca\uff0c\u9762\u5bf9\u9009\u9879\u65f6\u5c31\u4f1a\u611f\u89c9\u6a21\u68f1\u4e24\u53ef\uff0c\u5bb9\u6613\u8bef\u9009\u3002<\/div>\n<div class=\"paragraph\">\u56e0\u6b64\uff0c\u8981\u5c06\u5df2\u7ecf\u5b66\u8fc7\u7684\u6559\u79d1\u4e66\u4e2d\u7684\u6982\u5ff5\u8fdb\u884c\u6574\u7406\u3002\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u65b9\u6cd5\u52a0\u6df1\u5370\u8c61\uff1a<\/div>\n<ul>\n<li>\n<div class=\"paragraph\"><strong>\u9605\u8bfb<\/strong>\uff1a\u4ed4\u7ec6\u9605\u8bfb\u6559\u6750\u4e2d\u5bf9\u6982\u5ff5\u7684\u5b9a\u4e49\u548c\u89e3\u91ca\uff0c\u7406\u89e3\u5176\u5185\u6db5\u548c\u5916\u5ef6\u3002\u4f8b\u5982\uff0c\u5728\u5b66\u4e60\u51fd\u6570\u7684\u6982\u5ff5\u65f6\uff0c\u4e0d\u4ec5\u8981\u8bb0\u4f4f\u51fd\u6570\u7684\u5b9a\u4e49\uff0c\u8fd8\u8981\u7406\u89e3\u81ea\u53d8\u91cf\u3001\u56e0\u53d8\u91cf\u3001\u5b9a\u4e49\u57df\u3001\u503c\u57df\u7b49\u4e0e\u51fd\u6570\u76f8\u5173\u7684\u6982\u5ff5\u3002<\/div>\n<\/li>\n<li>\n<div class=\"paragraph\"><strong>\u6284\u5199<\/strong>\uff1a\u5c06\u91cd\u8981\u7684\u6982\u5ff5\u3001\u5b9a\u7406\u548c\u516c\u5f0f\u6284\u5199\u4e0b\u6765\uff0c\u52a0\u6df1\u8bb0\u5fc6\u3002\u5728\u6284\u5199\u8fc7\u7a0b\u4e2d\uff0c\u53ef\u4ee5\u8fdb\u4e00\u6b65\u601d\u8003\u6982\u5ff5\u4e4b\u95f4\u7684\u8054\u7cfb\u548c\u533a\u522b\u3002\u6bd4\u5982\uff0c\u533a\u5206\u4e00\u6b21\u51fd\u6570\u3001\u4e8c\u6b21\u51fd\u6570\u3001\u6307\u6570\u51fd\u6570\u3001\u5bf9\u6570\u51fd\u6570\u7b49\u4e0d\u540c\u7c7b\u578b\u7684\u51fd\u6570\u6982\u5ff5\uff0c\u660e\u786e\u5b83\u4eec\u7684\u8868\u8fbe\u5f0f\u3001\u56fe\u50cf\u7279\u5f81\u548c\u6027\u8d28\u3002<\/div>\n<\/li>\n<li>\n<div class=\"paragraph\"><strong>\u5bf9\u6bd4<\/strong>\uff1a\u5bf9\u4e8e\u5bb9\u6613\u6df7\u6dc6\u7684\u6982\u5ff5\uff0c\u8fdb\u884c\u5bf9\u6bd4\u5206\u6790\u3002\u4f8b\u5982\uff0c\u533a\u5206\u5145\u5206\u6761\u4ef6\u3001\u5fc5\u8981\u6761\u4ef6\u548c\u5145\u8981\u6761\u4ef6\uff0c\u901a\u8fc7\u5177\u4f53\u7684\u4f8b\u5b50\u6765\u7406\u89e3\u5b83\u4eec\u4e4b\u95f4\u7684\u5dee\u5f02\uff0c\u5f7b\u5e95\u641e\u6e05\u6982\u5ff5\uff0c\u4e0d\u7559\u9690\u60a3\u3002<\/div>\n<\/li>\n<\/ul>\n<h3>\uff08\u4e09\uff09\u5f3a\u5316\u5b9a\u65f6\u8bad\u7ec3\uff0c\u53ca\u65f6\u53cd\u9988\u77eb\u6b63<\/h3>\n<div class=\"paragraph\">\u5b66\u597d\u6570\u5b66\u9700\u8981\u505a\u5927\u91cf\u7684\u9898\u76ee\uff0c\u4f46\u5e76\u975e\u505a\u9898\u6570\u91cf\u8d8a\u591a\u8d8a\u597d\uff0c\u5173\u952e\u5728\u4e8e\u63d0\u9ad8\u89e3\u9898\u7684\u6548\u7387\u3002\u505a\u9898\u7684\u76ee\u7684\u662f\u68c0\u9a8c\u81ea\u5df1\u5bf9\u6240\u5b66\u77e5\u8bc6\u548c\u65b9\u6cd5\u7684\u638c\u63e1\u7a0b\u5ea6\u3002\u5982\u679c\u638c\u63e1\u5f97\u4e0d\u51c6\u786e\uff0c\u751a\u81f3\u6709\u504f\u5dee\uff0c\u90a3\u4e48\u591a\u505a\u9898\u53ea\u4f1a\u5de9\u56fa\u9519\u8bef\u7684\u7406\u89e3\u3002<\/div>\n<div