mirror of https://gitee.com/XmacsLabs/planet.git
142 lines
990 KiB
Tcl
142 lines
990 KiB
Tcl
<TeXmacs|2.1.2>
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<style|<tuple|generic|std-latex|chinese>>
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<\body>
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<doc-data|<doc-title|2021\<#5E74\>\<#5168\>\<#56FD\>\<#65B0\>\<#9AD8\>\<#8003\>II\<#5377\>\<#6570\>\<#5B66\>\<#8BD5\>\<#9898\>>>
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<\with|font-series|bold>
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\<#4E00\>\<#3001\>\<#5355\>\<#9009\>\<#9898\>
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</with>
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1\<#FF0E\>\<#590D\>\<#6570\><math|<frac|2-i|1-3*i>>\<#5728\>\<#590D\>\<#5E73\>\<#9762\>\<#5185\>\<#5BF9\>\<#5E94\>\<#7684\>\<#70B9\>\<#6240\>\<#5728\>\<#7684\>\<#8C61\>\<#9650\>\<#4E3A\>\<#FF08\><space|1.2em>\<#FF09\>
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<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A\<#FF0E\>\<#7B2C\>\<#4E00\>\<#8C61\>\<#9650\>>|<cell|B\<#FF0E\>\<#7B2C\>\<#4E8C\>\<#8C61\>\<#9650\>>|<cell|C\<#FF0E\>\<#7B2C\>\<#4E09\>\<#8C61\>\<#9650\>>|<cell|D\<#FF0E\>\<#7B2C\>\<#56DB\>\<#8C61\>\<#9650\>>>>>>\
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2\<#FF0E\>\<#8BBE\>\<#96C6\>\<#5408\><math|U=<around|{|1,2,3,4,5,6|}>,A=<around|{|1,3,6|}>,B=<around|{|2,3,4|}>>\<#FF0C\>\<#5219\><math|A\<cap\><around*|(|\<complement\><rsub|U>*B|)>=>\<#FF08\><space|1.2em>\<#FF09\>
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<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A\<#FF0E\><math|<around|{|3|}>>>|<cell|B\<#FF0E\><math|<around|{|1,6|}>>>|<cell|C\<#FF0E\><math|<around|{|5,6|}>>>|<cell|D\<#FF0E\><math|<around|{|1,3|}>>>>>>>\
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3\<#FF0E\>\<#629B\>\<#7269\>\<#7EBF\><math|y<rsup|2>=2*p*x*<around|(|p\<gtr\>0|)>>\<#7684\>\<#7126\>\<#70B9\>\<#5230\>\<#76F4\>\<#7EBF\><math|y=x+1>\<#7684\>\<#8DDD\>\<#79BB\>\<#4E3A\><math|<sqrt|2>>\<#FF0C\>\<#5219\><math|p=>\<#FF08\><space|1.2em>\<#FF09\>
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<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A\<#FF0E\>1>|<cell|B\<#FF0E\>2>|<cell|C\<#FF0E\><math|2*<sqrt|2>>>|<cell|D\<#FF0E\>4>>>>>\
