{"id":16269,"date":"2026-01-24T13:48:22","date_gmt":"2026-01-24T05:48:22","guid":{"rendered":"https:\/\/www.aiersheng.cc\/?p=16269"},"modified":"2026-01-24T13:48:22","modified_gmt":"2026-01-24T05:48:22","slug":"%e9%ab%98%e8%81%8c%e5%8d%95%e6%8b%9b%e6%95%b0%e5%ad%a6%e5%85%ac%e5%bc%8f%e5%a4%a7%e5%85%a8%ef%bc%88%e5%8d%95%e6%8b%9b%e4%ba%ba%e5%bf%85%e5%a4%87%e5%b7%a5%e5%85%b7%ef%bc%89","status":"publish","type":"post","link":"https:\/\/www.aiersheng.cc\/?p=16269","title":{"rendered":"\u9ad8\u804c\u5355\u62db\u6570\u5b66\u516c\u5f0f\u5927\u5168\uff08\u5355\u62db\u4eba\u5fc5\u5907\u5de5\u5177\uff09"},"content":{"rendered":"<h1>\u9ad8\u804c\u5355\u62db\u6570\u5b66\u516c\u5f0f\u5927\u5168\uff08\u5355\u62db\u4eba\u5fc5\u5907\u5de5\u5177\uff09<\/h1>\n<div>\u00a0<\/div>\n<h2>\u5fc5\u4fee 1 \u6570\u5b66\u77e5\u8bc6\u70b9<\/h2>\n<div>\u00a0<\/div>\n<h3>\u7b2c\u4e00\u7ae0\uff1a\u96c6\u5408\u4e0e\u51fd\u6570\u6982\u5ff5<\/h3>\n<div>\u00a0<\/div>\n<h4>$1.1.1 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aria-hidden=\"true\">R<\/span>\u3002<\/li>\n<li>\u96c6\u5408\u7684\u8868\u793a\u65b9\u6cd5\uff1a\u5217\u4e3e\u6cd5\u3001\u63cf\u8ff0\u6cd5\u3002<\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h4>$1.1.2 \u96c6\u5408\u95f4\u7684\u57fa\u672c\u5173\u7cfb<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li>\u4e00\u822c\u5730\uff0c\u5bf9\u4e8e\u4e24\u4e2a\u96c6\u5408<span aria-hidden=\"true\">A<\/span>\u3001<span aria-hidden=\"true\">B<\/span>\uff0c\u5982\u679c\u96c6\u5408<span aria-hidden=\"true\">A<\/span>\u4e2d\u4efb\u610f\u4e00\u4e2a\u5143\u7d20\u90fd\u662f\u96c6\u5408<span aria-hidden=\"true\">B<\/span>\u4e2d\u7684\u5143\u7d20\uff0c\u5219\u79f0\u96c6\u5408<span aria-hidden=\"true\">A<\/span>\u662f\u96c6\u5408<span aria-hidden=\"true\">B<\/span>\u7684\u5b50\u96c6\u3002\u8bb0\u4f5c<span aria-hidden=\"true\">A\u2286B<\/span>\u3002<\/li>\n<li>\u5982\u679c\u96c6\u5408<span aria-hidden=\"true\">A\u2286B<\/span>\uff0c\u4f46\u5b58\u5728\u5143\u7d20<span aria-hidden=\"true\">x\u2208B<\/span>\uff0c\u4e14<span aria-hidden=\"true\">x\u2208\/A<\/span>\uff0c\u5219\u79f0\u96c6\u5408<span aria-hidden=\"true\">A<\/span>\u662f\u96c6\u5408<span aria-hidden=\"true\">B<\/span>\u7684\u771f\u5b50\u96c6\u3002\u8bb0\u4f5c\uff1a<span aria-hidden=\"true\">A\u2acbB<\/span>\u3002<\/li>\n<li>\u628a\u4e0d\u542b\u4efb\u4f55\u5143\u7d20\u7684\u96c6\u5408\u53eb\u505a\u7a7a\u96c6\uff0c\u8bb0\u4f5c\uff1a<span aria-hidden=\"true\">\u2205<\/span>\u3002\u5e76\u89c4\u5b9a\uff1a\u7a7a\u96c6\u5408\u662f\u4efb\u4f55\u96c6\u5408\u7684\u5b50\u96c6\u3002<\/li>\n<li>\u5982\u679c\u96c6\u5408<span aria-hidden=\"true\">A<\/span>\u4e2d\u542b\u6709<span aria-hidden=\"true\">n<\/span>\u4e2a\u5143\u7d20\uff0c\u5219\u96c6\u5408<span aria-hidden=\"true\">A<\/span>\u6709<span aria-hidden=\"true\">2n<\/span>\u4e2a\u5b50\u96c6\uff0c<span aria-hidden=\"true\">2n\u22121<\/span>\u4e2a\u771f\u5b50\u96c6\u3002<\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h4>$1.1.3 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aria-hidden=\"true\">CU\u200bA={x\u2223x\u2208U<\/span>\uff0c\u4e14<span aria-hidden=\"true\">x\u2208\/A}<\/span>\u3002<\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h4>$1.2.1 \u51fd\u6570\u7684\u6982\u5ff5<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li>\u8bbe<span aria-hidden=\"true\">A<\/span>\u3001<span aria-hidden=\"true\">B<\/span>\u662f\u975e\u7a7a\u7684\u6570\u96c6\uff0c\u5982\u679c\u6309\u7167\u67d0\u79cd\u786e\u5b9a\u7684\u5bf9\u5e94\u5173\u7cfb<span aria-hidden=\"true\">f<\/span>\uff0c\u4f7f\u5bf9\u4e8e\u96c6\u5408<span aria-hidden=\"true\">A<\/span>\u4e2d\u7684\u4efb\u610f\u4e00\u4e2a\u6570<span aria-hidden=\"true\">x<\/span>\uff0c\u5728\u96c6\u5408<span aria-hidden=\"true\">B<\/span>\u4e2d\u90fd\u6709\u60df\u4e00\u786e\u5b9a\u7684\u6570<span aria-hidden=\"true\">f(x)<\/span>\u548c\u5b83\u5bf9\u5e94\uff0c\u90a3\u4e48\u5c31\u79f0<span aria-hidden=\"true\">f:A\u2192B<\/span>\u4e3a\u96c6\u5408<span aria-hidden=\"true\">A<\/span>\u5230\u96c6\u5408<span aria-hidden=\"true\">B<\/span>\u7684\u4e00\u4e2a\u51fd\u6570\uff0c\u8bb0\u4f5c\uff1a<span aria-hidden=\"true\">y=f(x)<\/span>\uff0c<span aria-hidden=\"true\">x\u2208A<\/span>\u3002<\/li>\n<li>\u4e00\u4e2a\u51fd\u6570\u7684\u6784\u6210\u8981\u7d20\u4e3a\uff1a\u5b9a\u4e49\u57df\u3001\u5bf9\u5e94\u5173\u7cfb\u3001\u503c\u57df\uff0c\u5982\u679c\u4e24\u4e2a\u51fd\u6570\u7684\u5b9a\u4e49\u57df\u76f8\u540c\uff0c\u5e76\u4e14\u5bf9\u5e94\u5173\u7cfb\u5b8c\u5168\u4e00\u81f4\uff0c\u5219\u79f0\u8fd9\u4e24\u4e2a\u51fd\u6570\u76f8\u7b49\u3002<\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h4>$1.2.2 \u51fd\u6570\u7684\u8868\u793a\u6cd5<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li>\u51fd\u6570\u7684\u4e09\u79cd\u8868\u793a\u65b9\u6cd5\uff1a\u89e3\u6790\u6cd5\u3001\u56fe\u8c61\u6cd5\u3001\u5217\u8868\u6cd5\u3002<\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h4>$1.3.1 \u5355\u8c03\u6027\u4e0e\u6700\u5927\uff08\u5c0f\uff09\u503c<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li>\u6ce8\u610f\u51fd\u6570\u5355\u8c03\u6027\u7684\u8bc1\u660e\u65b9\u6cd5\uff1a\n<ul>\n<li>\u5b9a\u4e49\u6cd5\uff1a\u8bbe<span aria-hidden=\"true\">x1\u200b<\/span>\u3001<span aria-hidden=\"true\">x2\u200b\u2208[a,b]<\/span>\uff0c<span aria-hidden=\"true\">x1\u200b&lt;x2\u200b<\/span>\uff0c\u90a3\u4e48<span aria-hidden=\"true\">f(x1\u200b)\u2212f(x2\u200b)&lt;0\u21d4f(x)<\/span>\u5728<span aria-hidden=\"true\">[a,b]<\/span>\u4e0a\u662f\u589e\u51fd\u6570\uff1b<span aria-hidden=\"true\">f(x1\u200b)\u2212f(x2\u200b)&gt;0\u21d4f(x)<\/span>\u5728<span aria-hidden=\"true\">[a,b]<\/span>\u4e0a\u662f\u51cf\u51fd\u6570\u3002<\/li>\n<li>\u6b65\u9aa4\uff1a\u53d6\u503c \u2014 \u4f5c\u5dee \u2014 \u53d8\u5f62 \u2014 \u5b9a\u53f7 \u2014 \u5224\u65ad<\/li>\n<li>\u683c\u5f0f\uff1a\u89e3\uff1a\u8bbe<span aria-hidden=\"true\">x1\u200b<\/span>\uff0c<span aria-hidden=\"true\">x2\u200b\u2208[a,b]<\/span>\u4e14<span aria-hidden=\"true\">x1\u200b&lt;x2\u200b<\/span>\uff0c\u5219\uff1a<span aria-hidden=\"true\">f(x1\u200b)\u2212f(x2\u200b)=\u22ef<\/span><\/li>\n<li>\u5bfc\u6570\u6cd5\uff1a\u8bbe\u51fd\u6570<span aria-hidden=\"true\">y=f(x)<\/span>\u5728\u67d0\u4e2a\u533a\u95f4\u5185\u53ef\u5bfc\uff0c\u82e5<span aria-hidden=\"true\">f\u2032(x)&gt;0<\/span>\u5219<span aria-hidden=\"true\">f(x)<\/span>\u4e3a\u589e\u51fd\u6570\uff1b\u82e5<span aria-hidden=\"true\">f\u2032(x)&lt;0<\/span>\uff0c\u5219<span aria-hidden=\"true\">f(x)<\/span>\u4e3a\u51cf\u51fd\u6570\u3002<\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h4>$1.3.2 \u5947\u5076\u6027<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li>\u4e00\u822c\u5730\uff0c\u5982\u679c\u5bf9\u4e8e\u51fd\u6570<span aria-hidden=\"true\">f(x)<\/span>\u7684\u5b9a\u4e49\u57df\u5185\u4efb\u610f\u4e00\u4e2a<span aria-hidden=\"true\">x<\/span>\uff0c\u90fd\u6709<span aria-hidden=\"true\">f(\u2212x)=f(x)<\/span>\uff0c\u90a3\u4e48\u5c31\u79f0\u51fd\u6570<span aria-hidden=\"true\">f(x)<\/span>\u4e3a\u5076\u51fd\u6570\u3002\u5076\u51fd\u6570\u56fe\u8c61\u5173\u4e8e<span aria-hidden=\"true\">y<\/span>\u8f74\u5bf9\u79f0\u3002<\/li>\n<li>\u4e00\u822c\u5730\uff0c\u5982\u679c\u5bf9\u4e8e\u51fd\u6570<span aria-hidden=\"true\">f(x)<\/span>\u7684\u5b9a\u4e49\u57df\u5185\u4efb\u610f\u4e00\u4e2a<span aria-hidden=\"true\">x<\/span>\uff0c\u90fd\u6709<span aria-hidden=\"true\">f(\u2212x)=\u2212f(x)<\/span>\uff0c\u90a3\u4e48\u5c31\u79f0\u51fd\u6570<span aria-hidden=\"true\">f(x)<\/span>\u4e3a\u5947\u51fd\u6570\u3002\u5947\u51fd\u6570\u56fe\u8c61\u5173\u4e8e\u539f\u70b9\u5bf9\u79f0\u3002<\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h3>\u7b2c\u4e8c\u7ae0\uff1a\u57fa\u672c\u521d\u7b49\u51fd\u6570\uff08I\uff09<\/h3>\n<div>\u00a0<\/div>\n<h4>$2.1.1 \u6307\u6570\u4e0e\u6307\u6570\u5e42\u7684\u8fd0\u7b97<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li>\u4e00\u822c\u5730\uff0c\u5982\u679c<span aria-hidden=\"true\">xn=a<\/span>\uff0c\u90a3\u4e48<span aria-hidden=\"true\">x<\/span>\u53eb\u505a<span aria-hidden=\"true\">a<\/span>\u7684<span aria-hidden=\"true\">n<\/span>\u6b21\u65b9\u6839\u3002\u5176\u4e2d<span aria-hidden=\"true\">n&gt;1<\/span>\uff0c<span aria-hidden=\"true\">n\u2208N+\u200b<\/span>\u3002<\/li>\n<li>\u5f53<span aria-hidden=\"true\">n<\/span>\u4e3a\u5947\u6570\u65f6\uff0c<span aria-hidden=\"true\">nan\u200b=a<\/span>\uff1b\u5f53<span aria-hidden=\"true\">n<\/span>\u4e3a\u5076\u6570\u65f6\uff0c<span aria-hidden=\"true\">nan\u200b=\u2223a\u2223<\/span>\u3002<\/li>\n<li>\u89c4\u5b9a\uff1a\n<ul>\n<li><span aria-hidden=\"true\">amn\u200b=man\u200b<\/span>\uff08<span aria-hidden=\"true\">a&gt;0<\/span>\uff0c<span aria-hidden=\"true\">m<\/span>\uff0c<span aria-hidden=\"true\">n\u2208N\u2217<\/span>\uff0c<span aria-hidden=\"true\">m&gt;1<\/span>\uff09<\/li>\n<li><span aria-hidden=\"true\">a\u2212n=an1\u200b<\/span>\uff08<span aria-hidden=\"true\">n&gt;0<\/span>\uff09<\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<li>\u8fd0\u7b97\u6027\u8d28\uff1a\n<ul>\n<li><span aria-hidden=\"true\">aras=ar+s<\/span>\uff08<span aria-hidden=\"true\">a&gt;0<\/span>\uff0c<span aria-hidden=\"true\">r<\/span>\uff0c<span aria-hidden=\"true\">s\u2208Q<\/span>\uff09<\/li>\n<li><span aria-hidden=\"true\">(ar)s=ars<\/span>\uff08<span aria-hidden=\"true\">a&gt;0<\/span>\uff0c<span aria-hidden=\"true\">r<\/span>\uff0c<span aria-hidden=\"true\">s\u2208Q<\/span>\uff09<\/li>\n<li><span aria-hidden=\"true\">(ab)r=arbr<\/span>\uff08<span aria-hidden=\"true\">a&gt;0<\/span>\uff0c<span aria-hidden=\"true\">b&gt;0<\/span>\uff0c<span aria-hidden=\"true\">r\u2208Q<\/span>\uff09<\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h4>$2.1.2 \u6307\u6570\u51fd\u6570\u53ca\u5176\u6027\u8d28<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li>\u56fe\u8c61\uff1a<span aria-hidden=\"true\">y=ax<\/span>\uff08<span aria-hidden=\"true\">a&gt;0<\/span>\uff0c<span aria-hidden=\"true\">a\ue020=1<\/span>\uff09<\/li>\n<li>\u6027\u8d28\uff1a<\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<div>\n<div>\n<table>\n<thead>\n<tr>\n<th>\u00a0<\/th>\n<th><span aria-hidden=\"true\">a&gt;1<\/span><\/th>\n<th><span aria-hidden=\"true\">0&lt;a&lt;1<\/span><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u5b9a\u4e49\u57df<\/td>\n<td><span aria-hidden=\"true\">R<\/span><\/td>\n<td><span aria-hidden=\"true\">R<\/span><\/td>\n<\/tr>\n<tr>\n<td>\u503c\u57df<\/td>\n<td><span aria-hidden=\"true\">(0,+\u221e)<\/span><\/td>\n<td><span aria-hidden=\"true\">(0,+\u221e)<\/span><\/td>\n<\/tr>\n<tr>\n<td>\u8fc7\u5b9a\u70b9<\/td>\n<td><span