mirror of https://gitee.com/XmacsLabs/planet.git
175 lines
600 KiB
Tcl
175 lines
600 KiB
Tcl
<TeXmacs|2.1.2>
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<style|<tuple|generic|chinese>>
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<\body>
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<doc-data|<doc-title|2021\<#5E74\>\<#4E0A\>\<#6D77\>\<#5E02\>\<#9AD8\>\<#8003\>\<#6570\>\<#5B66\>\<#8BD5\>\<#5377\>>>
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<subsubsection*|\<#4E00\>\<#3001\>\<#5355\>\<#9009\>\<#9898\>>
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<\enumerate>
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<item>\<#5DF2\>\<#77E5\><math|<around*|{|a<rsub|n>|}>>\<#4E3A\>\<#65E0\>\<#7A77\>\<#7B49\>\<#6BD4\>\<#6570\>\<#5217\>\<#FF0C\><math|a<rsub|1>=3>\<#FF0C\><math|a<rsub|n>>\<#7684\>\<#5404\>\<#9879\>\<#548C\>\<#4E3A\>9\<#FF0C\><math|b<rsub|n>=a<rsub|2n>>\<#FF0C\>\<#5219\>\<#6570\>\<#5217\><math|<around*|{|b<rsub|n>|}>>\<#7684\>\<#5404\>\<#9879\>\<#548C\>\<#4E3A\><underline|<space|3em>>.
|
|
|
|
<item>\<#5DF2\>\<#77E5\>\<#5706\>\<#67F1\>\<#7684\>\<#5E95\>\<#9762\>\<#5706\>\<#534A\>\<#5F84\>\<#4E3A\>1\<#FF0C\>\<#9AD8\>\<#4E3A\>2\<#FF0C\><math|AB>\<#4E3A\>\<#4E0A\>\<#5E95\>\<#9762\>\<#5706\>\<#7684\>\<#4E00\>\<#6761\>\<#76F4\>\<#5F84\>\<#FF0C\><math|C>\<#662F\>\<#4E0B\>\<#5E95\>\<#9762\>\<#5706\>\<#5468\>\<#4E0A\>\<#7684\>\<#4E00\>\<#4E2A\>\<#52A8\>\<#70B9\>\<#FF0C\>\<#5219\>ABC\<#7684\>\<#9762\>\<#79EF\>\<#7684\>\<#53D6\>\<#503C\>\<#8303\>\<#56F4\>\<#4E3A\><underline|<space|3em>>.
|
|
|
|
<item>\<#5DF2\>\<#77E5\>\<#82B1\>\<#535A\>\<#4F1A\>\<#6709\>\<#56DB\>\<#4E2A\>\<#4E0D\>\<#540C\>\<#7684\>\<#573A\>\<#9986\><math|A,B,C,D>\<#FF0C\>\<#7532\>\<#3001\>\<#4E59\>\<#4E24\>\<#4EBA\>\<#6BCF\>\<#4EBA\>\<#9009\>2\<#4E2A\>\<#53BB\>\<#53C2\>\<#89C2\>\<#FF0C\>\<#5219\>\<#4ED6\>\<#4EEC\>\<#7684\>\<#9009\>\<#62E9\>\<#4E2D\>\<#FF0C\>\<#6070\>\<#6709\>\<#4E00\>\<#4E2A\>\<#9986\>\<#76F8\>\<#540C\>\<#7684\>\<#6982\>\<#7387\>\<#4E3A\><underline|<space|3em>>.
|
|
|
|
<item>\<#5DF2\>\<#77E5\>\<#629B\>\<#7269\>\<#7EBF\><math|y<rsup|2>=2*p*x<around*|(|p\<gtr\>0|)>>\<#FF0C\>\<#82E5\>\<#7B2C\>\<#4E00\>\<#8C61\>\<#9650\>\<#7684\><math|A,B>\<#5728\>\<#629B\>\<#7269\>\<#7EBF\>\<#4E0A\>\<#FF0C\>\<#7126\>\<#70B9\>\<#4E3A\><math|F>\<#FF0C\><math|<around*|\||AF|\|>=2>\<#FF0C\><math|<around*|\||BF|\|>=4>\<#FF0C\><math|<around*|\||AB|\|>=3>\<#FF0C\>\<#6C42\>\<#76F4\>\<#7EBF\><math|AB>\<#7684\>\<#659C\>\<#7387\>\<#4E3A\><underline|<space|3em>>.