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4\<#FF0E\>\<#5317\>\<#6597\>\<#4E09\>\<#53F7\>\<#5168\>\<#7403\>\<#536B\>\<#661F\>\<#5BFC\>\<#822A\>\<#7CFB\>\<#7EDF\>\<#662F\>\<#6211\>\<#56FD\>\<#822A\>\<#5929\>\<#4E8B\>\<#4E1A\>\<#7684\>\<#91CD\>\<#8981\>\<#6210\>\<#679C\>\<#FF0E\>\<#5728\>\<#536B\>\<#661F\>\<#5BFC\>\<#822A\>\<#7CFB\>\<#7EDF\>\<#4E2D\>\<#FF0C\>\<#5730\>\<#7403\>\<#9759\>\<#6B62\>\<#540C\>\<#6B65\>\<#536B\>\<#661F\>\<#7684\>\<#8F68\>\<#9053\>\<#4F4D\>\<#4E8E\>\<#5730\>\<#7403\>\<#8D64\>\<#9053\>\<#6240\>\<#5728\>\<#5E73\>\<#9762\>\<#FF0C\>\<#8F68\>\<#9053\>\<#9AD8\>\<#5EA6\>\<#4E3A\><math|36000>km\<#FF08\>\<#8F68\>\<#9053\>\<#9AD8\>\<#5EA6\>\<#662F\>\<#6307\>\<#536B\>\<#661F\>\<#5230\>\<#5730\>\<#7403\>\<#8868\>\<#9762\>\<#7684\>\<#8DDD\>\<#79BB\>\<#FF09\>\<#FF0E\>\<#5C06\>\<#5730\>\<#7403\>\<#770B\>\<#4F5C\>\<#662F\>\<#4E00\>\<#4E2A\>\<#7403\>\<#5FC3\>\<#4E3A\><em|O>\<#FF0C\>\<#534A\>\<#5F84\><em|r>\<#4E3A\><math|6400>km\<#7684\>\<#7403\>\<#FF0C\>\<#5176\>\<#4E0A\>\<#70B9\><em|A>\<#7684\>\<#7EAC\>\<#5EA6\>\<#662F\>\<#6307\><math|O*A>\<#4E0E\>\<#8D64\>\<#9053\>\<#5E73\>\<#9762\>\<#6240\>\<#6210\>\<#89D2\>\<#7684\>\<#5EA6\>\<#6570\>\<#FF0E\>\<#5730\>\<#7403\>\<#8868\>\<#9762\>\<#4E0A\>\<#80FD\>\<#76F4\>\<#63A5\>\<#89C2\>\<#6D4B\>\<#5230\>\<#4E00\>\<#9897\>\<#5730\>\<#7403\>\<#9759\>\<#6B62\>\<#540C\>\<#6B65\>\<#8F68\>\<#9053\>\<#536B\>\<#661F\>\<#70B9\>\<#7684\>\<#7EAC\>\<#5EA6\>\<#6700\>\<#5927\>\<#503C\>\<#4E3A\><math|\<alpha\>>\<#FF0C\>\<#8BB0\>\<#536B\>\<#661F\>\<#4FE1\>\<#53F7\>\<#8986\>\<#76D6\>\<#5730\>\<#7403\>\<#8868\>\<#9762\>\<#7684\>\<#8868\>\<#9762\>\<#79EF\>\<#4E3A\><math|S=2*\<pi\>*r<rsup|2>*<around|(|1-cos
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\<alpha\>|)>>\<#FF08\>\<#5355\>\<#4F4D\>\<#FF1A\>km<rsup|<math|2>>\<#FF09\>\<#FF0C\>\<#5219\><em|S>\<#5360\>\<#5730\>\<#7403\>\<#8868\>\<#9762\>\<#79EF\>\<#7684\>\<#767E\>\<#5206\>\<#6BD4\>\<#7EA6\>\<#4E3A\>\<#FF08\><space|1.2em>\<#FF09\>
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<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A\<#FF0E\>26%>|<cell|B\<#FF0E\>34%>|<cell|C\<#FF0E\>42%>|<cell|D\<#FF0E\>50%>>>>>\
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5\<#FF0E\>\<#6B63\>\<#56DB\>\<#68F1\>\<#53F0\>\<#7684\>\<#4E0A\>\<#FF64\>\<#4E0B\>\<#5E95\>\<#9762\>\<#7684\>\<#8FB9\>\<#957F\>\<#5206\>\<#522B\>\<#4E3A\>2\<#FF0C\>4\<#FF0C\>\<#4FA7\>\<#68F1\>\<#957F\>\<#4E3A\>2\<#FF0C\>\<#5219\>\<#5176\>\<#4F53\>\<#79EF\>\<#4E3A\>\<#FF08\><space|1.2em>\<#FF09\>
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<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A\<#FF0E\><math|20+12*<sqrt|3>>>|<cell|B\<#FF0E\><math|28*<sqrt|2>>>|<cell|C\<#FF0E\><math|<frac|56|3>>>|<cell|D\<#FF0E\><math|<frac|28*<sqrt|2>|3>>>>>>>\