aria-hidden=\"true\">(0,1)<\/span>\uff0c\u5373<span aria-hidden=\"true\">x=0<\/span>\u65f6\uff0c<span aria-hidden=\"true\">y=1<\/span><\/td>\n<td><span aria-hidden=\"true\">(0,1)<\/span>\uff0c\u5373<span aria-hidden=\"true\">x=0<\/span>\u65f6\uff0c<span aria-hidden=\"true\">y=1<\/span><\/td>\n<\/tr>\n<tr>\n<td>\u5355\u8c03\u6027<\/td>\n<td>\u5728<span aria-hidden=\"true\">R<\/span>\u4e0a\u662f\u589e\u51fd\u6570<\/td>\n<td>\u5728<span aria-hidden=\"true\">R<\/span>\u4e0a\u662f\u51cf\u51fd\u6570<\/td>\n<\/tr>\n<tr>\n<td>\u5176\u4ed6\u6027\u8d28<\/td>\n<td><span aria-hidden=\"true\">x&gt;0<\/span>\uff0c<span aria-hidden=\"true\">ax&gt;1<\/span>\uff1b<span aria-hidden=\"true\">x&lt;0<\/span>\uff0c<span aria-hidden=\"true\">0&lt;ax&lt;1<\/span><\/td>\n<td><span aria-hidden=\"true\">x&gt;0<\/span>\uff0c<span aria-hidden=\"true\">0&lt;ax&lt;1<\/span>\uff1b<span aria-hidden=\"true\">x&lt;0<\/span>\uff0c<span aria-hidden=\"true\">ax&gt;1<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<div>\u00a0<\/div>\n<h4>$2.2.1 \u5bf9\u6570\u4e0e\u5bf9\u6570\u8fd0\u7b97<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li>\u6307\u6570\u4e0e\u5bf9\u6570\u4e92\u5316\u5f0f\uff1a<span aria-hidden=\"true\">ax=N\u21d4x=loga\u200bN<\/span><\/li>\n<li>\u5bf9\u6570\u6052\u7b49\u5f0f\uff1a<span aria-hidden=\"true\">aloga\u200bN=N<\/span><\/li>\n<li>\u57fa\u672c\u6027\u8d28\uff1a<span aria-hidden=\"true\">loga\u200b1=0<\/span>\uff0c<span aria-hidden=\"true\">loga\u200ba=1<\/span><\/li>\n<li>\u8fd0\u7b97\u6027\u8d28\uff1a\u5f53<span aria-hidden=\"true\">a&gt;0<\/span>\uff0c<span aria-hidden=\"true\">a\ue020=1<\/span>\uff0c<span aria-hidden=\"true\">M&gt;0<\/span>\uff0c<span aria-hidden=\"true\">N&gt;0<\/span>\u65f6\uff1a\n<ul>\n<li><span aria-hidden=\"true\">loga\u200b(MN)=loga\u200bM+loga\u200bN<\/span><\/li>\n<li><span aria-hidden=\"true\">loga\u200b(NM\u200b)=loga\u200bM\u2212loga\u200bN<\/span><\/li>\n<li><span aria-hidden=\"true\">loga\u200bMn=nloga\u200bM<\/span><\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<li>\u6362\u5e95\u516c\u5f0f\uff1a<span aria-hidden=\"true\">loga\u200bb=logc\u200balogc\u200bb\u200b<\/span>\uff08<span aria-hidden=\"true\">a&gt;0<\/span>\uff0c<span aria-hidden=\"true\">a\ue020=1<\/span>\uff0c<span aria-hidden=\"true\">c&gt;0<\/span>\uff0c<span aria-hidden=\"true\">c\ue020=1<\/span>\uff0c<span aria-hidden=\"true\">b&gt;0<\/span>\uff09<\/li>\n<li>\u91cd\u8981\u516c\u5f0f\uff1a<span aria-hidden=\"true\">logan\u200bbm=nm\u200bloga\u200bb<\/span><\/li>\n<li>\u5012\u6570\u5173\u7cfb\uff1a<span aria-hidden=\"true\">loga\u200bb=logb\u200ba1\u200b<\/span>\uff08<span aria-hidden=\"true\">a&gt;0<\/span>\uff0c<span aria-hidden=\"true\">a\ue020=1<\/span>\uff0c<span aria-hidden=\"true\">b&gt;0<\/span>\uff0c<span aria-hidden=\"true\">b\ue020=1<\/span>\uff09<\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h4>$2.2.2 \u5bf9\u6570\u51fd\u6570\u53ca\u5176\u6027\u8d28<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li>\u56fe\u8c61\uff1a<span aria-hidden=\"true\">y=loga\u200bx<\/span>\uff08<span aria-hidden=\"true\">a&gt;0<\/span>\uff0c<span aria-hidden=\"true\">a\ue020=1<\/span>\uff09<\/li>\n<li>\u6027\u8d28\uff1a<\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<div>\n<div>\n<table>\n<thead>\n<tr>\n<th>\u00a0<\/th>\n<th><span aria-hidden=\"true\">a&gt;1<\/span><\/th>\n<th><span aria-hidden=\"true\">0&lt;a&lt;1<\/span><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u5b9a\u4e49\u57df<\/td>\n<td><span aria-hidden=\"true\">(0,+\u221e)<\/span><\/td>\n<td><span aria-hidden=\"true\">(0,+\u221e)<\/span><\/td>\n<\/tr>\n<tr>\n<td>\u503c\u57df<\/td>\n<td><span aria-hidden=\"true\">R<\/span><\/td>\n<td><span aria-hidden=\"true\">R<\/span><\/td>\n<\/tr>\n<tr>\n<td>\u8fc7\u5b9a\u70b9<\/td>\n<td><span aria-hidden=\"true\">(1,0)<\/span>\uff0c\u5373<span aria-hidden=\"true\">x=1<\/span>\u65f6\uff0c<span aria-hidden=\"true\">y=0<\/span><\/td>\n<td><span aria-hidden=\"true\">(1,0)<\/span>\uff0c\u5373<span aria-hidden=\"true\">x=1<\/span>\u65f6\uff0c<span aria-hidden=\"true\">y=0<\/span><\/td>\n<\/tr>\n<tr>\n<td>\u5355\u8c03\u6027<\/td>\n<td>\u5728<span aria-hidden=\"true\">(0,+\u221e)<\/span>\u4e0a\u662f\u589e\u51fd\u6570<\/td>\n<td>\u5728<span aria-hidden=\"true\">(0,+\u221e)<\/span>\u4e0a\u662f\u51cf\u51fd\u6570<\/td>\n<\/tr>\n<tr>\n<td>\u5176\u4ed6\u6027\u8d28<\/td>\n<td><span aria-hidden=\"true\">x&gt;1<\/span>\uff0c<span aria-hidden=\"true\">loga\u200bx&gt;0<\/span>\uff1b<span aria-hidden=\"true\">0&lt;x&lt;1<\/span>\uff0c<span aria-hidden=\"true\">loga\u200bx&lt;0<\/span><\/td>\n<td><span aria-hidden=\"true\">x&gt;1<\/span>\uff0c<span aria-hidden=\"true\">loga\u200bx&lt;0<\/span>\uff1b<span aria-hidden=\"true\">0&lt;x&lt;1<\/span>\uff0c<span aria-hidden=\"true\">loga\u200bx&gt;0<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<div>\u00a0<\/div>\n<h2>\u5fc5\u4fee 2 \u6570\u5b66\u77e5\u8bc6\u70b9<\/h2>\n<div>\u00a0<\/div>\n<h3>\u7b2c\u4e00\u7ae0\uff1a\u7a7a\u95f4\u51e0\u4f55\u4f53<\/h3>\n<div>\u00a0<\/div>\n<ol>\n<li>\u7a7a\u95f4\u51e0\u4f55\u4f53\u7684\u7ed3\u6784\n<ul>\n<li>\u5e38\u89c1\u7684\u591a\u9762\u4f53\u6709\uff1a\u68f1\u67f1\u3001\u68f1\u9525\u3001\u68f1\u53f0\uff1b\u5e38\u89c1\u7684\u65cb\u8f6c\u4f53\u6709\uff1a\u5706\u67f1\u3001\u5706\u9525\u3001\u5706\u53f0\u3001\u7403\u3002<\/li>\n<li>\u68f1\u67f1\uff1a\u6709\u4e24\u4e2a\u9762\u4e92\u76f8\u5e73\u884c\uff0c\u5176\u4f59\u5404\u9762\u90fd\u662f\u56db\u8fb9\u5f62\uff0c\u5e76\u4e14\u6bcf\u76f8\u90bb\u4e24\u4e2a\u56db\u8fb9\u5f62\u7684\u516c\u5171\u8fb9\u90fd\u4e92\u76f8\u5e73\u884c\uff0c\u7531\u8fd9\u4e9b\u9762\u6240\u56f4\u6210\u7684\u591a\u9762\u4f53\u53eb\u505a\u68f1\u67f1\u3002<\/li>\n<li>\u68f1\u53f0\uff1a\u7528\u4e00\u4e2a\u5e73\u884c\u4e8e\u68f1\u9525\u5e95\u9762\u7684\u5e73\u9762\u53bb\u622a\u68f1\u9525\uff0c\u5e95\u9762\u4e0e\u622a\u9762\u4e4b\u95f4\u7684\u90e8\u5206\uff0c\u8fd9\u6837\u7684\u591a\u9762\u4f53\u53eb\u505a\u68f1\u53f0\u3002<\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<li>\u7a7a\u95f4\u51e0\u4f55\u4f53\u7684\u4e09\u89c6\u56fe\u548c\u76f4\u89c2\u56fe\n<ul>\n<li>\u628a\u5149\u7531\u4e00\u70b9\u5411\u5916\u6563\u5c04\u5f62\u6210\u7684\u6295\u5f71\u53eb\u4e2d\u5fc3\u6295\u5f71\uff0c\u4e2d\u5fc3\u6295\u5f71\u7684\u6295\u5f71\u7ebf\u4ea4\u4e8e\u4e00\u70b9\uff1b\u628a\u5728\u4e00\u675f\u5e73\u884c\u5149\u7ebf\u7167\u5c04\u4e0b\u7684\u6295\u5f71\u53eb\u5e73\u884c\u6295\u5f71\uff0c\u5e73\u884c\u6295\u5f71\u7684\u6295\u5f71\u7ebf\u662f\u5e73\u884c\u7684\u3002<\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<li>\u7a7a\u95f4\u51e0\u4f55\u4f53\u7684\u8868\u9762\u79ef\u4e0e\u4f53\u79ef\n<ul>\n<li>\u5706\u67f1\u4fa7\u9762\u79ef\uff1a\u4fa7\u9762<\/li>\n<li>\u5706\u9525\u4fa7\u9762\u79ef\uff1a\u4fa7\u9762<\/li>\n<li>\u5706\u53f0\u4fa7\u9762\u79ef\uff1a\u4fa7\u9762<\/li>\n<li>\u4f53\u79ef\u516c\u5f0f\uff1a\u67f1\u4f53\uff1b\u9525\u4f53\uff1b\u53f0\u4f53\u4e0a\u4e0a\u4e0b\u4e0b<\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h3>\u7b2c\u4e8c\u7ae0\uff1a\u70b9\u3001\u76f4\u7ebf\u3001\u5e73\u9762\u4e4b\u95f4\u7684\u4f4d\u7f6e\u5173\u7cfb<\/h3>\n<div>\u00a0<\/div>\n<ol>\n<li>\u516c\u7406 1\uff1a\u5982\u679c\u4e00\u6761\u76f4\u7ebf\u4e0a\u4e24\u70b9\u5728\u4e00\u4e2a\u5e73\u9762\u5185\uff0c\u90a3\u4e48\u8fd9\u6761\u76f4\u7ebf\u5728\u6b64\u5e73\u9762\u5185\u3002<\/li>\n<li>\u516c\u7406 2\uff1a\u8fc7\u4e0d\u5728\u4e00\u6761\u76f4\u7ebf\u4e0a\u7684\u4e09\u70b9\uff0c\u6709\u4e14\u53ea\u6709\u4e00\u4e2a\u5e73\u9762\u3002<\/li>\n<li>\u516c\u7406 3\uff1a\u5982\u679c\u4e24\u4e2a\u4e0d\u91cd\u5408\u7684\u5e73\u9762\u6709\u4e00\u4e2a\u516c\u5171\u70b9\uff0c\u90a3\u4e48\u5b83\u4eec\u6709\u4e14\u53ea\u6709\u4e00\u6761\u8fc7\u8be5\u70b9\u7684\u516c\u5171\u76f4\u7ebf\u3002<\/li>\n<li>\u516c\u7406 4\uff1a\u5e73\u884c\u4e8e\u540c\u4e00\u6761\u76f4\u7ebf\u7684\u4e24\u6761\u76f4\u7ebf\u5e73\u884c\u3002<\/li>\n<li>\u5b9a\u7406\uff1a\u7a7a\u95f4\u4e2d\u5982\u679c\u4e24\u4e2a\u89d2\u7684\u4e24\u8fb9\u5206\u522b\u5bf9\u5e94\u5e73\u884c\uff0c\u90a3\u4e48\u8fd9\u4e24\u4e2a\u89d2\u76f8\u7b49\u6216\u4e92\u8865\u3002<\/li>\n<li>\u7ebf\u7ebf\u4f4d\u7f6e\u5173\u7cfb\uff1a\u5e73\u884c\u3001\u76f8\u4ea4\u3001\u5f02\u9762\u3002<\/li>\n<li>\u7ebf\u9762\u4f4d\u7f6e\u5173\u7cfb\uff1a\u76f4\u7ebf\u5728\u5e73\u9762\u5185\u3001\u76f4\u7ebf\u548c\u5e73\u9762\u5e73\u884c\u3001\u76f4\u7ebf\u548c\u5e73\u9762\u76f8\u4ea4\u3002<\/li>\n<li>\u9762\u9762\u4f4d\u7f6e\u5173\u7cfb\uff1a\u5e73\u884c\u3001\u76f8\u4ea4\u3002<\/li>\n<li>\u7ebf\u9762\u5e73\u884c\uff1a\n<ul>\n<li>\u5224\u5b9a\uff1a\u5e73\u9762\u5916\u4e00\u6761\u76f4\u7ebf\u4e0e\u6b64\u5e73\u9762\u5185\u7684\u4e00\u6761\u76f4\u7ebf\u5e73\u884c\uff0c\u5219\u8be5\u76f4\u7ebf\u4e0e\u6b64\u9762\u5e73\u884c\uff08\u7b80\u79f0\u7ebf\u7ebf\u5e73\u884c\uff0c\u5219\u7ebf\u9762\u5e73\u884c\uff09\u3002<\/li>\n<li>\u6027\u8d28\uff1a\u4e00\u6761\u76f4\u7ebf\u4e0e\u4e00\u4e2a\u5e73\u9762\u5e73\u884c\uff0c\u5219\u8fc7\u8fd9\u6761\u76f4\u7ebf\u7684\u4efb\u4e00\u5e73\u9762\u4e0e\u6b64\u5e73\u9762\u7684\u4ea4\u7ebf\u4e0e\u8be5\u76f4\u7ebf\u5e73\u884c\uff08\u7b80\u79f0\u7ebf\u9762\u5e73\u884c\uff0c\u5219\u7ebf\u7ebf\u5e73\u884c\uff09\u3002<\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<li>\u9762\u9762\u5e73\u884c\uff1a\n<ul>\n<li>\u5224\u5b9a\uff1a\u4e00\u4e2a\u5e73\u9762\u5185\u7684\u4e24\u6761\u76f8\u4ea4\u76f4\u7ebf\u4e0e\u53e6\u4e00\u4e2a\u5e73\u9762\u5e73\u884c\uff0c\u5219\u8fd9\u4e24\u4e2a\u5e73\u9762\u5e73\u884c\uff08\u7b80\u79f0\u7ebf\u9762\u5e73\u884c\uff0c\u5219\u9762\u9762\u5e73\u884c\uff09\u3002<\/li>\n<li>\u6027\u8d28\uff1a\u5982\u679c\u4e24\u4e2a\u5e73\u884c\u5e73\u9762\u540c\u65f6\u548c\u7b2c\u4e09\u4e2a\u5e73\u9762\u76f8\u4ea4\uff0c\u90a3\u4e48\u5b83\u4eec\u7684\u4ea4\u7ebf\u5e73\u884c\uff08\u7b80\u79f0\u9762\u9762\u5e73\u884c\uff0c\u5219\u7ebf\u7ebf\u5e73\u884c\uff09\u3002<\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<li>\u7ebf\u9762\u5782\u76f4\uff1a\n<ul>\n<li>\u5b9a\u4e49\uff1a\u5982\u679c\u4e00\u6761\u76f4\u7ebf\u5782\u76f4\u4e8e\u4e00\u4e2a\u5e73\u9762\u5185\u7684\u4efb\u610f\u4e00\u6761\u76f4\u7ebf\uff0c\u90a3\u4e48\u5c31\u8bf4\u8fd9\u6761\u76f4\u7ebf\u548c\u8fd9\u4e2a\u5e73\u9762\u5782\u76f4\u3002<\/li>\n<li>\u5224\u5b9a\uff1a\u4e00\u6761\u76f4\u7ebf\u4e0e\u4e00\u4e2a\u5e73\u9762\u5185\u7684\u4e24\u6761\u76f8\u4ea4\u76f4\u7ebf\u90fd\u5782\u76f4\uff0c\u5219\u8be5\u76f4\u7ebf\u4e0e\u6b64\u5e73\u9762\u5782\u76f4\uff08\u7b80\u79f0\u7ebf\u7ebf\u5782\u76f4\uff0c\u5219\u7ebf\u9762\u5782\u76f4\uff09\u3002<\/li>\n<li>\u6027\u8d28\uff1a\u5782\u76f4\u4e8e\u540c\u4e00\u4e2a\u5e73\u9762\u7684\u4e24\u6761\u76f4\u7ebf\u5e73\u884c\u3002<\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<li>\u9762\u9762\u5782\u76f4\uff1a\n<ul>\n<li>\u5b9a\u4e49\uff1a\u4e24\u4e2a\u5e73\u9762\u76f8\u4ea4\uff0c\u5982\u679c\u5b83\u4eec\u6240\u6210\u7684\u4e8c\u9762\u89d2\u662f\u76f4\u4e8c\u9762\u89d2\uff0c\u5c31\u8bf4\u8fd9\u4e24\u4e2a\u5e73\u9762\u4e92\u76f8\u5782\u76f4\u3002<\/li>\n<li>\u5224\u5b9a\uff1a\u4e00\u4e2a\u5e73\u9762\u7ecf\u8fc7\u53e6\u4e00\u4e2a\u5e73\u9762\u7684\u4e00\u6761\u5782\u7ebf\uff0c\u5219\u8fd9\u4e24\u4e2a\u5e73\u9762\u5782\u76f4\uff08\u7b80\u79f0\u7ebf\u9762\u5782\u76f4\uff0c\u5219\u9762\u9762\u5782\u76f4\uff09\u3002<\/li>\n<li>\u6027\u8d28\uff1a\u4e24\u4e2a\u5e73\u9762\u4e92\u76f8\u5782\u76f4\uff0c\u5219\u4e00\u4e2a\u5e73\u9762\u5185\u5782\u76f4\u4e8e\u4ea4\u7ebf\u7684\u76f4\u7ebf\u5782\u76f4\u4e8e\u53e6\u4e00\u4e2a\u5e73\u9762\uff08\u7b80\u79f0\u9762\u9762\u5782\u76f4\uff0c\u5219\u7ebf\u9762\u5782\u76f4\uff09\u3002<\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h3>\u7b2c\u4e09\u7ae0\uff1a\u76f4\u7ebf\u4e0e\u65b9\u7a0b<\/h3>\n<div>\u00a0<\/div>\n<ol>\n<li>\u503e\u659c\u89d2\u4e0e\u659c\u7387\uff1a<span