|
|
|
|
<item>\<#5DF2\>\<#77E5\><math|a<rsub|i>\<in\>\<b-up-N\><rsup|\<ast\>><around*|(|i=1,2,\<ldots\>,9|)>>\<#5BF9\>\<#4EFB\>\<#610F\>\<#7684\><math|k\<in\>\<b-up-N\><rsup|\<ast\>><around*|(|2\<leqslant\>k\<leqslant\>8|)>>\<#FF0C\><math|a<rsub|k>=a<rsub|k-1>+1>\<#6216\><math|a<rsub|k>=a<rsub|k+1>-1>\<#4E2D\>\<#6709\>\<#4E14\>\<#4EC5\>\<#6709\>\<#4E00\>\<#4E2A\>\<#6210\>\<#7ACB\>\<#FF0C\><math|a<rsub|1>=6>\<#FF0C\><math|a<rsub|9>=9>\<#FF0C\>\<#5219\><math|a<rsub|1>+\<cdots\>+a<rsub|9>>\<#7684\>\<#6700\>\<#5C0F\>\<#503C\>\<#4E3A\><underline|<space|3em>>.
|
|
</enumerate>
|
|
|
|
<subsubsection*|\<#4E8C\>\<#3001\>\<#586B\>\<#7A7A\>\<#9898\>>
|
|
|
|
<\enumerate>
|
|
<assign|item-nr|12><item>\<#4E0B\>\<#5217\>\<#51FD\>\<#6570\>\<#4E2D\>\<#FF0C\>\<#65E2\>\<#662F\>\<#5947\>\<#51FD\>\<#6570\>\<#53C8\>\<#662F\>\<#51CF\>\<#51FD\>\<#6570\>\<#7684\>\<#662F\><underline|<space|3em>>
|
|
|
|
<\wide-tabular>
|
|
<tformat|<table|<row|<\cell>
|
|
A. <math|y=-3*x>
|
|
</cell>|<\cell>
|
|
B. <math|y=x<rsup|3>>
|
|
</cell>|<\cell>
|
|
C. <math|y=log<rsub|3> x>
|
|
</cell>|<\cell>
|
|
D. <math|y=3<rsup|x>>
|
|
</cell>>>>
|
|
</wide-tabular>
|
|
|
|
<item>\<#5DF2\>\<#77E5\>\<#53C2\>\<#6570\>\<#65B9\>\<#7A0B\><choice|<tformat|<table|<row|<cell|x=3*t-4*t<rsup|3>>>|<row|<cell|y=2*t*<sqrt|1-t<rsup|2>>>>>>><math|,t\<in\><around*|[|-1,1|]>>\<#FF0C\>\<#4E0B\>\<#5217\>\<#9009\>\<#9879\>\<#7684\>\<#56FE\>\<#4E2D\>\<#FF0C\>\<#7B26\>\<#5408\>\<#8BE5\>\<#65B9\>\<#7A0B\>\<#7684\>\<#662F\><underline|<space|3em>>
|
|
|
|
<\wide-tabular>
|
|
<tformat|<cwith|1|1|1|1|cell-hyphen|n>|<cwith|1|1|2|2|cell-hyphen|t>|<cwith|1|1|1|1|cell-valign|c>|<cwith|1|1|1|1|cell-halign|c>|<table|<row|<\cell>
|
|
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</cell>>>>
|
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</wide-tabular>
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|
|
|
<item>\<#5DF2\>\<#77E5\><math|f<around*|(|x|)>=3*sin
|
|
x+2>\<#FF0C\>\<#5BF9\>\<#4EFB\>\<#610F\>\<#7684\><math|x<rsub|1>\<in\><around*|[|0,<frac|\<pi\>|2>|]>>\<#FF0C\>\<#90FD\>\<#5B58\>\<#5728\><math|x<rsub|2>\<in\><around*|[|0,<frac|\<pi\>|2>|]>>\<#FF0C\>\<#4F7F\>\<#5F97\><math|f<around*|(|x|)>=2*f<around*|(|x+\<theta\>|)>+2>\<#6210\>\<#7ACB\>\<#FF0C\>\<#5219\>\<#4E0B\>\<#5217\>\<#9009\>\<#9879\>\<#4E2D\>\<#FF0C\><math|\<theta\>>\<#53EF\>\<#80FD\>\<#7684\>\<#503C\>\<#4E3A\><underline|<space|3em>>