class=\"paragraph\">\u56e0\u6b64\uff0c\u5728\u51c6\u786e\u628a\u63e1\u57fa\u672c\u77e5\u8bc6\u548c\u65b9\u6cd5\u7684\u57fa\u7840\u4e0a\uff0c\u8fdb\u884c\u4e00\u5b9a\u91cf\u7684\u5b9a\u65f6\u8bad\u7ec3\u662f\u5f88\u6709\u5fc5\u8981\u7684\u3002\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u65b9\u5f0f\u8fdb\u884c\uff1a<\/div>\n<ul>\n<li>\n<div class=\"paragraph\"><strong>\u5236\u5b9a\u8bad\u7ec3\u8ba1\u5212<\/strong>\uff1a\u6839\u636e\u81ea\u5df1\u7684\u5b66\u4e60\u8fdb\u5ea6\u548c\u65f6\u95f4\u5b89\u6392\uff0c\u5236\u5b9a\u5408\u7406\u7684\u5b9a\u65f6\u8bad\u7ec3\u8ba1\u5212\u3002\u4f8b\u5982\uff0c\u6bcf\u5929\u5b89\u6392\u4e00\u5b9a\u65f6\u95f4\uff08\u5982 30 \u5206\u949f\u81f3 1 \u5c0f\u65f6\uff09\u8fdb\u884c\u6570\u5b66\u9898\u76ee\u8bad\u7ec3\uff0c\u6bcf\u5468\u8fdb\u884c\u4e00\u6b21\u6a21\u62df\u8003\u8bd5\uff0c\u6a21\u62df\u771f\u5b9e\u7684\u8003\u8bd5\u73af\u5883\u548c\u65f6\u95f4\u9650\u5236\u3002<\/div>\n<\/li>\n<li>\n<div class=\"paragraph\"><strong>\u7cbe\u9009\u9898\u76ee<\/strong>\uff1a\u9009\u62e9\u5177\u6709\u4ee3\u8868\u6027\u548c\u9488\u5bf9\u6027\u7684\u9898\u76ee\u8fdb\u884c\u8bad\u7ec3\u3002\u53ef\u4ee5\u53c2\u8003\u5386\u5e74\u9ad8\u804c\u5355\u62db\u8003\u8bd5\u771f\u9898\u3001\u6a21\u62df\u8bd5\u9898\u4ee5\u53ca\u6559\u6750\u4e2d\u7684\u7ecf\u5178\u4e60\u9898\u3002\u907f\u514d\u76f2\u76ee\u505a\u9898\uff0c\u6ce8\u91cd\u9898\u76ee\u7684\u8d28\u91cf\u548c\u8bad\u7ec3\u6548\u679c\u3002<\/div>\n<\/li>\n<li>\n<div class=\"paragraph\"><strong>\u53ca\u65f6\u53cd\u9988<\/strong>\uff1a\u5728\u8bad\u7ec3\u7ed3\u675f\u540e\uff0c\u53ca\u65f6\u6279\u6539\u548c\u5206\u6790\u8bd5\u5377\u3002\u5bf9\u4e8e\u505a\u9519\u7684\u9898\u76ee\uff0c\u8981\u4ed4\u7ec6\u5206\u6790\u9519\u8bef\u539f\u56e0\uff0c\u662f\u6982\u5ff5\u7406\u89e3\u9519\u8bef\uff0c\u8ba1\u7b97\u5931\u8bef\uff0c\u8fd8\u662f\u89e3\u9898\u65b9\u6cd5\u4e0d\u5f53\u3002\u5c06\u9519\u9898\u6574\u7406\u5230\u9519\u9898\u672c\u4e0a\uff0c\u6ce8\u660e\u9519\u8bef\u539f\u56e0\u548c\u6b63\u786e\u89e3\u6cd5\uff0c\u5b9a\u671f\u56de\u987e\u548c\u590d\u4e60\u9519\u9898\uff0c\u907f\u514d\u91cd\u590d\u72af\u9519\u3002<\/div>\n<\/li>\n<\/ul>\n<div class=\"paragraph\">\u901a\u8fc7\u5f3a\u5316\u5b9a\u65f6\u8bad\u7ec3\u548c\u53ca\u65f6\u53cd\u9988\u77eb\u6b63\uff0c\u53ef\u4ee5\u4e0d\u65ad\u63d0\u9ad8\u89e3\u9898\u901f\u5ea6\u548c\u51c6\u786e\u7387\uff0c\u589e\u5f3a\u5bf9\u6570\u5b66\u77e5\u8bc6\u7684\u719f\u7ec3\u8fd0\u7528\u80fd\u529b\u3002<\/div>\n<h2>\u4e8c\u3001\u6570\u5b66\u77e5\u8bc6\u70b9\u68b3\u7406<\/h2>\n<h4>\uff08\u4e00\uff09\u51fd\u6570\u7684\u5b9a\u4e49\u57df<\/h4>\n<p>\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u662f\u6307\u51fd\u6570\u6709\u610f\u4e49\u65f6\u7684\u81ea\u53d8\u91cf\u53d6\u503c\u96c6\u5408\u3002\u5e38\u89c1\u7684\u5f71\u54cd\u51fd\u6570\u5b9a\u4e49\u57df\u7684\u60c5\u51b5\u5305\u62ec\uff1a<\/p>\n<ol>\n<li>\n<p><strong>\u5206\u5f0f\u51fd\u6570<\/strong>\uff1a \u5206\u5f0f\u51fd\u6570\u8981\u6c42\u5206\u6bcd\u4e0d\u80fd\u4e3a\u96f6\u3002\u6bd4\u5982\u5bf9\u4e8e\u51fd\u6570 $ f(x) = \\frac{1}{x-2} $\uff0c\u8981\u6c42\u5206\u6bcd $ x &#8211; 2 \\neq 0 $\uff0c\u5373 $ x \\neq 2 $\u3002\u56e0\u6b64\uff0c\u5b9a\u4e49\u57df\u4e3a $ (-\\infty, 2) \\cup (2, +\\infty) $\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u5076\u6b21\u6839\u5f0f<\/strong>\uff1a \u5076\u6b21\u6839\u5f0f\uff08\u5982\u5e73\u65b9\u6839\u3001\u56db\u6b21\u6839\u7b49\uff09\u8981\u6c42\u6839\u53f7\u5185\u7684\u8868\u8fbe\u5f0f\u975e\u8d1f\u3002\u4f8b\u5982\uff0c\u5bf9\u4e8e\u51fd\u6570 $ g(x) = \\sqrt{x &#8211; 3} $\uff0c\u8981\u6c42 $ x &#8211; 3 \\geq 0 $\uff0c\u5373 $ x \\geq 3 $\u3002\u56e0\u6b64\uff0c\u5b9a\u4e49\u57df\u4e3a $ [3, +\\infty) $\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u96f6\u6b21\u5e42\u4e0e\u8d1f\u6307\u6570\u5e42<\/strong>\uff1a \u5bf9\u4e8e\u5e95\u6570\u4e3a\u96f6\u7684\u5e42\uff0c\u51fd\u6570\u6ca1\u6709\u610f\u4e49\u3002\u56e0\u6b64\uff0c\u5bf9\u4e8e $ h(x) = x^{-2} $\uff0c\u8981\u6c42 $ x \\neq 0 $\uff0c\u5b9a\u4e49\u57df\u4e3a $ (-\\infty, 0) \\cup (0, +\\infty) $\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u5bf9\u6570\u51fd\u6570<\/strong>\uff1a \u5bf9\u6570\u51fd\u6570\u8981\u6c42\u771f\u6570\u5927\u4e8e\u96f6\uff0c\u4e14\u5e95\u6570\u4e3a\u6b63\u4e14\u4e0d\u7b49\u4e8e1\u3002\u4f8b\u5982\uff0c\u5bf9\u4e8e\u51fd\u6570 $ y = \\log_a x $\uff08\u5176\u4e2d $ a &gt; 0 $ \u4e14 $ a \\neq 1 $\uff09\uff0c\u8981\u6c42 $ x &gt; 0 $\u3002\u56e0\u6b64\uff0c\u5b9a\u4e49\u57df\u4e3a $ (0, +\\infty) $\u3002<\/p>\n<\/li>\n<\/ol>\n<hr \/>\n<h4>\uff08\u4e8c\uff09\u5176\u4ed6\u91cd\u8981\u77e5\u8bc6\u70b9<\/h4>\n<ol>\n<li>\n<p><strong>\u51fd\u6570\u7684\u6027\u8d28<\/strong>\uff1a<\/p>\n<ul>\n<li><strong>\u5355\u8c03\u6027<\/strong>\uff1a\u51fd\u6570\u7684\u5355\u8c03\u6027\u6307\u7684\u662f\u51fd\u6570\u5728\u67d0\u4e2a\u533a\u95f4\u4e0a\u662f\u5426\u5355\u8c03\u9012\u589e\u6216\u9012\u51cf\u3002\u4f8b\u5982\uff0c\u4e00\u6b21\u51fd\u6570 $ y = kx + b $\uff08\u5176\u4e2d $ k \\neq 0 $\uff09\u662f\u5355\u8c03\u51fd\u6570\u3002\u5f53 $ k &gt; 0 $ \u65f6\uff0c\u51fd\u6570\u5355\u8c03\u9012\u589e\uff1b\u5f53 $ k &lt; 0 $ \u65f6\uff0c\u51fd\u6570\u5355\u8c03\u9012\u51cf\u3002<\/li>\n<li><strong>\u5947\u5076\u6027<\/strong>\uff1a\u5947\u51fd\u6570\u6ee1\u8db3 $ f(-x) = -f(x) $\uff0c\u5076\u51fd\u6570\u6ee1\u8db3 $ f(-x) = f(x) $\u3002<\/li>\n<li><strong>\u5468\u671f\u6027<\/strong>\uff1a\u5468\u671f\u6027\u51fd\u6570\u662f\u6307\u51fd\u6570\u7684\u56fe\u50cf\u5728\u4e00\u5b9a\u533a\u95f4\u5185\u91cd\u590d\u3002\u4f8b\u5982\uff0c\u6b63\u5f26\u51fd\u6570 $ y = \\sin x $ \u7684\u5468\u671f\u4e3a $ 2\\pi $\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p><strong>\u65b9\u7a0b\u4e0e\u4e0d\u7b49\u5f0f<\/strong>\uff1a<\/p>\n<ul>\n<li>\n<p><strong>\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b<\/strong>\uff1a\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u7684\u6c42\u89e3\u5e38\u7528\u6c42\u6839\u516c\u5f0f\uff1a<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">x=\u2212b\u00b1b2\u22124ac2ax = \\frac{-b \\pm \\sqrt{b^2 &#8211; 4ac}}{2a}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\">2<span class=\"mord mathnormal\">a<\/span>\u2212<span class=\"mord mathnormal\">b<\/span><span class=\"mbin\">\u00b1<\/span><span class=\"mord sqrt\"><span class=\"svg-align\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"mbin\">\u2212<\/span>4<span class=\"mord mathnormal\">a<\/span><span class=\"mord mathnormal\">c<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u8fd9\u662f\u6807\u51c6\u7684\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u7684\u6c42\u89e3\u516c\u5f0f\uff0c\u7528\u6765\u627e\u5230\u65b9\u7a0b $ ax^2 + bx + c = 0 $ \u7684\u89e3\uff0c\u5176\u4e2d $ a \\neq 0 $\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u4e00\u5143\u4e00\u6b21\u4e0d\u7b49\u5f0f\u4e0e\u4e8c\u6b21\u4e0d\u7b49\u5f0f<\/strong>\uff1a<\/p>\n<ul>\n<li>\u4e00\u5143\u4e00\u6b21\u4e0d\u7b49\u5f0f\u4e00\u822c\u901a\u8fc7\u79fb\u9879\u3001\u6bd4\u5927\u5c0f\u7684\u65b9\u5f0f\u6c42\u89e3\uff1b\u4f8b\u5982\uff0c$ ax + b &gt; 0 $ \u53ef\u4ee5\u901a\u8fc7\u79fb\u9879\u5f97\u5230 $ x &gt; -\\frac{b}{a} $\uff0c\u7136\u540e\u6839\u636e $ a $ \u7684\u7b26\u53f7\u5224\u65ad\u89e3\u96c6\u3002<\/li>\n<li>\u4e00\u5143\u4e8c\u6b21\u4e0d\u7b49\u5f0f\u901a\u5e38\u4f7f\u7528\u6c42\u6839\u516c\u5f0f\u548c\u7b26\u53f7\u5206\u6790\u6cd5\u8fdb\u884c\u6c42\u89e3\u3002\u9996\u5148\uff0c\u901a\u8fc7\u6c42\u89e3\u5bf9\u5e94\u7684\u4e8c\u6b21\u65b9\u7a0b $ ax^2 + bx + c = 0 $ \u5f97\u5230\u6839\uff0c\u518d\u6839\u636e\u4e0d\u7b49\u5f0f\u7684\u7b26\u53f7\u8fdb\u884c\u5206\u6790\uff0c\u5f97\u5230\u89e3\u96c6\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li>\n<p><strong>\u6570\u5217<\/strong>\uff1a<\/p>\n<ul>\n<li><strong>\u7b49\u5dee\u6570\u5217<\/strong>\uff1a\u7b49\u5dee\u6570\u5217\u7684\u901a\u9879\u516c\u5f0f\u4e3a\uff1a <span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">an=a1+(n\u22121)da_n = a_1 + (n &#8211; 1)d<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><span class=\"mord mathnormal\">d<\/span><\/span><\/span><\/span><\/span> \u5176\u4e2d $ a_1 $ \u4e3a\u9996\u9879\uff0c$ d $ \u4e3a\u516c\u5dee\u3002<\/li>\n<li><strong>\u7b49\u6bd4\u6570\u5217<\/strong>\uff1a\u7b49\u6bd4\u6570\u5217\u7684\u901a\u9879\u516c\u5f0f\u4e3a\uff1a <span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">an=a1qn\u22121a_n = a_1 q^{n &#8211; 1}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5176\u4e2d $ a_1 $ \u4e3a\u9996\u9879\uff0c$ q $ \u4e3a\u516c\u6bd4\u3002<\/li>\n<li><strong>\u6c42\u548c\u516c\u5f0f<\/strong>\uff1a\n<ul>\n<li>\u5bf9\u4e8e\u7b49\u5dee\u6570\u5217\uff0c\u6c42\u548c\u516c\u5f0f\u4e3a\uff1a <span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">Sn=n2(a1+an)S_n = \\frac{n}{2}(a_1 + a_n)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">S<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\">2<span