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6\<#FF0E\>\<#67D0\>\<#7269\>\<#7406\>\<#91CF\>\<#7684\>\<#6D4B\>\<#91CF\>\<#7ED3\>\<#679C\>\<#670D\>\<#4ECE\>\<#6B63\>\<#6001\>\<#5206\>\<#5E03\><math|N<around*|(|10,\<sigma\><rsup|2>|)>>\<#FF0C\>\<#4E0B\>\<#5217\>\<#7ED3\>\<#8BBA\>\<#4E2D\>\<#4E0D\>\<#6B63\>\<#786E\>\<#7684\>\<#662F\>\<#FF08\><space|1.2em>\<#FF09\>
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A\<#FF0E\><math|\<sigma\>>\<#8D8A\>\<#5C0F\>\<#FF0C\>\<#8BE5\>\<#7269\>\<#7406\>\<#91CF\>\<#5728\>\<#4E00\>\<#6B21\>\<#6D4B\>\<#91CF\>\<#4E2D\>\<#5728\><math|<around|(|9.9,10.1|)>>\<#7684\>\<#6982\>\<#7387\>\<#8D8A\>\<#5927\>
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B\<#FF0E\><math|\<sigma\>>\<#8D8A\>\<#5C0F\>\<#FF0C\>\<#8BE5\>\<#7269\>\<#7406\>\<#91CF\>\<#5728\>\<#4E00\>\<#6B21\>\<#6D4B\>\<#91CF\>\<#4E2D\>\<#5927\>\<#4E8E\>10\<#7684\>\<#6982\>\<#7387\>\<#4E3A\>0.5
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C\<#FF0E\><math|\<sigma\>>\<#8D8A\>\<#5C0F\>\<#FF0C\>\<#8BE5\>\<#7269\>\<#7406\>\<#91CF\>\<#5728\>\<#4E00\>\<#6B21\>\<#6D4B\>\<#91CF\>\<#4E2D\>\<#5C0F\>\<#4E8E\>9.99\<#4E0E\>\<#5927\>\<#4E8E\>10.01\<#7684\>\<#6982\>\<#7387\>\<#76F8\>\<#7B49\>
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D\<#FF0E\><math|\<sigma\>>\<#8D8A\>\<#5C0F\>\<#FF0C\>\<#8BE5\>\<#7269\>\<#7406\>\<#91CF\>\<#5728\>\<#4E00\>\<#6B21\>\<#6D4B\>\<#91CF\>\<#4E2D\>\<#843D\>\<#5728\><math|<around|(|9.9,10.2|)>>\<#4E0E\>\<#843D\>\<#5728\><math|<around|(|10,10.3|)>>\<#7684\>\<#6982\>\<#7387\>\<#76F8\>\<#7B49\>
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7\<#FF0E\>\<#5DF2\>\<#77E5\><math|a=log<rsub|5>2>\<#FF0C\><math|b=log<rsub|8>3>\<#FF0C\><math|c=<frac|1|2>>\<#FF0C\>\<#5219\>\<#4E0B\>\<#5217\>\<#5224\>\<#65AD\>\<#6B63\>\<#786E\>\<#7684\>\<#662F\>\<#FF08\><space|1.2em>\<#FF09\>
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<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A\<#FF0E\><math|c\<less\>b\<less\>a>>|<cell|B\<#FF0E\><math|b\<less\>a\<less\>c>>|<cell|C\<#FF0E\><math|a\<less\>c\<less\>b>>|<cell|D\<#FF0E\><math|a\<less\>b\<less\>c>>>>>>\
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8\<#FF0E\>\<#5DF2\>\<#77E5\>\<#51FD\>\<#6570\><math|f<around|(|x|)>>\<#7684\>\<#5B9A\>\<#4E49\>\<#57DF\>\<#4E3A\><math|<math-bf|R>>\<#FF0C\><math|f*<around|(|x+2|)>>\<#4E3A\>\<#5076\>\<#51FD\>\<#6570\>\<#FF0C\><math|f*<around|(|2*x+1|)>>\<#4E3A\>\<#5947\>\<#51FD\>\<#6570\>\<#FF0C\>\<#5219\>\<#FF08\><space|1.2em>\<#FF09\>