|
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|
|
<\wide-tabular>
|
|
<tformat|<table|<row|<\cell>
|
|
A. <math|<frac|3*\<pi\>|5>>
|
|
</cell>|<\cell>
|
|
B. <math|<frac|4*\<pi\>|5>>
|
|
</cell>|<\cell>
|
|
C. <math|<frac|6*\<pi\>|5>>
|
|
</cell>|<\cell>
|
|
D. <math|<frac|7*\<pi\>|5>>
|
|
</cell>>>>
|
|
</wide-tabular>
|
|
|
|
<item>\<#5DF2\>\<#77E5\><math|x<rsub|1>,y<rsub|1>,x<rsub|2>,y<rsub|2>,x<rsub|3>,y<rsub|3>>\<#540C\>\<#65F6\>\<#6EE1\>\<#8DB3\>:\<#2460\><math|x<rsub|1>\<less\>y<rsub|2>,x<rsub|2>\<less\>y<rsub|2>,x<rsub|3>\<less\>y<rsub|3>>;
|
|
\<#2461\><math|x<rsub|1>+y<rsub|1>=x<rsub|2>+y<rsub|2>=x<rsub|3>+y<rsub|3>;>
|
|
\<#2462\><math|x<rsub|1>y<rsub|1>+x<rsub|3>y<rsub|3>=2*x<rsub|2>y<rsub|2>>\<#FF0C\>\<#4EE5\>\<#4E0B\>\<#54EA\>\<#4E2A\>\<#9009\>\<#9879\>\<#6052\>\<#6210\>\<#7ACB\><underline|<space|3em>>
|
|
|
|
<\wide-tabular>
|
|
<tformat|<table|<row|<\cell>
|
|
A. <math|2*x<rsub|2>\<less\>x<rsub|1>+x<rsub|3>>
|
|
</cell>|<\cell>
|
|
B. <math|2*x<rsub|2>\<gtr\>x<rsub|1>+x<rsub|3>>
|
|
</cell>|<\cell>
|
|
C. <math|x<rsub|2><rsup|2>\<less\>x<rsub|1>x<rsub|3>>
|
|
</cell>|<\cell>
|
|
D. <math|x<rsub|2><rsup|2>\<gtr\>x<rsub|1>x<rsub|3>>
|
|
</cell>>>>
|
|
</wide-tabular>
|
|
</enumerate>
|
|
|
|
\;
|
|
|
|
<subsubsection*|\<#4E09\>\<#3001\>\<#89E3\>\<#7B54\>\<#9898\>>
|
|
|
|
<\enumerate>
|
|
<assign|item-nr|16><item>\<#5982\>\<#56FE\>\<#FF0C\>\<#5728\>\<#957F\>\<#65B9\>\<#4F53\><math|ABCD-A<rsub|1>B<rsub|1>C<rsub|1>D<rsub|1>>\<#4E2D\>\<#FF0C\>\<#5DF2\>\<#77E5\><math|AB=BC=2>\<#FF0C\><math|AA<rsub|1>=3>.
|
|
|
|
\<#FF08\>1\<#FF09\>\<#82E5\><math|P>\<#662F\>\<#68F1\><math|A<rsub|1>D<rsub|1>>\<#4E0A\>\<#7684\>\<#52A8\>\<#70B9\>\<#FF0C\>\<#6C42\>\<#4E09\>\<#68F1\>\<#9525\><math|C-PAD>\<#7684\>\<#4F53\>\<#79EF\>\<#FF1B\>
|
|
|
|
\<#FF08\>2\<#FF09\>\<#6C42\>\<#76F4\>\<#7EBF\><math|AB<rsub|1>>\<#4E0E\>\<#5E73\>\<#9762\><math|ACC<rsub|1>A<rsub|1>>\<#7684\>\<#5939\>\<#89D2\>\<#5927\>\<#5C0F\>.
|
|
|
|
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<item>\<#5DF2\>\<#77E5\>\<#5728\><math|\<vartriangle\>ABC>\<#4E2D\>\<#FF0C\><math|A,B,C>\<#6240\>\<#5BF9\>\<#8FB9\>\<#5206\>\<#522B\>\<#4E3A\><math|a,b,c>\<#FF0C\>\<#4E14\><math|a=3>\<#FF0C\><math|b=2*c>.
