mirror of https://gitee.com/XmacsLabs/planet.git
178 lines
78 KiB
Tcl
178 lines
78 KiB
Tcl
<TeXmacs|2.1.2>
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<style|<tuple|exam|std-latex|chinese>>
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<\body>
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<doc-data|<doc-title|2022\<#5E74\>\<#6570\>\<#5B66\>\<#5168\>\<#56FD\>\<#4E59\>\<#5377\>\<#FF08\>\<#7406\>\<#79D1\>\<#FF09\>>>
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\<#4E00\>\<#3001\>\<#5355\>\<#9009\>\<#9898\>\<#FF08\>\<#672C\>\<#5927\>\<#9898\>\<#5171\>12\<#5C0F\>\<#9898\>\<#FF0C\>\<#5171\>60\<#5206\>\<#FF09\>
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<\enumerate-numeric>
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<item>\<#8BBE\>\<#5168\>\<#96C6\><math|U=<around|{|1,2,3,4,5|}>>\<#FF0C\>\<#96C6\>\<#5408\><math|M>\<#6EE1\>\<#8DB3\><math|\<complement\><rsub|U>*M=<around|{|1,3|}>>\<#FF0C\>\<#5219\>
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<tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-halign|l>|<table|<row|<cell|A.
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<math|2\<in\>M>>|<cell|B. <math|3\<in\>M>>|<cell|C.
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<math|4*\<nin\>M>>|<cell|D. <math|5*\<nin\>M>>>>>>
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<item>\<#5DF2\>\<#77E5\><math|z=1-2*i>\<#FF0C\>\<#4E14\><math|z+a*<wide|z|\<bar\>>+b=0>\<#FF0C\>\<#5176\>\<#4E2D\><math|a>\<#FF0C\><math|b>\<#4E3A\>\<#5B9E\>\<#6570\>\<#FF0C\>\<#5219\>
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<tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-halign|l>|<cwith|2|2|1|2|cell-valign|c>|<cwith|2|2|1|2|cell-halign|l>|<table|<row|<cell|A.
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<math|a=1>\<#FF0C\><math|b=-2>>|<cell|B.
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<math|a=-1>\<#FF0C\><math|b=2>>>|<row|<cell|C.
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<math|a=1>\<#FF0C\><math|b=2>>|<cell|D.
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<math|a=-1>\<#FF0C\><math|b=-2>>>>>>
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<item>\<#5DF2\>\<#77E5\>\<#5411\>\<#91CF\><math|a>\<#FF0C\><math|b>\<#6EE1\>\<#8DB3\><math|<around|\||<wide|a|\<wide-varrightarrow\>>|\|>=1>\<#FF0C\><math|<around|\||<wide|b|\<wide-varrightarrow\>>|\|>=<sqrt|3>>\<#FF0C\><math|<around|\||<wide|a|\<wide-varrightarrow\>>-2*<wide|b|\<wide-varrightarrow\>>|\|>=3>\<#FF0C\>\<#5219\><math|<wide|a|\<wide-varrightarrow\>>*\<cdot\>*<wide|b|\<wide-varrightarrow\>>=>
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<tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-halign|l>|<table|<row|<cell|A.