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<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A\<#FF0E\><math|f*<around*|(|-<frac|1|2>|)>=0>>|<cell|B\<#FF0E\><math|f*<around|(|-1|)>=0>>|<cell|C\<#FF0E\><math|f<around|(|2|)>=0>>|<cell|D\<#FF0E\><math|f<around|(|4|)>=0>>>>>>\
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<with|font-series|bold|\<#4E8C\>\<#3001\>\<#591A\>\<#9009\>\<#9898\>>
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9\<#FF0E\>\<#4E0B\>\<#5217\>\<#7EDF\>\<#8BA1\>\<#91CF\>\<#4E2D\>\<#FF0C\>\<#80FD\>\<#5EA6\>\<#91CF\>\<#6837\>\<#672C\><math|x<rsub|1>,x<rsub|2>,\<cdots\>,x<rsub|n>>\<#7684\>\<#79BB\>\<#6563\>\<#7A0B\>\<#5EA6\>\<#7684\>\<#662F\>\<#FF08\><space|1.2em>\<#FF09\>
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<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A\<#FF0E\>\<#6837\>\<#672C\><math|x<rsub|1>,x<rsub|2>,\<cdots\>,x<rsub|n>>\<#7684\>\<#6807\>\<#51C6\>\<#5DEE\>>|<cell|B\<#FF0E\>\<#6837\>\<#672C\><math|x<rsub|1>,x<rsub|2>,\<cdots\>,x<rsub|n>>\<#7684\>\<#4E2D\>\<#4F4D\>\<#6570\>>>|<row|<cell|C\<#FF0E\>\<#6837\>\<#672C\><math|x<rsub|1>,x<rsub|2>,\<cdots\>,x<rsub|n>>\<#7684\>\<#6781\>\<#5DEE\>>|<cell|D\<#FF0E\>\<#6837\>\<#672C\><math|x<rsub|1>,x<rsub|2>,\<cdots\>,x<rsub|n>>\<#7684\>\<#5E73\>\<#5747\>\<#6570\>>>>>>\
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10\<#FF0E\>\<#5982\>\<#56FE\>\<#FF0C\>\<#5728\>\<#6B63\>\<#65B9\>\<#4F53\>\<#4E2D\>\<#FF0C\><em|O>\<#4E3A\>\<#5E95\>\<#9762\>\<#7684\>\<#4E2D\>\<#5FC3\>\<#FF0C\><em|P>\<#4E3A\>\<#6240\>\<#5728\>\<#68F1\>\<#7684\>\<#4E2D\>\<#70B9\>\<#FF0C\><em|M>\<#FF0C\><em|N>\<#4E3A\>\<#6B63\>\<#65B9\>\<#4F53\>\<#7684\>\<#9876\>\<#70B9\>\<#FF0E\>\<#5219\>\<#6EE1\>\<#8DB3\><math|M*N*\<bot\>*O*P>\<#7684\>\<#662F\>\<#FF08\><space|1.2em>\<#FF09\>
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11\<#FF0E\>\<#5DF2\>\<#77E5\>\<#76F4\>\<#7EBF\><math|l:a*x+b*y-r<rsup|2>=0>\<#4E0E\>\<#5706\><math|C:x<rsup|2>+y<rsup|2>=r<rsup|2>>\<#FF0C\>\<#70B9\><math|A*<around|(|a,b|)>>\<#FF0C\>\<#5219\>\<#4E0B\>\<#5217\>\<#8BF4\>\<#6CD5\>\<#6B63\>\<#786E\>\<#7684\>\<#662F\>\<#FF08\><space|1.2em>\<#FF09\>
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A\<#FF0E\>\<#82E5\>\<#70B9\><em|A>\<#5728\>\<#5706\><em|C>\<#4E0A\>\<#FF0C\>\<#5219\>\<#76F4\>\<#7EBF\><em|l>\<#4E0E\>\<#5706\><em|C>\<#76F8\>\<#5207\>\
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B\<#FF0E\>\<#82E5\>\<#70B9\><em|A>\<#5728\>\<#5706\><em|C>\<#5185\>\<#FF0C\>\<#5219\>\<#76F4\>\<#7EBF\><em|l>\<#4E0E\>\<#5706\><em|C>\<#76F8\>\<#79BB\>