aria-hidden=\"true\">k=tan\u03b1=x2\u200b\u2212x1\u200by2\u200b\u2212y1\u200b\u200b<\/span><\/li>\n<li>\u76f4\u7ebf\u65b9\u7a0b\uff1a\n<ul>\n<li>\u70b9\u659c\u5f0f\uff1a<span aria-hidden=\"true\">y\u2212y0\u200b=k(x\u2212x0\u200b)<\/span><\/li>\n<li>\u659c\u622a\u5f0f\uff1a<span aria-hidden=\"true\">y=kx+b<\/span><\/li>\n<li>\u4e24\u70b9\u5f0f\uff1a<span aria-hidden=\"true\">x\u2212x1\u200by\u2212y1\u200b\u200b=x2\u200b\u2212x1\u200by2\u200b\u2212y1\u200b\u200b<\/span><\/li>\n<li>\u622a\u8ddd\u5f0f\uff1a<span aria-hidden=\"true\">ax\u200b+by\u200b=1<\/span><\/li>\n<li>\u4e00\u822c\u5f0f\uff1a<span aria-hidden=\"true\">Ax+By+C=0<\/span><\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<li>\u5bf9\u4e8e\u76f4\u7ebf\uff1a<span aria-hidden=\"true\">l1\u200b:y=k1\u200bx+b1\u200b<\/span>\uff0c<span aria-hidden=\"true\">l2\u200b:y=k2\u200bx+b2\u200b<\/span>\u6709\uff1a\n<ul>\n<li><span aria-hidden=\"true\">l1\u200b\u2225l2\u200b\u21d4{k1\u200b=k2\u200bb1\u200b\ue020=b2\u200b\u200b<\/span><\/li>\n<li><span aria-hidden=\"true\">l1\u200b<\/span>\u548c<span aria-hidden=\"true\">l2\u200b<\/span>\u76f8\u4ea4<span aria-hidden=\"true\">\u21d4k1\u200b\ue020=k2\u200b<\/span><\/li>\n<li><span aria-hidden=\"true\">l1\u200b<\/span>\u548c<span aria-hidden=\"true\">l2\u200b<\/span>\u91cd\u5408<span aria-hidden=\"true\">\u21d4{k1\u200b=k2\u200bb1\u200b=b2\u200b\u200b<\/span><\/li>\n<li><span aria-hidden=\"true\">l1\u200b\u22a5l2\u200b\u21d4k1\u200bk2\u200b=\u22121<\/span><\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<li>\u5bf9\u4e8e\u76f4\u7ebf\uff1a<span aria-hidden=\"true\">l1\u200b:A1\u200bx+B1\u200by+C1\u200b=0<\/span>\uff0c<span aria-hidden=\"true\">l2\u200b:A2\u200bx+B2\u200by+C2\u200b=0<\/span>\u6709\uff1a\n<ul>\n<li><span aria-hidden=\"true\">l1\u200b\u2225l2\u200b\u21d4{A1\u200bB2\u200b=A2\u200bB1\u200bB1\u200bC2\u200b\ue020=B2\u200bC1\u200b\u200b<\/span><\/li>\n<li><span aria-hidden=\"true\">l1\u200b<\/span>\u548c<span aria-hidden=\"true\">l2\u200b<\/span>\u76f8\u4ea4<span aria-hidden=\"true\">\u21d4A1\u200bB2\u200b\ue020=A2\u200bB1\u200b<\/span><\/li>\n<li><span aria-hidden=\"true\">l1\u200b<\/span>\u548c<span aria-hidden=\"true\">l2\u200b<\/span>\u91cd\u5408<span aria-hidden=\"true\">\u21d4{A1\u200bB2\u200b=A2\u200bB1\u200bB1\u200bC2\u200b=B2\u200bC1\u200b\u200b<\/span><\/li>\n<li><span aria-hidden=\"true\">l1\u200b\u22a5l2\u200b\u21d4A1\u200bA2\u200b+B1\u200bB2\u200b=0<\/span><\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<li>\u4e24\u70b9\u95f4\u8ddd\u79bb\u516c\u5f0f\uff1a<span aria-hidden=\"true\">\u2223P1\u200bP2\u200b\u2223=(x2\u200b\u2212x1\u200b)2+(y2\u200b\u2212y1\u200b)2\u200b<\/span><\/li>\n<li>\u70b9\u5230\u76f4\u7ebf\u8ddd\u79bb\u516c\u5f0f\uff1a<span aria-hidden=\"true\">d=A2+B2\u200b\u2223Ax0\u200b+By0\u200b+C\u2223\u200b<\/span><\/li>\n<li>\u4e24\u5e73\u884c\u7ebf\u95f4\u7684\u8ddd\u79bb\u516c\u5f0f\uff1a<span aria-hidden=\"true\">l1\u200b:Ax+By+C1\u200b=0<\/span>\uff0c<span aria-hidden=\"true\">l2\u200b:Ax+By+C2\u200b=0<\/span>\uff0c\u5219<span aria-hidden=\"true\">d=A2+B2\u200b\u2223C1\u200b\u2212C2\u200b\u2223\u200b<\/span><\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h3>\u7b2c\u56db\u7ae0\uff1a\u5706\u4e0e\u65b9\u7a0b<\/h3>\n<div>\u00a0<\/div>\n<ol>\n<li>\u5706\u7684\u65b9\u7a0b\uff1a\n<ul>\n<li>\u6807\u51c6\u65b9\u7a0b\uff1a<span aria-hidden=\"true\">(x\u2212a)2+(y\u2212b)2=r2<\/span>\uff0c\u5176\u4e2d\u5706\u5fc3\u4e3a<span aria-hidden=\"true\">(a,b)<\/span>\uff0c\u534a\u5f84\u4e3a<span aria-hidden=\"true\">r<\/span><\/li>\n<li>\u4e00\u822c\u65b9\u7a0b\uff1a<span aria-hidden=\"true\">x2+y2+Dx+Ey+F=0<\/span>\uff0c\u5176\u4e2d\u5706\u5fc3\u4e3a<span aria-hidden=\"true\">(\u22122D\u200b,\u22122E\u200b)<\/span>\uff0c\u534a\u5f84\u4e3a<span aria-hidden=\"true\">r=21\u200bD2+E2\u22124F\u200b<\/span><\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<li>\u76f4\u7ebf\u4e0e\u5706\u7684\u4f4d\u7f6e\u5173\u7cfb\uff1a\u76f4\u7ebf<span aria-hidden=\"true\">Ax+By+C=0<\/span>\u4e0e\u5706<span aria-hidden=\"true\">(x\u2212a)2+(y\u2212b)2=r2<\/span>\u7684\u4f4d\u7f6e\u5173\u7cfb\u6709\u4e09\u79cd\uff1a\n<ul>\n<li><span aria-hidden=\"true\">d&gt;r\u21d4<\/span>\u76f8\u79bb<span aria-hidden=\"true\">\u21d4\u0394&lt;0<\/span><\/li>\n<li><span aria-hidden=\"true\">d=r\u21d4<\/span>\u76f8\u5207<span aria-hidden=\"true\">\u21d4\u0394=0<\/span><\/li>\n<li><span aria-hidden=\"true\">d&lt;r\u21d4<\/span>\u76f8\u4ea4<span aria-hidden=\"true\">\u21d4\u0394&gt;0<\/span><\/li>\n<li>\u5f26\u957f\u516c\u5f0f\uff1a<span aria-hidden=\"true\">l=2r2\u2212d2\u200b=1+k2\u200b(x1\u200b\u2212x2\u200b)2\u22124&#215;1\u200bx2\u200b\u200b<\/span><\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<li>\u4e24\u5706\u4f4d\u7f6e\u5173\u7cfb\uff1a<span aria-hidden=\"true\">d=\u2223O1\u200bO2\u200b\u2223<\/span>\n<ul>\n<li>\u5916\u79bb\uff1a<span aria-hidden=\"true\">d&gt;R+r<\/span><\/li>\n<li>\u5916\u5207\uff1a<span aria-hidden=\"true\">d=R+r<\/span><\/li>\n<li>\u76f8\u4ea4\uff1a<span aria-hidden=\"true\">R\u2212r&lt;d&lt;R+r<\/span><\/li>\n<li>\u5185\u5207\uff1a<span aria-hidden=\"true\">d=R\u2212r<\/span><\/li>\n<li>\u5185\u542b\uff1a<span aria-hidden=\"true\">d&lt;R\u2212r<\/span><\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<li>\u7a7a\u95f4\u4e2d\u4e24\u70b9\u95f4\u8ddd\u79bb\u516c\u5f0f\uff1a<span aria-hidden=\"true\">\u2223P1\u200bP2\u200b\u2223=(x2\u200b\u2212x1\u200b)2+(y2\u200b\u2212y1\u200b)2+(z2\u200b\u2212z1\u200b)2\u200b<\/span><\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h2>\u5fc5\u4fee 3 \u6570\u5b66\u77e5\u8bc6\u70b9<\/h2>\n<div>\u00a0<\/div>\n<h3>\u7b2c\u4e8c\u7ae0\uff1a\u7edf\u8ba1<\/h3>\n<div>\u00a0<\/div>\n<ol>\n<li>\u62bd\u6837\u65b9\u6cd5\uff1a\n<ul>\n<li>\u7b80\u5355\u968f\u673a\u62bd\u6837\uff08\u603b\u4f53\u4e2a\u6570\u8f83\u5c11\uff09<\/li>\n<li>\u7cfb\u7edf\u62bd\u6837\uff08\u603b\u4f53\u4e2a\u6570\u8f83\u591a\uff09<\/li>\n<li>\u5206\u5c42\u62bd\u6837\uff08\u603b\u4f53\u4e2d\u5dee\u5f02\u660e\u663e\uff09<\/li>\n<li>\u6ce8\u610f\uff1a\u5728<span aria-hidden=\"true\">N<\/span>\u4e2a\u4e2a\u4f53\u7684\u603b\u4f53\u4e2d\u62bd\u53d6\u51fa<span aria-hidden=\"true\">n<\/span>\u4e2a\u4e2a\u4f53\u7ec4\u6210\u6837\u672c\uff0c\u6bcf\u4e2a\u4e2a\u4f53\u88ab\u62bd\u5230\u7684\u673a\u4f1a\uff08\u6982\u7387\uff09\u5747\u4e3a<span aria-hidden=\"true\">Nn\u200b<\/span><\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h3>\u7b2c\u4e09\u7ae0\uff1a\u6982\u7387<\/h3>\n<div>\u00a0<\/div>\n<ol>\n<li>\u968f\u673a\u4e8b\u4ef6\u53ca\u5176\u6982\u7387\uff1a\n<ul>\n<li>\u4e8b\u4ef6\uff1a\u8bd5\u9a8c\u7684\u6bcf\u4e00\u79cd\u53ef\u80fd\u7684\u7ed3\u679c\uff0c\u7528\u5927\u5199\u82f1\u6587\u5b57\u6bcd\u8868\u793a<\/li>\n<li>\u5fc5\u7136\u4e8b\u4ef6\u3001\u4e0d\u53ef\u80fd\u4e8b\u4ef6\u3001\u968f\u673a\u4e8b\u4ef6\u7684\u7279\u70b9<\/li>\n<li>\u968f\u673a\u4e8b\u4ef6<span aria-hidden=\"true\">A<\/span>\u7684\u6982\u7387\uff1a<span aria-hidden=\"true\">P(A)=nm\u200b<\/span>\uff0c<span aria-hidden=\"true\">0\u2264P(A)\u22641<\/span><\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<li>\u53e4\u5178\u6982\u578b\uff1a\n<ul>\n<li>\u57fa\u672c\u4e8b\u4ef6\uff1a\u4e00\u6b21\u8bd5\u9a8c\u4e2d\u53ef\u80fd\u51fa\u73b0\u7684\u6bcf\u4e00\u4e2a\u57fa\u672c\u7ed3\u679c<\/li>\n<li>\u53e4\u5178\u6982\u578b\u7684\u7279\u70b9\uff1a\u6240\u6709\u7684\u57fa\u672c\u4e8b\u4ef6\u53ea\u6709\u6709\u9650\u4e2a\uff1b\u6bcf\u4e2a\u57fa\u672c\u4e8b\u4ef6\u90fd\u662f\u7b49\u53ef\u80fd\u53d1\u751f<\/li>\n<li>\u53e4\u5178\u6982\u578b\u6982\u7387\u8ba1\u7b97\u516c\u5f0f\uff1a\u4e00\u6b21\u8bd5\u9a8c\u7684\u7b49\u53ef\u80fd\u57fa\u672c\u4e8b\u4ef6\u5171\u6709<span aria-hidden=\"true\">n<\/span>\u4e2a\uff0c\u4e8b\u4ef6<span aria-hidden=\"true\">A<\/span>\u5305\u542b\u4e86\u5176\u4e2d\u7684<span aria-hidden=\"true\">m<\/span>\u4e2a\u57fa\u672c\u4e8b\u4ef6\uff0c\u5219\u4e8b\u4ef6<span aria-hidden=\"true\">A<\/span>\u53d1\u751f\u7684\u6982\u7387<span aria-hidden=\"true\">P(A)=nm\u200b<\/span><\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h2>\u5fc5\u4fee 4 \u6570\u5b66\u77e5\u8bc6\u70b9<\/h2>\n<div>\u00a0<\/div>\n<h3>\u7b2c\u4e00\u7ae0\uff1a\u4e09\u89d2\u51fd\u6570<\/h3>\n<div>\u00a0<\/div>\n<h4>$1.1.1 \u4efb\u610f\u89d2<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li>\u6b63\u89d2\u3001\u8d1f\u89d2\u3001\u96f6\u89d2\u3001\u8c61\u9650\u89d2\u7684\u6982\u5ff5<\/li>\n<li>\u4e0e\u89d2<span aria-hidden=\"true\">\u03b1<\/span>\u7ec8\u8fb9\u76f8\u540c\u7684\u89d2\u7684\u96c6\u5408\uff1a<span aria-hidden=\"true\">{\u03b2\u2223\u03b2=\u03b1+2k\u03c0,k\u2208Z}<\/span><\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h4>$1.1.2 \u5f27\u5ea6\u5236<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li>\u628a\u957f\u5ea6\u7b49\u4e8e\u534a\u5f84\u957f\u7684\u5f27\u6240\u5bf9\u7684\u5706\u5fc3\u89d2\u53eb\u505a 1 \u5f27\u5ea6\u7684\u89d2<\/li>\n<li><span aria-hidden=\"true\">\u2223\u03b1\u2223=rl\u200b<\/span><\/li>\n<li>\u5f27\u957f\u516c\u5f0f\uff1a<span aria-hidden=\"true\">l=180n\u03c0R\u200b=\u2223\u03b1\u2223R<\/span><\/li>\n<li>\u6247\u5f62\u9762\u79ef\u516c\u5f0f\uff1a<span aria-hidden=\"true\">S=360n\u03c0R2\u200b=21\u200blR<\/span><\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h4>$1.2.1 \u4efb\u610f\u89d2\u7684\u4e09\u89d2\u51fd\u6570<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li>\u8bbe<span aria-hidden=\"true\">\u03b1<\/span>\u662f\u4e00\u4e2a\u4efb\u610f\u89d2\uff0c\u5b83\u7684\u7ec8\u8fb9\u4e0e\u5355\u4f4d\u5706\u4ea4\u4e8e\u70b9<span