class=\"mord mathnormal\">n<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<p>\u6216\u8005\uff1a <span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">Sn=na1+n(n\u22121)2dS_n = n a_1 + \\frac{n(n &#8211; 1)}{2}d<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">S<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><span class=\"mord\"><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\">2<span class=\"mord mathnormal\">n<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mbin\">\u2212<\/span>1<span class=\"mclose\">)<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\">d<\/span><\/span><\/span><\/span><\/span><\/p>\n<ul>\n<li>\u5bf9\u4e8e\u7b49\u6bd4\u6570\u5217\uff0c\u6c42\u548c\u516c\u5f0f\u4e3a\uff1a <span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">Sn=a1(1\u2212qn)1\u2212q(\u5f53\u00a0q\u22601\u00a0\u65f6)S_n = \\frac{a_1(1 &#8211; q^n)}{1 &#8211; q} \\quad \\text{(\u5f53 } q \\neq 1 \\text{ \u65f6)}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">S<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\">1<span class=\"mbin\">\u2212<\/span><span class=\"mord mathnormal\">q<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"msupsub\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"mopen\">(<\/span>1<span class=\"mbin\">\u2212<\/span><span class=\"mord mathnormal\">q<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord text\"><span class=\"mord\">(<\/span><span class=\"mord cjk_fallback\">\u5f53<\/span><span class=\"mord\">\u00a0<\/span><\/span><span class=\"mord mathnormal\">q<\/span><span class=\"mrel\"><span class=\"mord vbox\"><span class=\"thinbox\"><span class=\"rlap\"><span class=\"inner\"><span class=\"mord\">\ue020<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mord text\"><span class=\"mord\">\u00a0<\/span><span class=\"mord cjk_fallback\">\u65f6<\/span><span class=\"mord\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li>\n<p><strong>\u4e09\u89d2\u51fd\u6570<\/strong>\uff1a<\/p>\n<ul>\n<li>\n<p><strong>\u57fa\u672c\u4e09\u89d2\u51fd\u6570<\/strong>\uff1a\u5305\u62ec $ \\sin x, \\cos x, \\tan x $ \u7b49\u7684\u5b9a\u4e49\u548c\u6027\u8d28\uff0c\u7279\u522b\u662f\u5b83\u4eec\u7684\u5468\u671f\u6027\u548c\u5355\u8c03\u6027\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u8bf1\u5bfc\u516c\u5f0f<\/strong>\uff1a\u4f8b\u5982\uff1a<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">sin\u2061(\u2212x)=\u2212sin\u2061x,cos\u2061(\u2212x)=cos\u2061x\\sin(-x) = -\\sin x, \\quad \\cos(-x) = \\cos x<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mop\">sin<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">\u2212<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">\u2212<\/span><span