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C\<#FF0E\>\<#82E5\>\<#70B9\><em|A>\<#5728\>\<#5706\><em|C>\<#5916\>\<#FF0C\>\<#5219\>\<#76F4\>\<#7EBF\><em|l>\<#4E0E\>\<#5706\><em|C>\<#76F8\>\<#79BB\>\
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D\<#FF0E\>\<#82E5\>\<#70B9\><em|A>\<#5728\>\<#76F4\>\<#7EBF\><em|l>\<#4E0A\>\<#FF0C\>\<#5219\>\<#76F4\>\<#7EBF\><em|l>\<#4E0E\>\<#5706\><em|C>\<#76F8\>\<#5207\>
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12\<#FF0E\>\<#8BBE\>\<#6B63\>\<#6574\>\<#6570\><math|n=a<rsub|0>\<cdot\>2<rsup|0>+a<rsub|1>\<cdot\>2+\<cdots\>+a<rsub|k-1>\<cdot\>2<rsup|k-1>+a<rsub|k>\<cdot\>2<rsup|k>>\<#FF0C\>\<#5176\>\<#4E2D\><math|a<rsub|i>\<in\><around*|{|0,1|}>>\<#FF0C\>\<#8BB0\><math|\<omega\><around|(|n|)>=a<rsub|0>+a<rsub|1>+\<cdots\>+a<rsub|k>>\<#FF0E\>\<#5219\>\<#FF08\><space|1.2em>\<#FF09\>
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<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A\<#FF0E\><math|\<omega\>*<around|(|2*n|)>=\<omega\><around|(|n|)>>>|<cell|B\<#FF0E\><math|\<omega\>*<around|(|2*n+3|)>=\<omega\><around|(|n|)>+1>>>|<row|<cell|C\<#FF0E\><math|\<omega\>*<around|(|8*n+5|)>=\<omega\>*<around|(|4*n+3|)>>>|<cell|D\<#FF0E\><math|\<omega\>*<around*|(|2<rsup|n>-1|)>=n>>>>>>\
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<with|font-series|bold|\<#4E09\>\<#3001\>\<#586B\>\<#7A7A\>\<#9898\>>
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13\<#FF0E\>\<#82E5\>\<#53CC\>\<#66F2\>\<#7EBF\><math|<frac|x<rsup|2>|a<rsup|2>>-<frac|y<rsup|2>|b<rsup|2>>=1>\<#7684\>\<#79BB\>\<#5FC3\>\<#7387\>\<#4E3A\>2\<#FF0C\>\<#5219\>\<#6B64\>\<#53CC\>\<#66F2\>\<#7EBF\>\<#7684\>\<#6E10\>\<#8FD1\>\<#7EBF\>\<#65B9\>\<#7A0B\><underline|<space|2cm>>\<#FF0E\>
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14\<#FF0E\>\<#5199\>\<#51FA\>\<#4E00\>\<#4E2A\>\<#540C\>\<#65F6\>\<#5177\>\<#6709\>\<#4E0B\>\<#5217\>\<#6027\>\<#8D28\>\<#2460\>\<#2461\>\<#2462\>\<#7684\>\<#51FD\>\<#6570\><math|f<around|(|x|)>>:
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<underline|<space|2cm>>\<#FF0E\>
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\<#2460\><math|f*<around*|(|x<rsub|1>*x<rsub|2>|)>=f<around*|(|x<rsub|1>|)>*f<around*|(|x<rsub|2>|)>>\<#FF1B\>\<#2461\>\<#5F53\><math|x\<in\>
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<around*|(|0,+\<infty\>|)>>\<#65F6\>\<#FF0C\><math|f<rprime|'><around|(|x|)>\<gtr\>0>\<#FF1B\>\<#2462\><math|f<rprime|'><around|(|x|)>>\<#662F\>\<#5947\>\<#51FD\>\<#6570\>\<#FF0E\>