aria-hidden=\"true\">P(x,y)<\/span>\uff0c\u90a3\u4e48\uff1a<span aria-hidden=\"true\">sin\u03b1=y<\/span>\uff0c<span aria-hidden=\"true\">cos\u03b1=x<\/span>\uff0c<span aria-hidden=\"true\">tan\u03b1=xy\u200b<\/span><\/li>\n<li>\u8bbe\u70b9<span aria-hidden=\"true\">A(x,y)<\/span>\u4e3a\u89d2<span aria-hidden=\"true\">\u03b1<\/span>\u7ec8\u8fb9\u4e0a\u4efb\u610f\u4e00\u70b9\uff0c\u90a3\u4e48\uff08\u8bbe<span aria-hidden=\"true\">r=x2+y2\u200b<\/span>\uff09\uff1a<span aria-hidden=\"true\">sin\u03b1=ry\u200b<\/span>\uff0c<span aria-hidden=\"true\">cos\u03b1=rx\u200b<\/span>\uff0c<span aria-hidden=\"true\">tan\u03b1=xy\u200b<\/span>\uff0c<span aria-hidden=\"true\">cot\u03b1=yx\u200b<\/span><\/li>\n<li>\u7279\u6b8a\u89d2<span aria-hidden=\"true\">0\u2218<\/span>\uff0c<span aria-hidden=\"true\">30\u2218<\/span>\uff0c<span aria-hidden=\"true\">45\u2218<\/span>\uff0c<span aria-hidden=\"true\">60\u2218<\/span>\uff0c<span aria-hidden=\"true\">90\u2218<\/span>\uff0c<span aria-hidden=\"true\">180\u2218<\/span>\uff0c<span aria-hidden=\"true\">270\u2218<\/span>\u7b49\u7684\u4e09\u89d2\u51fd\u6570\u503c\uff1a<\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<div>\n<div>\n<table>\n<thead>\n<tr>\n<th>\u89d2<span aria-hidden=\"true\">\u03b1<\/span><\/th>\n<th><span aria-hidden=\"true\">0\u2218<\/span><\/th>\n<th><span aria-hidden=\"true\">30\u2218<\/span><\/th>\n<th><span aria-hidden=\"true\">45\u2218<\/span><\/th>\n<th><span aria-hidden=\"true\">60\u2218<\/span><\/th>\n<th><span aria-hidden=\"true\">90\u2218<\/span><\/th>\n<th><span aria-hidden=\"true\">180\u2218<\/span><\/th>\n<th><span aria-hidden=\"true\">270\u2218<\/span><\/th>\n<th><span aria-hidden=\"true\">360\u2218<\/span><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u89d2<span aria-hidden=\"true\">\u03b1<\/span>\u7684\u5f27\u5ea6\u6570<\/td>\n<td><span aria-hidden=\"true\">0<\/span><\/td>\n<td><span aria-hidden=\"true\">6\u03c0\u200b<\/span><\/td>\n<td><span aria-hidden=\"true\">4\u03c0\u200b<\/span><\/td>\n<td><span aria-hidden=\"true\">3\u03c0\u200b<\/span><\/td>\n<td><span aria-hidden=\"true\">2\u03c0\u200b<\/span><\/td>\n<td><span aria-hidden=\"true\">\u03c0<\/span><\/td>\n<td><span aria-hidden=\"true\">23\u03c0\u200b<\/span><\/td>\n<td><span aria-hidden=\"true\">2\u03c0<\/span><\/td>\n<\/tr>\n<tr>\n<td><span aria-hidden=\"true\">sin\u03b1<\/span><\/td>\n<td><span aria-hidden=\"true\">0<\/span><\/td>\n<td><span aria-hidden=\"true\">21\u200b<\/span><\/td>\n<td><span aria-hidden=\"true\">22\u200b\u200b<\/span><\/td>\n<td><span aria-hidden=\"true\">23\u200b\u200b<\/span><\/td>\n<td><span aria-hidden=\"true\">1<\/span><\/td>\n<td><span aria-hidden=\"true\">0<\/span><\/td>\n<td><span aria-hidden=\"true\">\u22121<\/span><\/td>\n<td><span aria-hidden=\"true\">0<\/span><\/td>\n<\/tr>\n<tr>\n<td><span aria-hidden=\"true\">cos\u03b1<\/span><\/td>\n<td><span aria-hidden=\"true\">1<\/span><\/td>\n<td><span aria-hidden=\"true\">23\u200b\u200b<\/span><\/td>\n<td><span aria-hidden=\"true\">22\u200b\u200b<\/span><\/td>\n<td><span aria-hidden=\"true\">21\u200b<\/span><\/td>\n<td><span aria-hidden=\"true\">0<\/span><\/td>\n<td><span aria-hidden=\"true\">\u22121<\/span><\/td>\n<td><span aria-hidden=\"true\">0<\/span><\/td>\n<td><span aria-hidden=\"true\">1<\/span><\/td>\n<\/tr>\n<tr>\n<td><span aria-hidden=\"true\">tan\u03b1<\/span><\/td>\n<td><span aria-hidden=\"true\">0<\/span><\/td>\n<td><span aria-hidden=\"true\">33\u200b\u200b<\/span><\/td>\n<td><span aria-hidden=\"true\">1<\/span><\/td>\n<td><span aria-hidden=\"true\">3\u200b<\/span><\/td>\n<td>\u4e0d\u5b58\u5728<\/td>\n<td><span aria-hidden=\"true\">0<\/span><\/td>\n<td>\u4e0d\u5b58\u5728<\/td>\n<td><span aria-hidden=\"true\">0<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<div>\u00a0<\/div>\n<h4>$1.2.2 \u540c\u89d2\u4e09\u89d2\u51fd\u6570\u7684\u57fa\u672c\u5173\u7cfb\u5f0f<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li>\u5e73\u65b9\u5173\u7cfb\uff1a<span aria-hidden=\"true\">sin2\u03b1+cos2\u03b1=1<\/span><\/li>\n<li>\u5546\u6570\u5173\u7cfb\uff1a<span aria-hidden=\"true\">tan\u03b1=cos\u03b1sin\u03b1\u200b<\/span><\/li>\n<li>\u5012\u6570\u5173\u7cfb\uff1a<span aria-hidden=\"true\">tan\u03b1cot\u03b1=1<\/span><\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h4>\u4e09\u89d2\u51fd\u6570\u7684\u8bf1\u5bfc\u516c\u5f0f\uff08\u6982\u62ec\u4e3a\u5947\u53d8\u5076\u4e0d\u53d8\uff0c\u7b26\u53f7\u770b\u8c61\u9650\uff0ck in Z$\uff09<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li>\u8bf1\u5bfc\u516c\u5f0f\u4e00\uff1a<span aria-hidden=\"true\">sin(\u03b1+2k\u03c0)=sin\u03b1<\/span>\uff0c<span aria-hidden=\"true\">cos(\u03b1+2k\u03c0)=cos\u03b1<\/span>\uff0c<span aria-hidden=\"true\">tan(\u03b1+2k\u03c0)=tan\u03b1<\/span>\uff08\u5176\u4e2d\uff1a<span aria-hidden=\"true\">k\u2208Z<\/span>\uff09<\/li>\n<li>\u8bf1\u5bfc\u516c\u5f0f\u4e8c\uff1a<span aria-hidden=\"true\">sin(\u03c0+\u03b1)=\u2212sin\u03b1<\/span>\uff0c<span aria-hidden=\"true\">cos(\u03c0+\u03b1)=\u2212cos\u03b1<\/span>\uff0c<span aria-hidden=\"true\">tan(\u03c0+\u03b1)=tan\u03b1<\/span><\/li>\n<li>\u8bf1\u5bfc\u516c\u5f0f\u4e09\uff1a<span aria-hidden=\"true\">sin(\u2212\u03b1)=\u2212sin\u03b1<\/span>\uff0c<span aria-hidden=\"true\">cos(\u2212\u03b1)=cos\u03b1<\/span>\uff0c<span aria-hidden=\"true\">tan(\u2212\u03b1)=\u2212tan\u03b1<\/span><\/li>\n<li>\u8bf1\u5bfc\u516c\u5f0f\u56db\uff1a<span aria-hidden=\"true\">sin(\u03c0\u2212\u03b1)=sin\u03b1<\/span>\uff0c<span aria-hidden=\"true\">cos(\u03c0\u2212\u03b1)=\u2212cos\u03b1<\/span>\uff0c<span aria-hidden=\"true\">tan(\u03c0\u2212\u03b1)=\u2212tan\u03b1<\/span><\/li>\n<li>\u8bf1\u5bfc\u516c\u5f0f\u4e94\uff1a<span aria-hidden=\"true\">sin(2\u03c0\u200b\u2212\u03b1)=cos\u03b1<\/span>\uff0c<span aria-hidden=\"true\">cos(2\u03c0\u200b\u2212\u03b1)=sin\u03b1<\/span><\/li>\n<li>\u8bf1\u5bfc\u516c\u5f0f\u516d\uff1a<span aria-hidden=\"true\">sin(2\u03c0\u200b+\u03b1)=cos\u03b1<\/span>\uff0c<span aria-hidden=\"true\">cos(2\u03c0\u200b+\u03b1)=\u2212sin\u03b1<\/span><\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h4>$1.4.1 \u6b63\u5f26\u3001\u4f59\u5f26\u51fd\u6570\u7684\u56fe\u8c61\u548c\u6027\u8d28<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li>\u6b63\u5f26\u51fd\u6570<span aria-hidden=\"true\">y=sinx<\/span>\u5728<span aria-hidden=\"true\">x\u2208[0,2\u03c0]<\/span>\u4e0a\u7684\u4e94\u4e2a\u5173\u952e\u70b9\u4e3a\uff1a<span aria-hidden=\"true\">(0,0)<\/span>\uff0c<span aria-hidden=\"true\">(2\u03c0\u200b,1)<\/span>\uff0c<span aria-hidden=\"true\">(\u03c0,0)<\/span>\uff0c<span aria-hidden=\"true\">(23\u03c0\u200b,\u22121)<\/span>\uff0c<span aria-hidden=\"true\">(2\u03c0,0)<\/span><\/li>\n<li>\u80fd\u591f\u5bf9\u7167\u56fe\u8c61\u8bb2\u51fa\u6b63\u5f26\u3001\u4f59\u5f26\u51fd\u6570\u7684\u76f8\u5173\u6027\u8d28\uff1a\u5b9a\u4e49\u57df\u3001\u503c\u57df\u3001\u6700\u5927\u6700\u5c0f\u503c\u3001\u5bf9\u79f0\u6027\u3001\u5bf9\u79f0\u4e2d\u5fc3\u3001\u5947\u5076\u6027\u3001\u5355\u8c03\u6027\u3001\u5468\u671f\u6027<\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h4>$1.4.3 \u6b63\u5207\u51fd\u6570\u7684\u56fe\u8c61\u4e0e\u6027\u8d28<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li>\u80fd\u591f\u5bf9\u7167\u56fe\u8c61\u8bb2\u51fa\u6b63\u5207\u51fd\u6570\u7684\u76f8\u5173\u6027\u8d28\uff1a\u5b9a\u4e49\u57df\u3001\u503c\u57df\u3001\u5bf9\u79f0\u4e2d\u5fc3\u3001\u5947\u5076\u6027\u3001\u5355\u8c03\u6027\u3001\u5468\u671f\u6027<\/li>\n<li>\u5468\u671f\u51fd\u6570\u5b9a\u4e49\uff1a\u5bf9\u4e8e\u51fd\u6570<span aria-hidden=\"true\">f(x)<\/span>\uff0c\u5982\u679c\u5b58\u5728\u4e00\u4e2a\u975e\u96f6\u5e38\u6570<span aria-hidden=\"true\">T<\/span>\uff0c\u4f7f\u5f97\u5f53<span aria-hidden=\"true\">x<\/span>\u53d6\u5b9a\u4e49\u57df\u5185\u7684\u6bcf\u4e00\u4e2a\u503c\u65f6\uff0c\u90fd\u6709<span aria-hidden=\"true\">f(x+T)=f(x)<\/span>\uff0c\u90a3\u4e48\u51fd\u6570<span aria-hidden=\"true\">f(x)<\/span>\u5c31\u53eb\u505a\u5468\u671f\u51fd\u6570\uff0c\u975e\u96f6\u5e38\u6570<span aria-hidden=\"true\">T<\/span>\u53eb\u505a\u8fd9\u4e2a\u51fd\u6570\u7684\u5468\u671f<\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h4>\u56fe\u8868\u5f52\u7eb3\uff1a\u6b63\u5f26\u3001\u4f59\u5f26\u3001\u6b63\u5207\u51fd\u6570\u7684\u56fe\u50cf\u53ca\u5176\u6027\u8d28<\/h4>\n<div>\u00a0<\/div>\n<div>\n<div>\n<table>\n<thead>\n<tr>\n<th>\u00a0<\/th>\n<th><span aria-hidden=\"true\">y=sinx<\/span><\/th>\n<th><span aria-hidden=\"true\">y=cosx<\/span><\/th>\n<th><span aria-hidden=\"true\">y=tanx<\/span><\/th>\n<th>\u00a0<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u5b9a\u4e49\u57df<\/td>\n<td><span aria-hidden=\"true\">R<\/span><\/td>\n<td><span aria-hidden=\"true\">R<\/span><\/td>\n<td>${x<\/td>\n<td>x neq kpi + frac{pi}{2}, k in Z}$<\/td>\n<\/tr>\n<tr>\n<td>\u503c\u57df<\/td>\n<td><span aria-hidden=\"true\">[\u22121,1]<\/span><\/td>\n<td><span aria-hidden=\"true\">[\u22121,1]<\/span><\/td>\n<td><span aria-hidden=\"true\">R<\/span><\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>\u6700\u503c<\/td>\n<td><span aria-hidden=\"true\">x=2k\u03c0+2\u03c0\u200b<\/span>\uff0c<span aria-hidden=\"true\">k\u2208Z<\/span>\u65f6\uff0c<span aria-hidden=\"true\">y=1<\/span>\uff1b<span aria-hidden=\"true\">x=2k\u03c0\u22122\u03c0\u200b<\/span>\uff0c<span aria-hidden=\"true\">k\u2208Z<\/span>\u65f6\uff0c<span aria-hidden=\"true\">y=\u22121<\/span><\/td>\n<td><span aria-hidden=\"true\">x=2k\u03c0<\/span>\uff0c<span aria-hidden=\"true\">k\u2208Z<\/span>\u65f6\uff0c<span aria-hidden=\"true\">y=1<\/span>\uff1b<span aria-hidden=\"true\">x=2k\u03c0+\u03c0<\/span>\uff0c<span aria-hidden=\"true\">k\u2208Z<\/span>\u65f6\uff0c<span aria-hidden=\"true\">y=\u22121<\/span><\/td>\n<td>\u65e0<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>\u5468\u671f\u6027<\/td>\n<td><span aria-hidden=\"true\">T=2\u03c0<\/span><\/td>\n<td><span aria-hidden=\"true\">T=2\u03c0<\/span><\/td>\n<td><span aria-hidden=\"true\">T=\u03c0<\/span><\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>\u5947\u5076\u6027<\/td>\n<td>\u5947<\/td>\n<td>\u5076<\/td>\n<td>\u5947<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>\u5355\u8c03\u6027\uff08<span aria-hidden=\"true\">k\u2208Z<\/span>\uff09<\/td>\n<td>\u5728<span aria-hidden=\"true\">[2k\u03c0\u22122\u03c0\u200b,2k\u03c0+2\u03c0\u200b]<\/span>\u4e0a\u5355\u8c03\u9012\u589e\uff1b\u5728<span aria-hidden=\"true\">[2k\u03c0+2\u03c0\u200b,2k\u03c0+23\u03c0\u200b]<\/span>\u4e0a\u5355\u8c03\u9012\u51cf<\/td>\n<td>\u5728<span