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<math|-2>>|<cell|B. <math|-1>>|<cell|C. <math|1>>|<cell|D. <math|2>>>>>>
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<item>\<#5AE6\>\<#5A25\>\<#4E8C\>\<#53F7\>\<#536B\>\<#661F\>\<#5728\>\<#5B8C\>\<#6210\>\<#63A2\>\<#6708\>\<#4EFB\>\<#52A1\>\<#540E\>\<#FF0C\>\<#7EE7\>\<#7EED\>\<#8FDB\>\<#884C\>\<#6DF1\>\<#7A7A\>\<#63A2\>\<#6D4B\>\<#FF0C\>\<#6210\>\<#4E3A\>\<#6211\>\<#56FD\>\<#7B2C\>\<#4E00\>\<#9897\>\<#73AF\>\<#7ED5\>\<#592A\>\<#9633\>\<#98DE\>\<#884C\>\<#7684\>\<#4EBA\>\<#9020\>\<#884C\>\<#661F\>.\<#4E3A\>\<#7814\>\<#7A76\>\<#5AE6\>\<#5A25\>\<#4E8C\>\<#53F7\>\<#7ED5\>\<#65E5\>\<#5468\>\<#671F\>\<#4E0E\>\<#5730\>\<#7403\>\<#7ED5\>\<#65E5\>\<#5468\>\<#671F\>\<#7684\>\<#6BD4\>\<#503C\>\<#FF0C\>\<#7528\>\<#5230\>\<#6570\>\<#5217\><math|<around|{|b<rsub|n>|}>:b<rsub|1>=1+<frac|1|\<alpha\><rsub|1>>>\<#FF0C\><math|b<rsub|2>=1+<frac|1|\<alpha\><rsub|1>+<frac|1|\<alpha\><rsub|2>>>>\<#FF0C\><math|b<rsub|3>=1+<frac|1|\<alpha\><rsub|1>+<frac|1|\<alpha\><rsub|2>+<frac|1|\<alpha\><rsub|3>>>>>\<#FF0C\>\<cdots\>\<#FF0C\>\<#4F9D\>\<#6B64\>\<#7C7B\>\<#63A8\>\<#FF0C\>\<#5176\>\<#4E2D\><math|\<alpha\><rsub|k>\<in\>N<rsup|\<ast\>>(k=1,2,\<cdots\>)>.\<#5219\>
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<tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-halign|l>|<table|<row|<cell|A.
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<math|b<rsub|1>\<less\>b<rsub|5>>>|<cell|B.
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<math|b<rsub|3>\<less\>b<rsub|s>>>|<cell|C.
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<math|b<rsub|6>\<less\>b<rsub|2>>>|<cell|D.
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<math|b<rsub|4>\<less\>b<rsub|7>>>>>>>
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<item>\<#8BBE\><math|F>\<#4E3A\>\<#629B\>\<#7269\>\<#7EBF\><math|C:y<rsup|2>=4*x>\<#7684\>\<#7126\>\<#70B9\>\<#FF0C\>\<#70B9\><math|A>\<#5728\><math|C>\<#4E0A\>\<#FF0C\>\<#70B9\><math|B*<around|(|3,0|)>>\<#FF0C\>\<#82E5\><math|<around|\||A*F|\|>=<around|\||B*F|\|>>\<#FF0C\>\<#5219\><math|<around|\||A*B|\|>=>
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<tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-halign|l>|<table|<row|<cell|A.
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<math|2>>|<cell|B. <math|2*<sqrt|2>>>|<cell|C. <math|3>>|<cell|D.
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<math|3*<sqrt|2>>>>>>>
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<item>\<#6267\>\<#884C\>\<#53F3\>\<#8FB9\>\<#7684\>\<#7A0B\>\<#5E8F\>\<#6846\>\<#56FE\>\<#FF0C\>\<#8F93\>\<#51FA\>\<#7684\><math|n=>
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|png>|90pt|117pt||>
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<tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-halign|l>|<table|<row|<cell|A.
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<math|3>>|<cell|B. <math|4>>|<cell|C. <math|5>>|<cell|D. <math|6>>>>>>
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<item>\<#5728\>\<#6B63\>\<#65B9\>\<#4F53\><math|A*B*C*D-A<rsub|1>*B<rsub|1>*C<rsub|1>*D<rsub|1>>\<#4E2D\>\<#FF0C\><math|E>\<#FF0C\><math|F>\<#5206\>\<#522B\>\<#4E3A\><math|A*B>\<#FF0C\><math|B*C>\<#7684\>\<#4E2D\>\<#70B9\>\<#FF0C\>\<#5219\>
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<tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<cwith|2|2|1|2|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|-1|1|-1|cell-halign|l>|<table|<row|<cell|A.
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\<#5E73\>\<#9762\><math|B<rsub|1>*E*F*\<bot\>>\<#5E73\>\<#9762\><math|B*D*D<rsub|1>>>|<cell|B.
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\<#5E73\>\<#9762\><math|B<rsub|1>*E*F*\<bot\>>\<#5E73\>\<#9762\><math|A<rsub|1>*B*D>>>|<row|<cell|C.
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\<#5E73\>\<#9762\><math|B<rsub|1>*E*F//>\<#5E73\>\<#9762\><math|A<rsub|1>*A*C>>|<cell|D.