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\<#FF08\>1\<#FF09\>\<#82E5\><math|A=<frac|2*\<pi\>|3>>\<#FF0C\>\<#6C42\><math|S<rsub|\<vartriangle\>ABC>>\<#FF1B\>
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\<#FF08\>2\<#FF09\>\<#82E5\><math|2*sin B-sin
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C=1>\<#FF0C\>\<#6C42\><math|C<rsub|\<vartriangle\>ABC>>.
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<item>\<#5DF2\>\<#77E5\>\<#4E00\>\<#4F01\>\<#4E1A\>\<#4ECA\>\<#5E74\>\<#7B2C\>\<#4E00\>\<#5B63\>\<#5EA6\>\<#7684\>\<#8425\>\<#4E1A\>\<#989D\>\<#4E3A\>1.1\<#4EBF\>\<#5143\>\<#FF0C\>\<#5F80\>\<#540E\>\<#6BCF\>\<#4E2A\>\<#5B63\>\<#5EA6\>\<#589E\>\<#52A0\>0.05\<#4EBF\>\<#5143\>\<#FF0C\>\<#7B2C\>\<#4E00\>\<#5B63\>\<#5EA6\>\<#7684\>\<#5229\>\<#6DA6\>\<#4E3A\>0.16\<#4EBF\>\<#5143\>\<#FF0C\>\<#5F80\>\<#540E\>\<#6BCF\>\<#4E00\>\<#5B63\>\<#5EA6\>\<#6BD4\>\<#524D\>\<#4E00\>\<#5B63\>\<#5EA6\>\<#589E\>\<#957F\>4%.
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\<#FF08\>1\<#FF09\>\<#6C42\>\<#4ECA\>\<#5E74\>\<#8D77\>\<#7684\>\<#524D\>20\<#4E2A\>\<#5B63\>\<#5EA6\>\<#7684\>\<#603B\>\<#8425\>\<#4E1A\>\<#989D\>\<#FF1B\>
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\<#FF08\>2\<#FF09\>\<#8BF7\>\<#95EE\>\<#54EA\>\<#4E00\>\<#5B63\>\<#5EA6\>\<#7684\>\<#5229\>\<#6DA6\>\<#9996\>\<#6B21\>\<#8D85\>\<#8FC7\>\<#8BE5\>\<#5B63\>\<#5EA6\>\<#8425\>\<#4E1A\>\<#989D\>\<#7684\>18%?
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<item>\<#5DF2\>\<#77E5\><math|\<Gamma\>>\<#FF1A\><math|<frac|x<rsup|2>|2>+y<rsup|2>=1>\<#FF0C\><math|F<rsub|1>>\<#FF0C\><math|F<rsub|2>>\<#662F\>\<#5176\>\<#5DE6\>\<#3001\>\<#53F3\>\<#7126\>\<#70B9\>\<#FF0C\>\<#76F4\>\<#7EBF\><math|l>\<#8FC7\>\<#70B9\><math|P<around*|(|m,0|)><around*|(|m\<leqslant\>-<sqrt|2>|)>>\<#FF0C\>\<#4EA4\>\<#692D\>\<#5706\>\<#4E0E\>A,B\<#4E24\>\<#70B9\>\<#FF0C\>\<#4E14\><math|A>\<#FF0C\><math|B>\<#5728\><math|x>\<#8F74\>\<#4E0A\>\<#65B9\>\<#FF0C\>\<#70B9\><math|A>\<#5728\>\<#7EBF\>\<#6BB5\><math|BP>\<#4E0A\>.
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\<#FF08\>1\<#FF09\>\<#82E5\><math|B>\<#662F\>\<#4E0A\>\<#9876\>\<#70B9\>\<#FF0C\><math|<around*|\||<wide|BF<rsub|1>|\<vect\>>|\|>=<around*|\||<wide|PF<rsub|1>|\<vect\>>|\|>>\<#FF0C\>\<#6C42\><math|m>\<#7684\>\<#503C\>\<#FF1B\>
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\<#FF08\>2\<#FF09\>\<#82E5\><math|<wide|F<rsub|1>A|\<vect\>>\<cdot\><wide|F<rsub|2>A|\<vect\>>=<frac|1|3>>\<#FF0C\>\<#4E14\>\<#539F\>\<#70B9\><math|O>\<#5230\>\<#76F4\>\<#7EBF\><math|l>\<#7684\>\<#8DDD\>\<#79BB\>\<#4E3A\><math|<frac|4<sqrt|15>|15>>\<#FF0C\>\<#6C42\>\<#76F4\>\<#7EBF\><math|l>\<#7684\>\<#65B9\>\<#7A0B\>\<#FF1B\>
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\<#FF08\>3\<#FF09\>\<#8BC1\>\<#660E\>\<#FF1A\>\<#5BF9\>\<#4E8E\>\<#4EFB\>\<#610F\><math|m\<less\>-<sqrt|2>>\<#FF0C\>\<#4F7F\>\<#5F97\><math|<wide|F<rsub|1>A|\<vect\>>//<wide|F<rsub|2>B|\<vect\>>>\<#7684\>\<#76F4\>\<#7EBF\>\<#6709\>\<#4E14\>\<#4EC5\>\<#6709\>\<#4E00\>\<#6761\>.