aria-hidden=\"true\">[2k\u03c0\u2212\u03c0,2k\u03c0]<\/span>\u4e0a\u5355\u8c03\u9012\u589e\uff1b\u5728<span aria-hidden=\"true\">[2k\u03c0,2k\u03c0+\u03c0]<\/span>\u4e0a\u5355\u8c03\u9012\u51cf<\/td>\n<td>\u5728<span aria-hidden=\"true\">(k\u03c0\u22122\u03c0\u200b,k\u03c0+2\u03c0\u200b)<\/span>\u4e0a\u5355\u8c03\u9012\u589e<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>\u5bf9\u79f0\u6027\uff08<span aria-hidden=\"true\">k\u2208Z<\/span>\uff09<\/td>\n<td>\u5bf9\u79f0\u8f74\u65b9\u7a0b\uff1a<span aria-hidden=\"true\">x=k\u03c0+2\u03c0\u200b<\/span>\uff1b\u5bf9\u79f0\u4e2d\u5fc3<span aria-hidden=\"true\">(k\u03c0,0)<\/span><\/td>\n<td>\u5bf9\u79f0\u8f74\u65b9\u7a0b\uff1a<span aria-hidden=\"true\">x=k\u03c0<\/span>\uff1b\u5bf9\u79f0\u4e2d\u5fc3<span aria-hidden=\"true\">(k\u03c0+2\u03c0\u200b,0)<\/span><\/td>\n<td>\u65e0\u5bf9\u79f0\u8f74\uff1b\u5bf9\u79f0\u4e2d\u5fc3<span aria-hidden=\"true\">(2k\u03c0\u200b,0)<\/span><\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<div>\u00a0<\/div>\n<h4>\u51fd\u6570y = Asin (omega x + varphi)$ \u7684\u56fe\u8c61<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li>\u5bf9\u4e8e\u51fd\u6570\uff1a<span aria-hidden=\"true\">y=Asin(\u03c9x+\u03c6)+B<\/span>\uff08<span aria-hidden=\"true\">A&gt;0<\/span>\uff0c<span aria-hidden=\"true\">\u03c9&gt;0<\/span>\uff09\u6709\uff1a\u632f\u5e45<span aria-hidden=\"true\">A<\/span>\uff0c\u5468\u671f<span aria-hidden=\"true\">T=\u03c92\u03c0\u200b<\/span>\uff0c\u521d\u76f8<span aria-hidden=\"true\">\u03c6<\/span>\uff0c\u76f8\u4f4d<span aria-hidden=\"true\">\u03c9x+\u03c6<\/span>\uff0c\u9891\u7387<span aria-hidden=\"true\">f=T1\u200b=2\u03c0\u03c9\u200b<\/span><\/li>\n<li>\u51fd\u6570<span aria-hidden=\"true\">y=sinx<\/span>\u7684\u56fe\u8c61\u4e0e<span aria-hidden=\"true\">y=Asin(\u03c9x+\u03c6)+B<\/span>\u7684\u56fe\u8c61\u4e4b\u95f4\u7684\u5e73\u79fb\u4f38\u7f29\u53d8\u6362\u5173\u7cfb\uff1a\n<ul>\n<li>\u5148\u5e73\u79fb\u540e\u4f38\u7f29\uff1a<span aria-hidden=\"true\">y=sinx<\/span>\u5e73\u79fb<span aria-hidden=\"true\">\u2223\u03c6\u2223<\/span>\u4e2a\u5355\u4f4d<span aria-hidden=\"true\">\u2192y=sin(x+\u03c6)<\/span>\uff1b\u6a2a\u5750\u6807\u4e0d\u53d8\uff0c\u7eb5\u5750\u6807\u53d8\u4e3a\u539f\u6765\u7684<span aria-hidden=\"true\">A<\/span>\u500d<span aria-hidden=\"true\">\u2192y=Asin(x+\u03c6)<\/span>\uff1b\u7eb5\u5750\u6807\u4e0d\u53d8\uff0c\u6a2a\u5750\u6807\u53d8\u4e3a\u539f\u6765\u7684<span aria-hidden=\"true\">\u2223\u03c91\u200b\u2223<\/span>\u500d<span aria-hidden=\"true\">\u2192y=Asin(\u03c9x+\u03c6)<\/span>\uff1b\u5e73\u79fb<span aria-hidden=\"true\">\u2223B\u2223<\/span>\u4e2a\u5355\u4f4d<span aria-hidden=\"true\">\u2192y=Asin(\u03c9x+\u03c6)+B<\/span>\uff08\u4e0a\u52a0\u4e0b\u51cf\uff09<\/li>\n<li>\u5148\u4f38\u7f29\u540e\u5e73\u79fb\uff1a<span aria-hidden=\"true\">y=sinx<\/span>\u6a2a\u5750\u6807\u4e0d\u53d8\uff0c\u7eb5\u5750\u6807\u53d8\u4e3a\u539f\u6765\u7684<span aria-hidden=\"true\">A<\/span>\u500d<span aria-hidden=\"true\">\u2192y=Asinx<\/span>\uff1b\u7eb5\u5750\u6807\u4e0d\u53d8\uff0c\u6a2a\u5750\u6807\u53d8\u4e3a\u539f\u6765\u7684<span aria-hidden=\"true\">\u2223\u03c91\u200b\u2223<\/span>\u500d<span aria-hidden=\"true\">\u2192y=Asin\u03c9x<\/span>\uff1b\u5e73\u79fb<span aria-hidden=\"true\">\u2223\u03c9\u03c6\u200b\u2223<\/span>\u4e2a\u5355\u4f4d<span aria-hidden=\"true\">\u2192y=Asin(\u03c9x+\u03c6)<\/span>\uff1b\u5e73\u79fb<span aria-hidden=\"true\">\u2223B\u2223<\/span>\u4e2a\u5355\u4f4d<span aria-hidden=\"true\">\u2192y=Asin(\u03c9x+\u03c6)+B<\/span>\uff08\u4e0a\u52a0\u4e0b\u51cf\uff09<\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<li>\u4e09\u89d2\u51fd\u6570\u7684\u5468\u671f\u3001\u5bf9\u79f0\u8f74\u548c\u5bf9\u79f0\u4e2d\u5fc3\uff1a\n<ul>\n<li>\u51fd\u6570<span aria-hidden=\"true\">y=sin(\u03c9x+\u03c6)<\/span>\uff0c<span aria-hidden=\"true\">x\u2208R<\/span>\u53ca\u51fd\u6570<span aria-hidden=\"true\">y=cos(\u03c9x+\u03c6)<\/span>\uff0c<span aria-hidden=\"true\">x\u2208R<\/span>\uff08<span aria-hidden=\"true\">A<\/span>\uff0c<span aria-hidden=\"true\">\u03c9<\/span>\uff0c<span aria-hidden=\"true\">\u03c6<\/span>\u4e3a\u5e38\u6570\uff0c\u4e14<span aria-hidden=\"true\">A\ue020=0<\/span>\uff09\u7684\u5468\u671f<span aria-hidden=\"true\">T=\u2223\u03c9\u22232\u03c0\u200b<\/span><\/li>\n<li>\u51fd\u6570<span aria-hidden=\"true\">y=tan(\u03c9x+\u03c6)<\/span>\uff0c<span aria-hidden=\"true\">x\ue020=k\u03c0+2\u03c0\u200b<\/span>\uff0c<span aria-hidden=\"true\">k\u2208Z<\/span>\uff08<span aria-hidden=\"true\">A<\/span>\uff0c<span aria-hidden=\"true\">\u03c9<\/span>\uff0c<span aria-hidden=\"true\">\u03c6<\/span>\u4e3a\u5e38\u6570\uff0c\u4e14<span aria-hidden=\"true\">A\ue020=0<\/span>\uff09\u7684\u5468\u671f<span aria-hidden=\"true\">T=\u2223\u03c9\u2223\u03c0\u200b<\/span><\/li>\n<li>\u6c42\u51fd\u6570<span aria-hidden=\"true\">y=Asin(\u03c9x+\u03c6)<\/span>\u56fe\u50cf\u7684\u5bf9\u79f0\u8f74\u4e0e\u5bf9\u79f0\u4e2d\u5fc3\uff0c\u53ea\u9700\u4ee4<span aria-hidden=\"true\">\u03c9x+\u03c6=k\u03c0+2\u03c0\u200b<\/span>\uff08<span aria-hidden=\"true\">k\u2208Z<\/span>\uff09\u4e0e<span aria-hidden=\"true\">\u03c9x+\u03c6=k\u03c0<\/span>\uff08<span aria-hidden=\"true\">k\u2208Z<\/span>\uff09\u89e3\u51fa<span aria-hidden=\"true\">x<\/span>\u5373\u53ef\uff0c\u4f59\u5f26\u51fd\u6570\u53ef\u4e0e\u6b63\u5f26\u51fd\u6570\u7c7b\u6bd4\u53ef\u5f97<\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h3>\u7b2c\u4e09\u7ae0\uff1a\u4e09\u89d2\u6052\u7b49\u53d8\u6362<\/h3>\n<div>\u00a0<\/div>\n<h4>$3.1.1 \u4e24\u89d2\u5dee\u7684\u4f59\u5f26\u516c\u5f0f<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li>15\u00b0 \u7684\u4e09\u89d2\u51fd\u6570\u503c\uff1a<\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<div>\n<div>\n<table>\n<thead>\n<tr>\n<th><span aria-hidden=\"true\">\u03b1<\/span><\/th>\n<th><span aria-hidden=\"true\">sin\u03b1<\/span><\/th>\n<th><span aria-hidden=\"true\">cos\u03b1<\/span><\/th>\n<th><span aria-hidden=\"true\">tan\u03b1<\/span><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><span aria-hidden=\"true\">15\u2218<\/span><\/td>\n<td><span aria-hidden=\"true\">46\u200b\u22122\u200b\u200b<\/span><\/td>\n<td><span aria-hidden=\"true\">46\u200b+2\u200b\u200b<\/span><\/td>\n<td><span aria-hidden=\"true\">2\u22123\u200b<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<div>\u00a0<\/div>\n<h4>$3.1.2 \u4e24\u89d2\u548c\u4e0e\u5dee\u7684\u6b63\u5f26\u3001\u4f59\u5f26\u3001\u6b63\u5207\u516c\u5f0f<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li><span aria-hidden=\"true\">sin(\u03b1+\u03b2)=sin\u03b1cos\u03b2+cos\u03b1sin\u03b2<\/span><\/li>\n<li><span aria-hidden=\"true\">sin(\u03b1\u2212\u03b2)=sin\u03b1cos\u03b2\u2212cos\u03b1sin\u03b2<\/span><\/li>\n<li><span aria-hidden=\"true\">cos(\u03b1+\u03b2)=cos\u03b1cos\u03b2\u2212sin\u03b1sin\u03b2<\/span><\/li>\n<li><span aria-hidden=\"true\">cos(\u03b1\u2212\u03b2)=cos\u03b1cos\u03b2+sin\u03b1sin\u03b2<\/span><\/li>\n<li><span aria-hidden=\"true\">tan(\u03b1+\u03b2)=1\u2212tan\u03b1tan\u03b2tan\u03b1+tan\u03b2\u200b<\/span><\/li>\n<li><span aria-hidden=\"true\">tan(\u03b1\u2212\u03b2)=1+tan\u03b1tan\u03b2tan\u03b1\u2212tan\u03b2\u200b<\/span><\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h4>$3.1.3 \u4e8c\u500d\u89d2\u7684\u6b63\u5f26\u3001\u4f59\u5f26\u3001\u6b63\u5207\u516c\u5f0f<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li><span aria-hidden=\"true\">sin2\u03b1=2sin\u03b1cos\u03b1<\/span>\uff0c\u53d8\u5f62\uff1a<span aria-hidden=\"true\">sin\u03b1cos\u03b1=21\u200bsin2\u03b1<\/span><\/li>\n<li><span aria-hidden=\"true\">cos2\u03b1=cos2\u03b1\u2212sin2\u03b1=2cos2\u03b1\u22121=1\u22122sin2\u03b1<\/span><\/li>\n<li><span aria-hidden=\"true\">tan2\u03b1=1\u2212tan2\u03b12tan\u03b1\u200b<\/span><\/li>\n<li><span aria-hidden=\"true\">tan\u03b1=1+cos2\u03b1sin2\u03b1\u200b=sin2\u03b11\u2212cos2\u03b1\u200b<\/span><\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h3>\u7b2c\u4e8c\u7ae0\uff1a\u5e73\u9762\u5411\u91cf<\/h3>\n<div>\u00a0<\/div>\n<h4>$2.1.2 \u5411\u91cf\u7684\u51e0\u4f55\u8868\u793a<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li>\u5e26\u6709\u65b9\u5411\u7684\u7ebf\u6bb5\u53eb\u505a\u6709\u5411\u7ebf\u6bb5\uff0c\u6709\u5411\u7ebf\u6bb5\u5305\u542b\u4e09\u4e2a\u8981\u7d20\uff1a\u8d77\u70b9\u3001\u65b9\u5411\u3001\u957f\u5ea6\u3002<\/li>\n<li>\u5411\u91cf<span aria-hidden=\"true\">AB<\/span>\u7684\u5927\u5c0f\uff0c\u4e5f\u5c31\u662f\u5411\u91cf<span aria-hidden=\"true\">AB<\/span>\u7684\u957f\u5ea6\uff08\u6216\u79f0\u6a21\uff09\uff0c\u8bb0\u4f5c<span aria-hidden=\"true\">\u2223AB\u2223<\/span>\uff1b\u957f\u5ea6\u4e3a\u96f6\u7684\u5411\u91cf\u53eb\u505a\u96f6\u5411\u91cf\uff1b\u957f\u5ea6\u7b49\u4e8e 1 \u4e2a\u5355\u4f4d\u7684\u5411\u91cf\u53eb\u505a\u5355\u4f4d\u5411\u91cf\u3002<\/li>\n<li>\u65b9\u5411\u76f8\u540c\u6216\u76f8\u53cd\u7684\u975e\u96f6\u5411\u91cf\u53eb\u505a\u5e73\u884c\u5411\u91cf\uff08\u6216\u5171\u7ebf\u5411\u91cf\uff09\uff0c\u89c4\u5b9a\uff1a\u96f6\u5411\u91cf\u4e0e\u4efb\u610f\u5411\u91cf\u5e73\u884c\u3002<\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h4>$2.1.3 \u76f8\u7b49\u5411\u91cf\u4e0e\u5171\u7ebf\u5411\u91cf<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li>\u957f\u5ea6\u76f8\u7b49\u4e14\u65b9\u5411\u76f8\u540c\u7684\u5411\u91cf\u53eb\u505a\u76f8\u7b49\u5411\u91cf\u3002<\/li>\n<li>\u5e73\u9762\u5411\u91cf\u5171\u7ebf\u5b9a\u7406\uff1a\u5411\u91cf<span aria-hidden=\"true\">a<\/span>\uff08<span aria-hidden=\"true\">a\ue020=0<\/span>\uff09\u4e0e<span aria-hidden=\"true\">b<\/span>\u5171\u7ebf\uff0c\u5f53\u4e14\u4ec5\u5f53\u6709\u552f\u4e00\u4e00\u4e2a\u5b9e\u6570<span aria-hidden=\"true\">\u03bb<\/span>\uff0c\u4f7f<span aria-hidden=\"true\">b=\u03bba<\/span><\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h4>$2.3.3 \u5e73\u9762\u5411\u91cf\u7684\u5750\u6807\u8fd0\u7b97<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li>\u8bbe<span aria-hidden=\"true\">a=(x1\u200b,y1\u200b)<\/span>\uff0c<span aria-hidden=\"true\">b=(x2\u200b,y2\u200b)<\/span>\u5219\uff1a\n<ul>\n<li><span aria-hidden=\"true\">a+b=(x1\u200b+x2\u200b,y1\u200b+y2\u200b)<\/span><\/li>\n<li><span aria-hidden=\"true\">a\u2212b=(x1\u200b\u2212x2\u200b,y1\u200b\u2212y2\u200b)<\/span><\/li>\n<li><span aria-hidden=\"true\">\u03bba=(\u03bbx1\u200b,\u03bby1\u200b)<\/span><\/li>\n<li><span aria-hidden=\"true\">a\u2225b\u21d4x1\u200by2\u200b=x2\u200by1\u200b<\/span><\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<li>\u8bbe<span aria-hidden=\"true\">A(x1\u200b,y1\u200b)<\/span>\uff0c<span aria-hidden=\"true\">B(x2\u200b,y2\u200b)<\/span>\uff0c\u5219\uff1a<span