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15\<#FF0E\>\<#5DF2\>\<#77E5\>\<#5411\>\<#91CF\><math|<wide|a|\<wide-varrightarrow\>>+<wide|b|\<wide-varrightarrow\>>+<wide|c|\<wide-varrightarrow\>>=<wide|0|\<wide-varrightarrow\>>>\<#FF0C\><math|<around*|\||<wide|a|\<wide-varrightarrow\>>|\|>=1>\<#FF0C\><math|<around*|\||<wide|b|\<wide-varrightarrow\>>|\|>=<around*|\||<wide|c|\<wide-varrightarrow\>>|\|>=2>\<#FF0C\><math|<wide|a|\<wide-varrightarrow\>>\<cdot\><wide|b|\<wide-varrightarrow\>>+<wide|b|\<wide-varrightarrow\>>\<cdot\><wide|c|\<wide-varrightarrow\>>+<wide|c|\<wide-varrightarrow\>>\<cdot\><wide|a|\<wide-varrightarrow\>>=><underline|<space|2cm>>\<#FF0E\>
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16\<#FF0E\>\<#5DF2\>\<#77E5\>\<#51FD\>\<#6570\><math|f<around|(|x|)>=<around*|\||e<rsup|x>-1|\|>,x<rsub|1>\<less\>0,x<rsub|2>\<gtr\>0>\<#FF0C\>\<#51FD\>\<#6570\><math|f<around|(|x|)>>\<#7684\>\<#56FE\>\<#8C61\>\<#5728\>\<#70B9\><math|A*<around*|(|x<rsub|1>,f<around*|(|x<rsub|1>|)>|)>>\<#548C\>\<#70B9\><math|B*<around*|(|x<rsub|2>,f<around*|(|x<rsub|2>|)>|)>>\<#7684\>\<#4E24\>\<#6761\>\<#5207\>\<#7EBF\>\<#4E92\>\<#76F8\>\<#5782\>\<#76F4\>\<#FF0C\>\<#4E14\>\<#5206\>\<#522B\>\<#4EA4\><em|y>\<#8F74\>\<#4E8E\><em|M>\<#FF0C\><em|N>\<#4E24\>\<#70B9\>\<#FF0C\>\<#5219\><math|<frac|<around|\||A*M|\|>|<around|\||B*N|\|>>>\<#53D6\>\<#503C\>\<#8303\>\<#56F4\>\<#662F\><underline|<space|2cm>>\<#FF0E\>
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<with|font-series|bold|\<#56DB\>\<#3001\>\<#89E3\>\<#7B54\>\<#9898\>>
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17\<#FF0E\>\<#8BB0\><math|S<rsub|n>>\<#662F\>\<#516C\>\<#5DEE\>\<#4E0D\>\<#4E3A\>0\<#7684\>\<#7B49\>\<#5DEE\>\<#6570\>\<#5217\><math|<around*|{|a<rsub|n>|}>>\<#7684\>\<#524D\><em|n>\<#9879\>\<#548C\>\<#FF0C\>\<#82E5\><math|a<rsub|3>=S<rsub|5>,a<rsub|2>*a<rsub|4>=S<rsub|4>>\<#FF0E\>
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\<#FF08\>1\<#FF09\>\<#6C42\>\<#6570\>\<#5217\><math|<around*|{|a<rsub|n>|}>>\<#7684\>\<#901A\>\<#9879\>\<#516C\>\<#5F0F\><math|a<rsub|n>>\<#FF1B\>
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\<#FF08\>2\<#FF09\>\<#6C42\>\<#4F7F\><math|S<rsub|n>\<gtr\>a<rsub|n>>\<#6210\>\<#7ACB\>\<#7684\><em|n>\<#7684\>\<#6700\>\<#5C0F\>\<#503C\>\<#FF0E\><vspace|3cm>
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18\<#FF0E\>\<#5728\><math|\<triangle\>A*B*C>\<#4E2D\>\<#FF0C\>\<#89D2\><math|A>\<#3001\><math|B>\<#3001\><math|C>\<#6240\>\<#5BF9\>\<#7684\>\<#8FB9\>\<#957F\>\<#5206\>\<#522B\>\<#4E3A\><math|a>\<#3001\><math|b>\<#3001\><math|c>\<#FF0C\><math|b=a+1>\<#FF0C\><math|c=a+2>.