class=\"mop\">sin<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mop\">cos<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">\u2212<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mop\">cos<\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\n<p><strong>\u4e24\u89d2\u548c\u4e0e\u5dee\u516c\u5f0f<\/strong>\uff1a<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">sin\u2061(a\u00b1b)=sin\u2061acos\u2061b\u00b1cos\u2061asin\u2061b\\sin(a \\pm b) = \\sin a \\cos b \\pm \\cos a \\sin b<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mop\">sin<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mbin\">\u00b1<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mop\">sin<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mop\">cos<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mbin\">\u00b1<\/span><\/span><span class=\"base\"><span class=\"mop\">cos<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mop\">sin<\/span><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span><\/span> <span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">cos\u2061(a\u00b1b)=cos\u2061acos\u2061b\u2213sin\u2061asin\u2061b\\cos(a \\pm b) = \\cos a \\cos b \\mp \\sin a \\sin b<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mop\">cos<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mbin\">\u00b1<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mop\">cos<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mop\">cos<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mbin\">\u2213<\/span><\/span><span class=\"base\"><span class=\"mop\">sin<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mop\">sin<\/span><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\n<p><strong>\u4e09\u89d2\u51fd\u6570\u7684\u56fe\u50cf<\/strong>\uff1a\u4f8b\u5982\uff0c\u6b63\u5f26\u51fd\u6570 $ y = \\sin x $ \u7684\u56fe\u50cf\u662f\u4e00\u4e2a\u5468\u671f\u6027\u6ce2\u52a8\uff0c\u5468\u671f\u4e3a $ 2\\pi $\uff0c\u5728\u533a\u95f4 $ \\left[-\\frac{\\pi}{2}, \\frac{\\pi}{2}\\right] $ \u4e0a\u5355\u8c03\u9012\u589e\uff0c\u5728\u533a\u95f4 $ \\left[\\frac{\\pi}{2}, \\frac{3\\pi}{2}\\right] $ \u4e0a\u5355\u8c03\u9012\u51cf\u3002<\/p>\n<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u6d59\u6c5f\u9ad8\u804c\u5355\u62db\u6570\u5b66\u5b66\u4e60\u65b9\u6cd5\u4e0e\u77e5\u8bc6\u70b9\u68b3\u7406 \u4e00&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[68],"tags":[],"class_list":["post-13267","post","type-post","status-publish","format-standard","hentry","category-zzjy"],"_links":{"self":[{"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=\/wp\/v2\/posts\/13267","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=13267"}],"version-history":[{"count":0,"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=\/wp\/v2\/posts\/13267\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13267"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13267"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.aiersheng.cc\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13267"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}