aria-hidden=\"true\">AB=(x2\u200b\u2212x1\u200b,y2\u200b\u2212y1\u200b)<\/span><\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h4>$2.3.4 \u5e73\u9762\u5411\u91cf\u5171\u7ebf\u7684\u5750\u6807\u8868\u793a<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li>\u8bbe<span aria-hidden=\"true\">A(x1\u200b,y1\u200b)<\/span>\uff0c<span aria-hidden=\"true\">B(x2\u200b,y2\u200b)<\/span>\uff0c<span aria-hidden=\"true\">C(x3\u200b,y3\u200b)<\/span>\uff0c\u5219\u7ebf\u6bb5<span aria-hidden=\"true\">AB<\/span>\u4e2d\u70b9\u5750\u6807\u4e3a<span aria-hidden=\"true\">(2&#215;1\u200b+x2\u200b\u200b,2y1\u200b+y2\u200b\u200b)<\/span><\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h4>$2.4.2 \u5e73\u9762\u5411\u91cf\u6570\u91cf\u79ef\u7684\u5750\u6807\u8868\u793a\u3001\u6a21\u3001\u5939\u89d2<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li>\u8bbe<span aria-hidden=\"true\">a=(x1\u200b,y1\u200b)<\/span>\uff0c<span aria-hidden=\"true\">b=(x2\u200b,y2\u200b)<\/span>\uff0c\u5219\uff1a\n<ul>\n<li><span aria-hidden=\"true\">a\u22c5b=x1\u200bx2\u200b+y1\u200by2\u200b<\/span><\/li>\n<li><span aria-hidden=\"true\">\u2223a\u2223=x12\u200b+y12\u200b\u200b<\/span><\/li>\n<li><span aria-hidden=\"true\">a\u22a5b\u21d4a\u22c5b=0\u21d4x1\u200bx2\u200b+y1\u200by2\u200b=0<\/span><\/li>\n<li><span aria-hidden=\"true\">a\u2225b\u21d4a=\u03bbb\u21d4x1\u200by2\u200b\u2212x2\u200by1\u200b=0<\/span><\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<li>\u8bbe<span aria-hidden=\"true\">A(x1\u200b,y1\u200b)<\/span>\uff0c<span aria-hidden=\"true\">B(x2\u200b,y2\u200b)<\/span>\uff0c\u5219\uff1a<span aria-hidden=\"true\">\u2223AB\u2223=(x2\u200b\u2212x1\u200b)2+(y2\u200b\u2212y1\u200b)2\u200b<\/span><\/li>\n<li>\u4e24\u5411\u91cf\u7684\u5939\u89d2\u516c\u5f0f\uff1a<span aria-hidden=\"true\">cos\u03b8=\u2223a\u2223\u2223b\u2223a\u22c5b\u200b=x12\u200b+y12\u200b\u200b\u22c5x22\u200b+y22\u200b\u200bx1\u200bx2\u200b+y1\u200by2\u200b\u200b<\/span><\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h2>\u5fc5\u4fee 5 \u6570\u5b66\u77e5\u8bc6\u70b9<\/h2>\n<div>\u00a0<\/div>\n<h3>\u7b2c\u4e00\u7ae0\uff1a\u89e3\u4e09\u89d2\u5f62<\/h3>\n<div>\u00a0<\/div>\n<ol>\n<li>\u6b63\u5f26\u5b9a\u7406\uff1a<span aria-hidden=\"true\">sinAa\u200b=sinBb\u200b=sinCc\u200b=2R<\/span>\uff08\u5176\u4e2d<span aria-hidden=\"true\">R<\/span>\u4e3a<span aria-hidden=\"true\">\u25b3ABC<\/span>\u5916\u63a5\u5706\u7684\u534a\u5f84\uff09\n<ul>\n<li><span aria-hidden=\"true\">a=2RsinA<\/span>\uff0c<span aria-hidden=\"true\">b=2RsinB<\/span>\uff0c<span aria-hidden=\"true\">c=2RsinC<\/span><\/li>\n<li><span aria-hidden=\"true\">sinA=2Ra\u200b<\/span>\uff0c<span aria-hidden=\"true\">sinB=2Rb\u200b<\/span>\uff0c<span aria-hidden=\"true\">sinC=2Rc\u200b<\/span><\/li>\n<li><span aria-hidden=\"true\">a:b:c=sinA:sinB:sinC<\/span><\/li>\n<li>\u7528\u9014\uff1a\u5df2\u77e5\u4e09\u89d2\u5f62\u4e24\u89d2\u548c\u4efb\u4e00\u8fb9\uff0c\u6c42\u5176\u5b83\u5143\u7d20\uff1b\u5df2\u77e5\u4e09\u89d2\u5f62\u4e24\u8fb9\u548c\u5176\u4e2d\u4e00\u8fb9\u7684\u5bf9\u89d2\uff0c\u6c42\u5176\u5b83\u5143\u7d20<\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<li>\u4f59\u5f26\u5b9a\u7406\uff1a\n<ul>\n<li><span aria-hidden=\"true\">a2=b2+c2\u22122bccosA<\/span><\/li>\n<li><span aria-hidden=\"true\">b2=a2+c2\u22122accosB<\/span><\/li>\n<li><span aria-hidden=\"true\">c2=a2+b2\u22122abcosC<\/span><\/li>\n<li><span aria-hidden=\"true\">cosA=2bcb2+c2\u2212a2\u200b<\/span><\/li>\n<li><span aria-hidden=\"true\">cosB=2aca2+c2\u2212b2\u200b<\/span><\/li>\n<li><span aria-hidden=\"true\">cosC=2aba2+b2\u2212c2\u200b<\/span><\/li>\n<li>\u7528\u9014\uff1a\u5df2\u77e5\u4e09\u89d2\u5f62\u4e24\u8fb9\u53ca\u5176\u5939\u89d2\uff0c\u6c42\u5176\u5b83\u5143\u7d20\uff1b\u5df2\u77e5\u4e09\u89d2\u5f62\u4e09\u8fb9\uff0c\u6c42\u5176\u5b83\u5143\u7d20<\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<li>\u4e09\u89d2\u5f62\u9762\u79ef\u516c\u5f0f\uff1a<span aria-hidden=\"true\">S\u25b3ABC\u200b=21\u200babsinC=21\u200bbcsinA=21\u200bacsinB<\/span><\/li>\n<li>\u4e09\u89d2\u5f62\u5185\u89d2\u548c\u5b9a\u7406\uff1a\u5728<span aria-hidden=\"true\">\u25b3ABC<\/span>\u4e2d\uff0c\u6709<span aria-hidden=\"true\">A+B+C=\u03c0\u21d4C=\u03c0\u2212(A+B)\u21d42C\u200b=2\u03c0\u200b\u22122A+B\u200b\u21d42C=2\u03c0\u22122(A+B)<\/span><\/li>\n<li>\u4e00\u4e2a\u5e38\u7528\u7ed3\u8bba\uff1a\u5728<span aria-hidden=\"true\">\u25b3ABC<\/span>\u4e2d\uff0c<span aria-hidden=\"true\">a&gt;b\u21d4sinA&gt;sinB\u21d4A&gt;B<\/span>\uff1b\u82e5<span aria-hidden=\"true\">sin2A=sin2B<\/span>\uff0c\u5219<span aria-hidden=\"true\">A=B<\/span>\u6216<span aria-hidden=\"true\">A+B=2\u03c0\u200b<\/span>\uff0c\u7279\u522b\u6ce8\u610f\uff0c\u5728\u4e09\u89d2\u51fd\u6570\u4e2d\uff0c<span aria-hidden=\"true\">sinA&gt;sinB\u21d4A&gt;B<\/span>\u4e0d\u6210\u7acb<\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h3>\u7b2c\u4e8c\u7ae0\uff1a\u6570\u5217<\/h3>\n<div>\u00a0<\/div>\n<ol>\n<li>\u6570\u5217\u4e2d<span aria-hidden=\"true\">an\u200b<\/span>\u4e0e<span aria-hidden=\"true\">Sn\u200b<\/span>\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a<span aria-hidden=\"true\">an\u200b={S1\u200bSn\u200b\u2212Sn\u22121\u200b\u200b(n=1)(n\u22652)\u200b<\/span>\uff0c\u6ce8\u610f\u901a\u9879\u80fd\u5408\u5e76<\/li>\n<li>\u7b49\u5dee\u6570\u5217\uff1a\n<ul>\n<li>\u5b9a\u4e49\uff1a\u5982\u679c\u4e00\u4e2a\u6570\u5217\u4ece\u7b2c 2 \u9879\u8d77\uff0c\u6bcf\u4e00\u9879\u4e0e\u5b83\u7684\u524d\u4e00\u9879\u7684\u5dee\u7b49\u4e8e\u540c\u4e00\u4e2a\u5e38\u6570\uff0c\u5373<span aria-hidden=\"true\">an\u200b\u2212an\u22121\u200b=d<\/span>\uff08<span aria-hidden=\"true\">n\u22652<\/span>\uff0c<span aria-hidden=\"true\">n\u2208N<\/span>\uff09\uff0c\u90a3\u4e48\u8fd9\u4e2a\u6570\u5217\u5c31\u53eb\u505a\u7b49\u5dee\u6570\u5217<\/li>\n<li>\u7b49\u5dee\u4e2d\u9879\uff1a\u82e5\u4e09\u6570<span aria-hidden=\"true\">a<\/span>\uff0c<span aria-hidden=\"true\">A<\/span>\uff0c<span aria-hidden=\"true\">b<\/span>\u6210\u7b49\u5dee\u6570\u5217\uff0c\u5219<span aria-hidden=\"true\">A=2a+b\u200b<\/span><\/li>\n<li>\u901a\u9879\u516c\u5f0f\uff1a<span aria-hidden=\"true\">an\u200b=a1\u200b+(n\u22121)d=am\u200b+(n\u2212m)d<\/span>\u6216<span aria-hidden=\"true\">an\u200b=pn+q<\/span>\uff08<span aria-hidden=\"true\">p<\/span>\u3001<span aria-hidden=\"true\">q<\/span>\u662f\u5e38\u6570\uff09<\/li>\n<li>\u524d<span aria-hidden=\"true\">n<\/span>\u9879\u548c\u516c\u5f0f\uff1a<span aria-hidden=\"true\">Sn\u200b=na1\u200b+2n(n\u22121)\u200bd=2n(a1\u200b+an\u200b)\u200b<\/span><\/li>\n<li>\u5e38\u7528\u6027\u8d28\uff1a\n<ul>\n<li>\u82e5<span aria-hidden=\"true\">m+n=p+q<\/span>\uff08<span aria-hidden=\"true\">m<\/span>\uff0c<span aria-hidden=\"true\">n<\/span>\uff0c<span aria-hidden=\"true\">p<\/span>\uff0c<span aria-hidden=\"true\">q\u2208N+\u200b<\/span>\uff09\uff0c\u5219<span aria-hidden=\"true\">am\u200b+an\u200b=ap\u200b+aq\u200b<\/span><\/li>\n<li>\u4e0b\u6807\u4e3a\u7b49\u5dee\u6570\u5217\u7684\u9879\uff08<span aria-hidden=\"true\">ak\u200b<\/span>\uff0c<span aria-hidden=\"true\">ak+m\u200b<\/span>\uff0c<span aria-hidden=\"true\">ak+2m\u200b<\/span>\uff0c<span aria-hidden=\"true\">\u22ef<\/span>\uff09\uff0c\u4ecd\u7ec4\u6210\u7b49\u5dee\u6570\u5217<\/li>\n<li>\u6570\u5217<span aria-hidden=\"true\">{\u03bban\u200b+b}<\/span>\uff08<span aria-hidden=\"true\">\u03bb<\/span>\uff0c<span aria-hidden=\"true\">b<\/span>\u4e3a\u5e38\u6570\uff09\u4ecd\u4e3a\u7b49\u5dee\u6570\u5217<\/li>\n<li>\u82e5<span aria-hidden=\"true\">{an\u200b}<\/span>\u3001<span aria-hidden=\"true\">{bn\u200b}<\/span>\u662f\u7b49\u5dee\u6570\u5217\uff0c\u5219<span aria-hidden=\"true\">{kan\u200b}<\/span>\u3001<span aria-hidden=\"true\">{kan\u200b+pbn\u200b}<\/span>\uff08<span aria-hidden=\"true\">k<\/span>\u3001<span aria-hidden=\"true\">p<\/span>\u662f\u975e\u96f6\u5e38\u6570\uff09\u3001<span aria-hidden=\"true\">{ap+nq\u200b}<\/span>\uff08<span aria-hidden=\"true\">p<\/span>\uff0c<span aria-hidden=\"true\">q\u2208N\u2217<\/span>\uff09\u7b49\u4e5f\u6210\u7b49\u5dee\u6570\u5217<\/li>\n<li>\u5355\u8c03\u6027\uff1a<span aria-hidden=\"true\">{an\u200b}<\/span>\u7684\u516c\u5dee\u4e3a<span aria-hidden=\"true\">d<\/span>\uff0c\u5219<span aria-hidden=\"true\">d&gt;0\u21d4{an\u200b}<\/span>\u4e3a\u9012\u589e\u6570\u5217\uff1b<span aria-hidden=\"true\">d&lt;0\u21d4{an\u200b}<\/span>\u4e3a\u9012\u51cf\u6570\u5217\uff1b<span aria-hidden=\"true\">d=0\u21d4{an\u200b}<\/span>\u4e3a\u5e38\u6570\u5217<\/li>\n<li>\u6570\u5217<span aria-hidden=\"true\">{an\u200b}<\/span>\u4e3a\u7b49\u5dee\u6570\u5217<span aria-hidden=\"true\">\u21d4an\u200b=pn+q<\/span>\uff08<span aria-hidden=\"true\">p<\/span>\uff0c<span aria-hidden=\"true\">q<\/span>\u662f\u5e38\u6570\uff09<\/li>\n<li>\u82e5\u7b49\u5dee\u6570\u5217<span aria-hidden=\"true\">{an\u200b}<\/span>\u7684\u524d<span aria-hidden=\"true\">n<\/span>\u9879\u548c<span aria-hidden=\"true\">Sn\u200b<\/span>\uff0c\u5219<span aria-hidden=\"true\">Sk\u200b<\/span>\u3001<span aria-hidden=\"true\">S2k\u200b\u2212Sk\u200b<\/span>\u3001<span aria-hidden=\"true\">S3k\u200b\u2212S2k\u200b<\/span><span aria-hidden=\"true\">\u22ef<\/span>\u662f\u7b49\u5dee\u6570\u5217<\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<li>\u7b49\u6bd4\u6570\u5217\uff1a\n<ul>\n<li>\u5b9a\u4e49\uff1a\u5982\u679c\u4e00\u4e2a\u6570\u5217\u4ece\u7b2c 2 \u9879\u8d77\uff0c\u6bcf\u4e00\u9879\u4e0e\u5b83\u7684\u524d\u4e00\u9879\u7684\u6bd4\u7b49\u4e8e\u540c\u4e00\u4e2a\u5e38\u6570\uff0c\u90a3\u4e48\u8fd9\u4e2a\u6570\u5217\u5c31\u53eb\u505a\u7b49\u6bd4\u6570\u5217<\/li>\n<li>\u7b49\u6bd4\u4e2d\u9879\uff1a\u82e5\u4e09\u6570<span aria-hidden=\"true\">a<\/span>\uff0c<span aria-hidden=\"true\">G<\/span>\uff0c<span aria-hidden=\"true\">b<\/span>\u6210\u7b49\u6bd4\u6570\u5217\uff0c\u5219<span aria-hidden=\"true\">G2=ab<\/span>\uff08<span aria-hidden=\"true\">ab<\/span>\u540c\u53f7\uff09\uff0c\u53cd\u4e4b\u4e0d\u4e00\u5b9a\u6210\u7acb<\/li>\n<li>\u901a\u9879\u516c\u5f0f\uff1a<span aria-hidden=\"true\">an\u200b=a1\u200bqn\u22121=am\u200bqn\u2212m<\/span><\/li>\n<li>\u524d<span aria-hidden=\"true\">n<\/span>\u9879\u548c\u516c\u5f0f\uff1a<span aria-hidden=\"true\">Sn\u200b=1\u2212qa1\u200b(1\u2212qn)\u200b=1\u2212qa1\u200b\u2212an\u200bq\u200b<\/span>\uff08<span aria-hidden=\"true\">q\ue020=1<\/span>\uff09<\/li>\n<li>\u5e38\u7528\u6027\u8d28\uff1a\n<ul>\n<li>\u82e5<span aria-hidden=\"true\">m+n=p+q<\/span>\uff08<span aria-hidden=\"true\">m<\/span>\uff0c<span aria-hidden=\"true\">n<\/span>\uff0c<span aria-hidden=\"true\">p<\/span>\uff0c<span