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\<#FF08\>1\<#FF09\>\<#82E5\><math|2*sin C=3*sin
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A>\<#FF0C\>\<#6C42\><math|\<triangle\>A*B*C>\<#7684\>\<#9762\>\<#79EF\>\<#FF1B\>
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\<#FF08\>2\<#FF09\>\<#662F\>\<#5426\>\<#5B58\>\<#5728\>\<#6B63\>\<#6574\>\<#6570\><math|a>\<#FF0C\>\<#4F7F\>\<#5F97\><math|\<triangle\>A*B*C>\<#4E3A\>\<#949D\>\<#89D2\>\<#4E09\>\<#89D2\>\<#5F62\>?\<#82E5\>\<#5B58\>\<#5728\>\<#FF0C\>\<#6C42\>\<#51FA\><math|a>\<#7684\>\<#503C\>\<#FF1B\>\<#82E5\>\<#4E0D\>\<#5B58\>\<#5728\>\<#FF0C\>\<#8BF4\>\<#660E\>\<#7406\>\<#7531\>\<#FF0E\><vspace|3cm>
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19\<#FF0E\>\<#5728\>\<#56DB\>\<#68F1\>\<#9525\><math|Q-A*B*C*D>\<#4E2D\>\<#FF0C\>\<#5E95\>\<#9762\><math|A*B*C*D>\<#662F\>\<#6B63\>\<#65B9\>\<#5F62\>\<#FF0C\>\<#82E5\><math|A*D=2,Q*D=Q*A=<sqrt|5>,Q*C=3>\<#FF0E\>
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21\<#FF0E\>\<#4E00\>\<#79CD\>\<#5FAE\>\<#751F\>\<#7269\>\<#7FA4\>\<#4F53\>\<#53EF\>\<#4EE5\>\<#7ECF\>\<#8FC7\>\<#81EA\>\<#8EAB\>\<#7E41\>\<#6B96\>\<#4E0D\>\<#65AD\>\<#751F\>\<#5B58\>\<#4E0B\>\<#6765\>\<#FF0C\>\<#8BBE\>\<#4E00\>\<#4E2A\>\<#8FD9\>\<#79CD\>\<#5FAE\>\<#751F\>\<#7269\>\<#4E3A\>\<#7B2C\>0\<#4EE3\>\<#FF0C\>\<#7ECF\>\<#8FC7\>\<#4E00\>\<#6B21\>\<#7E41\>\<#6B96\>\<#540E\>\<#4E3A\>\<#7B2C\>1\<#4EE3\>\<#FF0C\>\<#518D\>\<#7ECF\>\<#8FC7\>\<#4E00\>\<#6B21\>\<#7E41\>\<#6B96\>\<#540E\>\<#4E3A\>\<#7B2C\>2\<#4EE3\>......\<#FF0C\>\<#8BE5\>\<#5FAE\>\<#751F\>\<#7269\>\<#6BCF\>\<#4EE3\>\<#7E41\>\<#6B96\>\<#7684\>\<#4E2A\>\<#6570\>\<#662F\>\<#76F8\>\<#4E92\>\<#72EC\>\<#7ACB\>\<#7684\>\<#4E14\>\<#6709\>\<#76F8\>\<#540C\>\<#7684\>\<#5206\>\<#5E03\>\<#5217\>\<#FF0C\>\<#8BBE\><em|X>\<#8868\>\<#793A\>1\<#4E2A\>\<#5FAE\>\<#751F\>\<#7269\>\<#4E2A\>\<#4F53\>\<#7E41\>\<#6B96\>\<#4E0B\>\<#4E00\>\<#4EE3\>\<#7684\>\<#4E2A\>\<#6570\>\<#FF0C\><math|P*<around|(|X=i|)>=p<rsub|i>*<around|(|i=0,1,2,3|)>>\<#FF0E\>
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\<#FF08\>1\<#FF09\>\<#5DF2\>\<#77E5\><math|p<rsub|0>=0.4,p<rsub|1>=0.3,p<rsub|2>=0.2,p<rsub|3>=0.1>\<#FF0C\>\<#6C42\><math|E<around|(|X|)>>\<#FF1B\>