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<item>\<#5DF2\>\<#77E5\><math|x<rsub|1>,x<rsub|2>\<in\>\<b-up-R\>>\<#FF0C\>\<#82E5\>\<#5BF9\>\<#4EFB\>\<#610F\>\<#7684\><math|x<rsub|2>-x<rsub|1>\<in\>S>\<#FF0C\><math|f<around*|(|x<rsub|2>|)>-f<around*|(|x<rsub|1>|)>\<in\>S>\<#FF0C\>\<#5219\>\<#6709\>\<#5B9A\>\<#4E49\>\<#FF1A\><math|f<around*|(|x|)>>\<#662F\>\<#5728\><math|S>\<#5173\>\<#8054\>\<#7684\>.
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\<#FF08\>1\<#FF09\>\<#5224\>\<#65AD\>\<#548C\>\<#8BC1\>\<#660E\><math|f<around*|(|x|)>=2*x-1>\<#662F\>\<#5426\>\<#5728\><math|<around*|[|0,+\<infty\>|)>>\<#5173\>\<#8054\>\<#FF1F\>\<#662F\>\<#5426\>\<#6709\><math|<around*|[|0,1|]>>\<#5173\>\<#8054\>\<#FF1F\>
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\<#FF08\>2\<#FF09\>\<#82E5\><math|f<around*|(|x|)>>\<#662F\><math|<around*|{|3|}>>\<#5173\>\<#8054\>\<#FF0C\>\<#5F53\>\<#5728\><math|x\<in\><around*|[|0\<#FF0C\>3|]>><math|><math|>\<#65F6\>\<#FF0C\><math|f<around*|(|x|)>=x<rsup|2>-2*x>\<#FF0C\>\<#89E3\>\<#4E0D\>\<#7B49\>\<#5F0F\><math|2\<leqslant\>f<around*|(|x|)>\<leqslant\>3>\<#FF1B\>
|
|
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|
\<#FF08\>3\<#FF09\>\<#8BC1\>\<#660E\>\<#FF1A\>\P<math|f<around*|(|x|)>>\<#662F\><math|<around*|{|1|}>>\<#5173\>\<#8054\>\<#FF0C\>\<#4E14\>\<#662F\><math|<around*|[|0,+\<infty\>|)>>\<#5173\>\<#8054\>\Q\<#7684\>\<#5145\>\<#8981\>\<#6761\>\<#4EF6\>\<#662F\>\P<math|f<around*|(|x|)>>\<#662F\><math|[1,2]>\<#5173\>\<#8054\>\Q
|
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</enumerate>
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</body>
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|
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<\initial>
|
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<\collection>
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<associate|page-medium|paper>
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</collection>
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</initial>
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|
|
|
<\references>
|
|
<\collection>
|
|
<associate|auto-1|<tuple|?|1>>
|
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<associate|auto-2|<tuple|12|1>>
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<associate|auto-3|<tuple|16|2>>
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</collection>
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</references>
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|
|
|
<\auxiliary>
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<\collection>
|
|
<\associate|toc>
|
|
<with|par-left|<quote|2tab>|\<#4E00\>\<#3001\>\<#5355\>\<#9009\>\<#9898\>
|
|
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
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<no-break><pageref|auto-1>>
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|
|
|
<with|par-left|<quote|2tab>|\<#4E8C\>\<#3001\>\<#586B\>\<#7A7A\>\<#9898\>
|
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<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
|
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<no-break><pageref|auto-2>>
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<with|par-left|<quote|2tab>|\<#4E09\>\<#3001\>\<#89E3\>\<#7B54\>\<#9898\>
|
|
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
|
|
<no-break><pageref|auto-3>>
|
|
</associate>
|
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</collection>
|
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</auxiliary> |