aria-hidden=\"true\">q\u2208N+\u200b<\/span>\uff09\uff0c\u5219<span aria-hidden=\"true\">am\u200b\u22c5an\u200b=ap\u200b\u22c5aq\u200b<\/span><\/li>\n<li><span aria-hidden=\"true\">ak\u200b<\/span>\uff0c<span aria-hidden=\"true\">ak+m\u200b<\/span>\uff0c<span aria-hidden=\"true\">ak+2m\u200b<\/span>\uff0c<span aria-hidden=\"true\">\u22ef<\/span>\u4e3a\u7b49\u6bd4\u6570\u5217\uff0c\u516c\u6bd4\u4e3a<span aria-hidden=\"true\">qm<\/span>\uff08\u4e0b\u6807\u6210\u7b49\u5dee\u6570\u5217\uff0c\u5219\u5bf9\u5e94\u7684\u9879\u6210\u7b49\u6bd4\u6570\u5217\uff09<\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h2>\u9009\u4fee\u6570\u5b66\u77e5\u8bc6\u70b9<\/h2>\n<div>\u00a0<\/div>\n<h3>\u4e13\u9898\u4e00\uff1a\u5e38\u7528\u903b\u8f91\u7528\u8bed<\/h3>\n<div>\u00a0<\/div>\n<ol>\n<li>\u547d\u9898\uff1a\u53ef\u4ee5\u5224\u65ad\u771f\u5047\u7684\u8bed\u53e5\u53eb\u547d\u9898\uff1b\u903b\u8f91\u8054\u7ed3\u8bcd\uff1a\u201c\u6216\u201d\u201c\u4e14\u201d\u201c\u975e\u201d \u8fd9\u4e9b\u8bcd\u5c31\u53eb\u505a\u903b\u8f91\u8054\u7ed3\u8bcd\uff1b\u7b80\u5355\u547d\u9898\uff1a\u4e0d\u542b\u903b\u8f91\u8054\u7ed3\u8bcd\u7684\u547d\u9898\uff1b\u590d\u5408\u547d\u9898\uff1a\u7531\u7b80\u5355\u547d\u9898\u4e0e\u903b\u8f91\u8054\u7ed3\u8bcd\u6784\u6210\u7684\u547d\u9898\uff0c\u5e38\u7528\u5c0f\u5199\u7684\u62c9\u4e01\u5b57\u6bcd<span aria-hidden=\"true\">p<\/span>\uff0c<span aria-hidden=\"true\">q<\/span>\uff0c<span aria-hidden=\"true\">r<\/span>\uff0c<span aria-hidden=\"true\">s<\/span>\uff0c<span aria-hidden=\"true\">\u22ef<\/span>\u8868\u793a\u547d\u9898<\/li>\n<li>\u56db\u79cd\u547d\u9898\u53ca\u5176\u76f8\u4e92\u5173\u7cfb\uff1a\u539f\u547d\u9898\uff1a\u82e5<span aria-hidden=\"true\">p<\/span>\uff0c\u5219<span aria-hidden=\"true\">q<\/span>\uff1b\u9006\u547d\u9898\uff1a\u82e5<span aria-hidden=\"true\">q<\/span>\uff0c\u5219<span aria-hidden=\"true\">p<\/span>\uff1b\u5426\u547d\u9898\uff1a\u82e5<span aria-hidden=\"true\">\u00acp<\/span>\uff0c\u5219<span aria-hidden=\"true\">\u00acq<\/span>\uff1b\u9006\u5426\u547d\u9898\uff1a\u82e5<span aria-hidden=\"true\">\u00acq<\/span>\uff0c\u5219<span aria-hidden=\"true\">\u00acp<\/span>\n<ul>\n<li>\u56db\u79cd\u547d\u9898\u7684\u771f\u5047\u6027\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a\u4e24\u4e2a\u547d\u9898\u4e92\u4e3a\u9006\u5426\u547d\u9898\uff0c\u5b83\u4eec\u6709\u76f8\u540c\u7684\u771f\u5047\u6027\uff1b\u4e24\u4e2a\u547d\u9898\u4e3a\u4e92\u9006\u547d\u9898\u6216\u4e92\u5426\u547d\u9898\uff0c\u5b83\u4eec\u7684\u771f\u5047\u6027\u6ca1\u6709\u5173\u7cfb<\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<li>\u5145\u5206\u6761\u4ef6\u3001\u5fc5\u8981\u6761\u4ef6\u4e0e\u5145\u8981\u6761\u4ef6\uff1a\n<ul>\n<li>\u4e00\u822c\u5730\uff0c\u5982\u679c\u5df2\u77e5<span aria-hidden=\"true\">p\u21d2q<\/span>\uff0c\u90a3\u4e48\u5c31\u8bf4\uff1a<span aria-hidden=\"true\">p<\/span>\u662f<span aria-hidden=\"true\">q<\/span>\u7684\u5145\u5206\u6761\u4ef6\uff0c<span aria-hidden=\"true\">q<\/span>\u662f<span aria-hidden=\"true\">p<\/span>\u7684\u5fc5\u8981\u6761\u4ef6\uff1b\u82e5<span aria-hidden=\"true\">p\u21d4q<\/span>\uff0c\u5219<span aria-hidden=\"true\">p<\/span>\u662f<span aria-hidden=\"true\">q<\/span>\u7684\u5145\u5206\u5fc5\u8981\u6761\u4ef6\uff0c\u7b80\u79f0\u5145\u8981\u6761\u4ef6<\/li>\n<li>\u5145\u5206\u6761\u4ef6\u3001\u5fc5\u8981\u6761\u4ef6\u4e0e\u5145\u8981\u6761\u4ef6\u4e3b\u8981\u7528\u6765\u533a\u5206\u547d\u9898\u7684\u6761\u4ef6<span aria-hidden=\"true\">p<\/span>\u4e0e\u7ed3\u8bba<span aria-hidden=\"true\">q<\/span>\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a\n<ul>\n<li>\u4ece\u903b\u8f91\u63a8\u7406\u5173\u7cfb\u4e0a\u770b\uff1a\u82e5<span aria-hidden=\"true\">p\u21d2q<\/span>\uff0c\u5219<span aria-hidden=\"true\">p<\/span>\u662f<span aria-hidden=\"true\">q<\/span>\u5145\u5206\u6761\u4ef6\uff0c<span aria-hidden=\"true\">q<\/span>\u662f<span aria-hidden=\"true\">p<\/span>\u7684\u5fc5\u8981\u6761\u4ef6\uff1b\u82e5<span aria-hidden=\"true\">p\u21d2q<\/span>\uff0c\u4f46<span aria-hidden=\"true\">q\u21cfp<\/span>\uff0c\u5219<span aria-hidden=\"true\">p<\/span>\u662f<span aria-hidden=\"true\">q<\/span>\u5145\u5206\u800c\u4e0d\u5fc5\u8981\u6761\u4ef6\uff1b\u82e5<span aria-hidden=\"true\">p\u21cfq<\/span>\uff0c\u4f46<span aria-hidden=\"true\">q\u21d2p<\/span>\uff0c\u5219<span aria-hidden=\"true\">p<\/span>\u662f<span aria-hidden=\"true\">q<\/span>\u5fc5\u8981\u800c\u4e0d\u5145\u5206\u6761\u4ef6\uff1b\u82e5<span aria-hidden=\"true\">p\u21d2q<\/span>\u4e14<span aria-hidden=\"true\">q\u21d2p<\/span>\uff0c\u5219<span aria-hidden=\"true\">p<\/span>\u662f<span aria-hidden=\"true\">q<\/span>\u7684\u5145\u8981\u6761\u4ef6\uff1b\u82e5<span aria-hidden=\"true\">p\u21cfq<\/span>\u4e14<span aria-hidden=\"true\">q\u21cfp<\/span>\uff0c\u5219<span aria-hidden=\"true\">p<\/span>\u662f<span aria-hidden=\"true\">q<\/span>\u7684\u65e2\u4e0d\u5145\u5206\u4e5f\u4e0d\u5fc5\u8981\u6761\u4ef6<\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<h3>\u5706\u9525\u66f2\u7ebf<\/h3>\n<div>\u00a0<\/div>\n<h4>\u692d\u5706<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li>\u692d\u5706\u7684\u5b9a\u4e49\uff1a\u5e73\u9762\u5185\u4e0e\u4e24\u4e2a\u5b9a\u70b9<span aria-hidden=\"true\">F1\u200b<\/span>\uff0c<span aria-hidden=\"true\">F2\u200b<\/span>\u7684\u8ddd\u79bb\u4e4b\u548c\u7b49\u4e8e\u5e38\u6570\uff08\u5927\u4e8e<span aria-hidden=\"true\">\u2223F1\u200bF2\u200b\u2223<\/span>\uff09\u7684\u70b9\u7684\u8f68\u8ff9\u53eb\u505a\u692d\u5706\u3002\u8fd9\u4e24\u4e2a\u5b9a\u70b9<span aria-hidden=\"true\">F1\u200b<\/span>\uff0c<span aria-hidden=\"true\">F2\u200b<\/span>\u53eb\u505a\u692d\u5706\u7684\u7126\u70b9\uff0c\u4e24\u7126\u70b9\u95f4\u7684\u8ddd\u79bb\u53eb\u505a\u692d\u5706\u7684\u7126\u8ddd\u3002\u692d\u5706\u7684\u5b9a\u4e49\u7528\u7b26\u53f7\u8bed\u8a00\u8868\u793a\uff1a<span aria-hidden=\"true\">\u2223MF1\u200b\u2223+\u2223MF2\u200b\u2223=2a<\/span>\uff08<span aria-hidden=\"true\">2a&gt;\u2223F1\u200bF2\u200b\u2223<\/span>\uff09\n<ul>\n<li>\u8bf4\u660e\uff1a\u5f53<span aria-hidden=\"true\">\u2223MF1\u200b\u2223+\u2223MF2\u200b\u2223=2a&lt;\u2223F1\u200bF2\u200b\u2223<\/span>\u65f6\uff0c\u65e0\u8f68\u8ff9\uff1b\u5f53<span aria-hidden=\"true\">\u2223MF1\u200b\u2223+\u2223MF2\u200b\u2223=2a=\u2223F1\u200bF2\u200b\u2223<\/span>\u65f6\uff0c\u8f68\u8ff9\u4e3a\u7ebf\u6bb5<span aria-hidden=\"true\">F1\u200bF2\u200b<\/span><\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<li>\u692d\u5706\u7684\u6807\u51c6\u65b9\u7a0b\uff1a\n<ul>\n<li>\u7126\u70b9\u5728<span aria-hidden=\"true\">x<\/span>\u8f74\u4e0a\u7684\u692d\u5706\u7684\u6807\u51c6\u65b9\u7a0b\uff1a<span aria-hidden=\"true\">a2x2\u200b+b2y2\u200b=1<\/span>\uff08<span aria-hidden=\"true\">a&gt;b&gt;0<\/span>\uff09\uff0c\u7126\u70b9<span aria-hidden=\"true\">F1\u200b(\u2212c,0)<\/span>\uff0c<span aria-hidden=\"true\">F2\u200b(c,0)<\/span><\/li>\n<li>\u7126\u70b9\u5728<span aria-hidden=\"true\">y<\/span>\u8f74\u4e0a\u7684\u692d\u5706\u7684\u6807\u51c6\u65b9\u7a0b\uff1a<span aria-hidden=\"true\">a2y2\u200b+b2x2\u200b=1<\/span>\uff08<span aria-hidden=\"true\">a&gt;b&gt;0<\/span>\uff09\uff0c\u7126\u70b9<span aria-hidden=\"true\">F1\u200b(0,\u2212c)<\/span>\uff0c<span aria-hidden=\"true\">F2\u200b(0,c)<\/span><\/li>\n<li>\u5176\u4e2d<span aria-hidden=\"true\">a<\/span>\uff0c<span aria-hidden=\"true\">b<\/span>\uff0c<span aria-hidden=\"true\">c<\/span>\u51e0\u4f55\u610f\u4e49\uff1a<span aria-hidden=\"true\">a<\/span>\u8868\u793a\u957f\u8f74\u957f\u7684\u4e00\u534a\uff0c<span aria-hidden=\"true\">b<\/span>\u8868\u793a\u77ed\u8f74\u957f\u7684\u4e00\u534a\uff0c<span aria-hidden=\"true\">c<\/span>\u8868\u793a\u7126\u8ddd\u957f\u7684\u4e00\u534a\uff0c\u5e76\u4e14\u6709<span aria-hidden=\"true\">a2=b2+c2<\/span><\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<li>\u692d\u5706\u7684\u7b80\u5355\u51e0\u4f55\u6027\u8d28\uff08\u4ee5<span aria-hidden=\"true\">a2x2\u200b+b2y2\u200b=1<\/span>\uff08<span aria-hidden=\"true\">a&gt;b&gt;0<\/span>\uff09\u4e3a\u4f8b\uff09\uff1a\n<ul>\n<li>\u8303\u56f4\uff1a<span aria-hidden=\"true\">\u2223x\u2223\u2264a<\/span>\uff0c<span aria-hidden=\"true\">\u2223y\u2223\u2264b<\/span><\/li>\n<li>\u5bf9\u79f0\u6027\uff1a\u5173\u4e8e<span aria-hidden=\"true\">x<\/span>\u8f74\u3001<span aria-hidden=\"true\">y<\/span>\u8f74\u4ee5\u53ca\u539f\u70b9\u5bf9\u79f0\uff0c\u5bf9\u79f0\u8f74\u4e3a<span aria-hidden=\"true\">x<\/span>\u8f74\u3001<span aria-hidden=\"true\">y<\/span>\u8f74\uff0c\u5bf9\u79f0\u4e2d\u5fc3\u4e3a<span aria-hidden=\"true\">O(0,0)<\/span><\/li>\n<li>\u9876\u70b9\uff1a<span aria-hidden=\"true\">A1\u200b(\u2212a,0)<\/span>\uff0c<span aria-hidden=\"true\">A2\u200b(a,0)<\/span>\uff0c<span aria-hidden=\"true\">B1\u200b(0,\u2212b)<\/span>\uff0c<span aria-hidden=\"true\">B2\u200b(0,b)<\/span>\uff0c\u957f\u8f74\u957f<span aria-hidden=\"true\">\u2223A1\u200bA2\u200b\u2223=2a<\/span>\uff0c\u77ed\u8f74\u957f<span aria-hidden=\"true\">\u2223B1\u200bB2\u200b\u2223=2b<\/span><\/li>\n<li>\u79bb\u5fc3\u7387<span aria-hidden=\"true\">e=ac\u200b<\/span>\uff0c<span aria-hidden=\"true\">0&lt;e&lt;1<\/span>\uff0c<span aria-hidden=\"true\">e<\/span>\u8d8a\u5c0f\uff0c\u692d\u5706\u8d8a\u5706\uff1b<span aria-hidden=\"true\">e<\/span>\u8d8a\u5927\uff0c\u692d\u5706\u8d8a\u6241<\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<div>\n<div>\n<table>\n<thead>\n<tr>\n<th>\u7126\u70b9\u7684\u4f4d\u7f6e<\/th>\n<th>\u7126\u70b9\u5728<span aria-hidden=\"true\">x<\/span>\u8f74\u4e0a<\/th>\n<th>\u7126\u70b9\u5728<span aria-hidden=\"true\">y<\/span>\u8f74\u4e0a<\/th>\n<th>\u00a0<\/th>\n<th>\u00a0<\/th>\n<th>\u00a0<\/th>\n<th>\u00a0<\/th>\n<th>\u00a0<\/th>\n<th>\u00a0<\/th>\n<th>\u00a0<\/th>\n<th>\u00a0<\/th>\n<th>\u00a0<\/th>\n<th>\u00a0<\/th>\n<th>\u00a0<\/th>\n<th>\u00a0<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u6807\u51c6\u65b9\u7a0b<\/td>\n<td><span aria-hidden=\"true\">a2x2\u200b+b2y2\u200b=1<\/span>\uff08<span aria-hidden=\"true\">a&gt;b&gt;0<\/span>\uff09<\/td>\n<td><span aria-hidden=\"true\">a2y2\u200b+b2x2\u200b=1<\/span>\uff08<span aria-hidden=\"true\">a&gt;b&gt;0<\/span>\uff09<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>\u5b9a\u4e49<\/td>\n<td>\u5230\u4e24\u5b9a\u70b9<span aria-hidden=\"true\">F1\u200b<\/span>\u3001<span aria-hidden=\"true\">F2\u200b<\/span>\u7684\u8ddd\u79bb\u4e4b\u548c\u7b49\u4e8e\u5e38\u6570<span aria-hidden=\"true\">2a<\/span>\uff0c\u5373 $<\/td>\n<td>MF_1<\/td>\n<td>+<\/td>\n<td>MF_2<\/td>\n<td>= 2a$\uff08$2a &gt;<\/td>\n<td>F_1F_2<\/td>\n<td>$\uff09<\/td>\n<td>\u5230\u4e24\u5b9a\u70b9<span