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\<#FF08\>2\<#FF09\>\<#8BBE\><em|p>\<#8868\>\<#793A\>\<#8BE5\>\<#79CD\>\<#5FAE\>\<#751F\>\<#7269\>\<#7ECF\>\<#8FC7\>\<#591A\>\<#4EE3\>\<#7E41\>\<#6B96\>\<#540E\>\<#4E34\>\<#8FD1\>\<#706D\>\<#7EDD\>\<#7684\>\<#6982\>\<#7387\>\<#FF0C\><em|p>\<#662F\>\<#5173\>\<#4E8E\><em|x>\<#7684\>\<#65B9\>\<#7A0B\>\<#FF1A\><math|p<rsub|0>+p<rsub|1>*x+p<rsub|2>*x<rsup|2>+p<rsub|3>*x<rsup|3>=x>\<#7684\>\<#4E00\>\<#4E2A\>\<#6700\>\<#5C0F\>\<#6B63\>\<#5B9E\>\<#6839\>\<#FF0C\>\<#6C42\>\<#8BC1\>\<#FF1A\>\<#5F53\><math|E<around|(|X|)>\<leq\>1>\<#65F6\>\<#FF0C\><math|p=1>\<#FF0C\>\<#5F53\><math|E<around|(|X|)>\<gtr\>1>\<#65F6\>\<#FF0C\><math|p\<less\>1>\<#FF1B\>
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\<#FF08\>3\<#FF09\>\<#6839\>\<#636E\>\<#4F60\>\<#7684\>\<#7406\>\<#89E3\>\<#8BF4\>\<#660E\>\<#FF08\>2\<#FF09\>\<#95EE\>\<#7ED3\>\<#8BBA\>\<#7684\>\<#5B9E\>\<#9645\>\<#542B\>\<#4E49\>\<#FF0E\><vspace|3cm>
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22\<#FF0E\>\<#5DF2\>\<#77E5\>\<#51FD\>\<#6570\><math|f<around|(|x|)>=<around|(|x-1|)>*e<rsup|x>-a*x<rsup|2>+b>\<#FF0E\>
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\<#FF08\>1\<#FF09\>\<#8BA8\>\<#8BBA\><math|f<around|(|x|)>>\<#7684\>\<#5355\>\<#8C03\>\<#6027\>\<#FF1B\>
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\<#FF08\>2\<#FF09\>\<#4ECE\>\<#4E0B\>\<#9762\>\<#4E24\>\<#4E2A\>\<#6761\>\<#4EF6\>\<#4E2D\>\<#9009\>\<#4E00\>\<#4E2A\>\<#FF0C\>\<#8BC1\>\<#660E\>\<#FF1A\><math|f<around|(|x|)>>\<#53EA\>\<#6709\>\<#4E00\>\<#4E2A\>\<#96F6\>\<#70B9\>.
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\<#2460\><math|<frac|1|2>\<less\>a\<leq\><frac|e<rsup|2>|2>,b\<gtr\>2*a>\<#FF1B\>
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\<#2461\><math|0\<less\>a\<less\><frac|1|2>,b\<leq\>2*a>\<#FF0E\><vspace|3cm>
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</body>
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<initial|<\collection>
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</collection>> |