aria-hidden=\"true\">F1\u200b<\/span>\u3001<span aria-hidden=\"true\">F2\u200b<\/span>\u7684\u8ddd\u79bb\u4e4b\u548c\u7b49\u4e8e\u5e38\u6570<span aria-hidden=\"true\">2a<\/span>\uff0c\u5373 $<\/td>\n<td>MF_1<\/td>\n<td>+<\/td>\n<td>MF_2<\/td>\n<td>= 2a$\uff08$2a &gt;<\/td>\n<td>F_1F_2<\/td>\n<td>$\uff09<\/td>\n<\/tr>\n<tr>\n<td>\u8303\u56f4<\/td>\n<td><span aria-hidden=\"true\">\u2212a\u2264x\u2264a<\/span>\u4e14<span aria-hidden=\"true\">\u2212b\u2264y\u2264b<\/span><\/td>\n<td><span aria-hidden=\"true\">\u2212b\u2264x\u2264b<\/span>\u4e14<span aria-hidden=\"true\">\u2212a\u2264y\u2264a<\/span><\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>\u9876\u70b9<\/td>\n<td><span aria-hidden=\"true\">A1\u200b(\u2212a,0)<\/span>\uff0c<span aria-hidden=\"true\">A2\u200b(a,0)<\/span>\uff0c<span aria-hidden=\"true\">B1\u200b(0,\u2212b)<\/span>\uff0c<span aria-hidden=\"true\">B2\u200b(0,b)<\/span><\/td>\n<td><span aria-hidden=\"true\">A1\u200b(0,\u2212a)<\/span>\uff0c<span aria-hidden=\"true\">A2\u200b(0,a)<\/span>\uff0c<span aria-hidden=\"true\">B1\u200b(\u2212b,0)<\/span>\uff0c<span aria-hidden=\"true\">B2\u200b(b,0)<\/span><\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>\u8f74\u957f<\/td>\n<td>\u957f\u8f74\u7684\u957f<span aria-hidden=\"true\">=2a<\/span>\uff0c\u77ed\u8f74\u7684\u957f<span aria-hidden=\"true\">=2b<\/span><\/td>\n<td>\u957f\u8f74\u7684\u957f<span aria-hidden=\"true\">=2a<\/span>\uff0c\u77ed\u8f74\u7684\u957f<span aria-hidden=\"true\">=2b<\/span><\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>\u5bf9\u79f0\u6027<\/td>\n<td>\u5173\u4e8e<span aria-hidden=\"true\">x<\/span>\u8f74\u3001<span aria-hidden=\"true\">y<\/span>\u8f74\u5bf9\u79f0\uff0c\u5173\u4e8e\u539f\u70b9\u4e2d\u5fc3\u5bf9\u79f0<\/td>\n<td>\u5173\u4e8e<span aria-hidden=\"true\">x<\/span>\u8f74\u3001<span aria-hidden=\"true\">y<\/span>\u8f74\u5bf9\u79f0\uff0c\u5173\u4e8e\u539f\u70b9\u4e2d\u5fc3\u5bf9\u79f0<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>\u7126\u70b9<\/td>\n<td><span aria-hidden=\"true\">F1\u200b(\u2212c,0)<\/span>\u3001<span aria-hidden=\"true\">F2\u200b(c,0)<\/span><\/td>\n<td><span aria-hidden=\"true\">F1\u200b(0,\u2212c)<\/span>\u3001<span aria-hidden=\"true\">F2\u200b(0,c)<\/span><\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>\u7126\u8ddd<\/td>\n<td><span aria-hidden=\"true\">F1\u200bF2\u200b=2c<\/span>\uff08<span aria-hidden=\"true\">c2=a2\u2212b2<\/span>\uff09<\/td>\n<td><span aria-hidden=\"true\">F1\u200bF2\u200b=2c<\/span>\uff08<span aria-hidden=\"true\">c2=a2\u2212b2<\/span>\uff09<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>\u79bb\u5fc3\u7387<\/td>\n<td><span aria-hidden=\"true\">e=ac\u200b=a2c2\u200b\u200b=a2a2\u2212b2\u200b\u200b=1\u2212a2b2\u200b\u200b<\/span>\uff08<span aria-hidden=\"true\">0&lt;e&lt;1<\/span>\uff09<\/td>\n<td><span aria-hidden=\"true\">e=ac\u200b=a2c2\u200b\u200b=a2a2\u2212b2\u200b\u200b=1\u2212a2b2\u200b\u200b<\/span>\uff08<span aria-hidden=\"true\">0&lt;e&lt;1<\/span>\uff09<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<div>\u00a0<\/div>\n<h4>\u53cc\u66f2\u7ebf<\/h4>\n<div>\u00a0<\/div>\n<ol>\n<li>\u53cc\u66f2\u7ebf\u7684\u5b9a\u4e49\uff1a\u5e73\u9762\u5185\u4e0e\u4e24\u4e2a\u5b9a\u70b9<span aria-hidden=\"true\">F1\u200b<\/span>\uff0c<span aria-hidden=\"true\">F2\u200b<\/span>\u7684\u8ddd\u79bb\u7684\u5dee\u7684\u7edd\u5bf9\u503c\u7b49\u4e8e\u5e38\u6570\uff08\u5c0f\u4e8e<span aria-hidden=\"true\">\u2223F1\u200bF2\u200b\u2223<\/span>\uff09\u7684\u70b9\u7684\u8f68\u8ff9\u53eb\u505a\u53cc\u66f2\u7ebf\u3002\u8fd9\u4e24\u4e2a\u5b9a\u70b9<span aria-hidden=\"true\">F1\u200b<\/span>\uff0c<span aria-hidden=\"true\">F2\u200b<\/span>\u53eb\u505a\u53cc\u66f2\u7ebf\u7684\u7126\u70b9\uff0c\u4e24\u7126\u70b9\u95f4\u7684\u8ddd\u79bb\u53eb\u505a\u53cc\u66f2\u7ebf\u7684\u7126\u8ddd\u3002\u53cc\u66f2\u7ebf\u7684\u5b9a\u4e49\u7528\u7b26\u53f7\u8bed\u8a00\u8868\u793a\uff1a<span aria-hidden=\"true\">\u2223\u2223MF1\u200b\u2223\u2212\u2223MF2\u200b\u2223\u2223=2a<\/span>\uff08<span aria-hidden=\"true\">0&lt;2a&lt;\u2223F1\u200bF2\u200b\u2223<\/span>\uff09<\/li>\n<li>\u53cc\u66f2\u7ebf\u7684\u6807\u51c6\u65b9\u7a0b\uff1a\n<ul>\n<li>\u7126\u70b9\u5728<span aria-hidden=\"true\">x<\/span>\u8f74\u4e0a\u7684\u53cc\u66f2\u7ebf\u7684\u6807\u51c6\u65b9\u7a0b\uff1a<span aria-hidden=\"true\">a2x2\u200b\u2212b2y2\u200b=1<\/span>\uff08<span aria-hidden=\"true\">a&gt;0<\/span>\uff0c<span aria-hidden=\"true\">b&gt;0<\/span>\uff09\uff0c\u7126\u70b9<span aria-hidden=\"true\">F1\u200b(\u2212c,0)<\/span>\uff0c<span aria-hidden=\"true\">F2\u200b(c,0)<\/span><\/li>\n<li>\u7126\u70b9\u5728<span aria-hidden=\"true\">y<\/span>\u8f74\u4e0a\u7684\u53cc\u66f2\u7ebf\u7684\u6807\u51c6\u65b9\u7a0b\uff1a<span aria-hidden=\"true\">a2y2\u200b\u2212b2x2\u200b=1<\/span>\uff08<span aria-hidden=\"true\">a&gt;0<\/span>\uff0c<span aria-hidden=\"true\">b&gt;0<\/span>\uff09\uff0c\u7126\u70b9<span aria-hidden=\"true\">F1\u200b(0,\u2212c)<\/span>\uff0c<span aria-hidden=\"true\">F2\u200b(0,c)<\/span><\/li>\n<li>\u5176\u4e2d<span aria-hidden=\"true\">a<\/span>\uff0c<span aria-hidden=\"true\">b<\/span>\uff0c<span aria-hidden=\"true\">c<\/span>\u51e0\u4f55\u610f\u4e49\uff1a<span aria-hidden=\"true\">a<\/span>\u8868\u793a\u5b9e\u8f74\u957f\u7684\u4e00\u534a\uff0c<span aria-hidden=\"true\">b<\/span>\u8868\u793a\u865a\u8f74\u957f\u7684\u4e00\u534a\uff0c<span aria-hidden=\"true\">c<\/span>\u8868\u793a\u7126\u8ddd\u957f\u7684\u4e00\u534a\uff0c\u5e76\u4e14\u6709<span aria-hidden=\"true\">c2=a2+b2<\/span><\/li>\n<li>\u5f53<span aria-hidden=\"true\">a=b<\/span>\u65f6\uff0c\u53cc\u66f2\u7ebf\u79f0\u4e3a\u7b49\u8f74\u53cc\u66f2\u7ebf\uff0c\u5176\u65b9\u7a0b\u4e3a<span aria-hidden=\"true\">x2\u2212y2=a2<\/span>\u6216<span aria-hidden=\"true\">y2\u2212x2=a2<\/span><\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<li>\u53cc\u66f2\u7ebf\u7684\u7b80\u5355\u51e0\u4f55\u6027\u8d28\uff08\u4ee5<span aria-hidden=\"true\">a2x2\u200b\u2212b2y2\u200b=1<\/span>\uff08<span aria-hidden=\"true\">a&gt;0<\/span>\uff0c<span aria-hidden=\"true\">b&gt;0<\/span>\uff09\u4e3a\u4f8b\uff09\uff1a\n<ul>\n<li>\u8303\u56f4\uff1a<span aria-hidden=\"true\">\u2223x\u2223\u2265a<\/span>\uff0c<span aria-hidden=\"true\">y\u2208R<\/span><\/li>\n<li>\u5bf9\u79f0\u6027\uff1a\u5bf9\u79f0\u8f74\u4e3a<span aria-hidden=\"true\">x<\/span>\u8f74\u3001<span aria-hidden=\"true\">y<\/span>\u8f74\uff0c\u5bf9\u79f0\u4e2d\u5fc3\u4e3a<span aria-hidden=\"true\">O(0,0)<\/span><\/li>\n<li>\u9876\u70b9\uff1a<span aria-hidden=\"true\">A1\u200b(\u2212a,0)<\/span>\uff0c<span aria-hidden=\"true\">A2\u200b(a,0)<\/span>\uff0c<span aria-hidden=\"true\">B1\u200b(0,\u2212b)<\/span>\uff0c<span aria-hidden=\"true\">B2\u200b(0,b)<\/span>\uff0c\u5b9e\u8f74\u957f<span aria-hidden=\"true\">\u2223A1\u200bA2\u200b\u2223=2a<\/span>\uff0c\u865a\u8f74\u957f<span aria-hidden=\"true\">\u2223B1\u200bB2\u200b\u2223=2b<\/span><\/li>\n<li>\u79bb\u5fc3\u7387<span aria-hidden=\"true\">e=ac\u200b<\/span>\uff0c<span aria-hidden=\"true\">e&gt;1<\/span>\uff0c<span aria-hidden=\"true\">e<\/span>\u8d8a\u5c0f\uff0c\u53cc\u66f2\u7ebf\u8d8a\u6241\uff1b<span aria-hidden=\"true\">e<\/span>\u8d8a\u5927\uff0c\u53cc\u66f2\u7ebf\u8d8a\u5f00\u9614<\/li>\n<li>\u53cc\u66f2\u7ebf\u7684\u6e10\u8fd1\u7ebf\u65b9\u7a0b\uff1a<span aria-hidden=\"true\">y=\u00b1ab\u200bx<\/span><\/li>\n<\/ul>\n<div>\u00a0<\/div>\n<\/li>\n<\/ol>\n<div>\u00a0<\/div>\n<div>\n<div>\n<table>\n<thead>\n<tr>\n<th>\u7126\u70b9\u7684\u4f4d\u7f6e<\/th>\n<th>\u7126\u70b9\u5728<span aria-hidden=\"true\">x<\/span>\u8f74\u4e0a<\/th>\n<th>\u7126\u70b9\u5728<span aria-hidden=\"true\">y<\/span>\u8f74\u4e0a<\/th>\n<th>\u00a0<\/th>\n<th>\u00a0<\/th>\n<th>\u00a0<\/th>\n<th>\u00a0<\/th>\n<th>\u00a0<\/th>\n<th>\u00a0<\/th>\n<th>\u00a0<\/th>\n<th>\u00a0<\/th>\n<th>\u00a0<\/th>\n<th>\u00a0<\/th>\n<th>\u00a0<\/th>\n<th>\u00a0<\/th>\n<th>\u00a0<\/th>\n<th>\u00a0<\/th>\n<th>\u00a0<\/th>\n<th>\u00a0<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u6807\u51c6\u65b9\u7a0b<\/td>\n<td><span aria-hidden=\"true\">a2x2\u200b\u2212b2y2\u200b=1<\/span>\uff08<span aria-hidden=\"true\">a&gt;0<\/span>\uff0c<span aria-hidden=\"true\">b&gt;0<\/span>\uff09<\/td>\n<td><span aria-hidden=\"true\">a2y2\u200b\u2212b2x2\u200b=1<\/span>\uff08<span aria-hidden=\"true\">a&gt;0<\/span>\uff0c<span aria-hidden=\"true\">b&gt;0<\/span>\uff09<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>\u5b9a\u4e49<\/td>\n<td>\u5230\u4e24\u5b9a\u70b9<span aria-hidden=\"true\">F1\u200b<\/span>\u3001<span aria-hidden=\"true\">F2\u200b<\/span>\u7684\u8ddd\u79bb\u4e4b\u5dee\u7684\u7edd\u5bf9\u503c\u7b49\u4e8e\u5e38\u6570<span aria-hidden=\"true\">2a<\/span>\uff0c\u5373 $<\/td>\n<td>&nbsp;<\/td>\n<td>MF_1<\/td>\n<td>&#8211;<\/td>\n<td>MF_2<\/td>\n<td>&nbsp;<\/td>\n<td>= 2a$\uff08$0 &lt; 2a &lt;<\/td>\n<td>F_1F_2<\/td>\n<td>$\uff09<\/td>\n<td>\u5230\u4e24\u5b9a\u70b9<span aria-hidden=\"true\">F1\u200b<\/span>\u3001<span aria-hidden=\"true\">F2\u200b<\/span>\u7684\u8ddd\u79bb\u4e4b\u5dee\u7684\u7edd\u5bf9\u503c\u7b49\u4e8e\u5e38\u6570<span aria-hidden=\"true\">2a<\/span>\uff0c\u5373 $<\/td>\n<td>&nbsp;<\/td>\n<td>MF_1<\/td>\n<td>&#8211;<\/td>\n<td>MF_2<\/td>\n<td>&nbsp;<\/td>\n<td>= 2a$\uff08$0 &lt; 2a &lt;<\/td>\n<td>F_1F_2<\/td>\n<td>$\uff09<\/td>\n<\/tr>\n<tr>\n<td>\u8303\u56f4<\/td>\n<td><span aria-hidden=\"true\">x\u2264\u2212a<\/span>\u6216<span aria-hidden=\"true\">x\u2265a<\/span>\uff0c<span aria-hidden=\"true\">y\u2208R<\/span><\/td>\n<td><span aria-hidden=\"true\">y\u2264\u2212a<\/span>\u6216<span aria-hidden=\"true\">y\u2265a<\/span>\uff0c<span aria-hidden=\"true\">x\u2208R<\/span><\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>\u9876\u70b9<\/td>\n<td><span aria-hidden=\"true\">A1\u200b(\u2212a,0)<\/span>\u3001<span aria-hidden=\"true\">A2\u200b(a,0)<\/span><\/td>\n<td><span aria-hidden=\"true\">A1\u200b(0,\u2212a)<\/span>\u3001<span aria-hidden=\"true\">A2\u200b(0,a)<\/span><\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>\u8f74\u957f<\/td>\n<td>\u5b9e\u8f74\u7684\u957f<span 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aria-hidden=\"true\">y<\/span>\u8f74\u5bf9\u79f0\uff0c\u5173\u4e8e\u539f\u70b9\u4e2d\u5fc3\u5bf9\u79f0<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<td>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>\u7126\u70b9<\/td>\n<td><span aria-hidden=\"true\">F1\u200b(\u2212c,0)<\/span>\u3001<span aria-hidden=\"true\">F2\u200b(c,0)<\/span><\/td>\n<td><span aria-hidden=\"true\">F1\u200b(0,\u2212c)<\/span>\u3001<span 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