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\<#5E73\>\<#9762\><math|B<rsub|1>*E*F//>\<#5E73\>\<#9762\><math|A<rsub|1>*C<rsub|1>*D>>>>>>
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<item>\<#5DF2\>\<#77E5\>\<#7B49\>\<#6BD4\>\<#6570\>\<#5217\><math|<around|{|a<rsub|n>|}>>\<#7684\>\<#524D\><math|3>\<#9879\>\<#548C\>\<#4E3A\><math|168>\<#FF0C\><math|a<rsub|2>-a<rsub|5>=42>\<#FF0C\>\<#5219\><math|a<rsub|6>=>
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<tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-halign|l>|<table|<row|<cell|A.
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<math|14>>|<cell|B. <math|12>>|<cell|C. <math|6>>|<cell|D. <math|3>>>>>>
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<item>\<#5DF2\>\<#77E5\>\<#7403\><math|O>\<#7684\>\<#534A\>\<#5F84\>\<#4E3A\><math|1>\<#FF0C\>\<#56DB\>\<#68F1\>\<#9525\>\<#7684\>\<#9876\>\<#70B9\>\<#4E3A\><math|O>\<#FF0C\>\<#5E95\>\<#9762\>\<#7684\>\<#56DB\>\<#4E2A\>\<#9876\>\<#70B9\>\<#5747\>\<#5728\>\<#7403\><math|O>\<#7684\>\<#7403\>\<#9762\>\<#4E0A\>\<#FF0C\>\<#5219\>\<#5F53\>\<#8BE5\>\<#56DB\>\<#68F1\>\<#9525\>\<#7684\>\<#4F53\>\<#79EF\>\<#6700\>\<#5927\>\<#65F6\>\<#FF0C\>\<#5176\>\<#9AD8\>\<#4E3A\>
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<tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-halign|l>|<table|<row|<cell|A.
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<math|<frac|1|3>>>|<cell|B. <math|<frac|1|2>>>|<cell|C.
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<math|<frac|<sqrt|3>|3>>>|<cell|D. <math|<frac|<sqrt|2>|2>>>>>>>
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<item>\<#67D0\>\<#68CB\>\<#624B\>\<#4E0E\>\<#7532\>\<#3001\>\<#4E59\>\<#3001\>\<#4E19\>\<#4E09\>\<#4F4D\>\<#68CB\>\<#624B\>\<#5404\>\<#6BD4\>\<#8D5B\>\<#4E00\>\<#76D8\>\<#FF0C\>\<#5404\>\<#76D8\>\<#6BD4\>\<#8D5B\>\<#7ED3\>\<#679C\>\<#76F8\>\<#4E92\>\<#72EC\>\<#7ACB\>.\<#5DF2\>\<#77E5\>\<#8BE5\>\<#68CB\>\<#624B\>\<#4E0E\>\<#7532\>\<#3001\>\<#4E59\>\<#3001\>\<#4E19\>\<#6BD4\>\<#8D5B\>\<#83B7\>\<#80DC\>\<#7684\>\<#6982\>\<#7387\>\<#5206\>\<#522B\>\<#4E3A\><math|p<rsub|1>>\<#FF0C\><math|p<rsub|2>>\<#FF0C\><math|p<rsub|3>>\<#FF0C\>\<#4E14\><math|p<rsub|3>\<gtr\>p<rsub|2>\<gtr\>p<rsub|1>\<gtr\>0>.\<#8BB0\>\<#8BE5\>\<#68CB\>\<#624B\>\<#8FDE\>\<#80DC\>\<#4E24\>\<#76D8\>\<#7684\>\<#6982\>\<#7387\>\<#4E3A\><math|p>\<#FF0C\>\<#5219\>
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A. <math|p>\<#4E0E\>\<#8BE5\>\<#68CB\>\<#624B\>\<#548C\>\<#7532\>\<#3001\>\<#4E59\>\<#3001\>\<#4E19\>\<#7684\>\<#6BD4\>\<#8D5B\>\<#6B21\>\<#5E8F\>\<#65E0\>\<#5173\>
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B. \<#8BE5\>\<#68CB\>\<#624B\>\<#5728\>\<#7B2C\>\<#4E8C\>\<#76D8\>\<#4E0E\>\<#7532\>\<#6BD4\>\<#8D5B\>\<#FF0C\><math|p>\<#6700\>\<#5927\>
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C. \<#8BE5\>\<#68CB\>\<#624B\>\<#5728\>\<#7B2C\>\<#4E8C\>\<#76D8\>\<#4E0E\>\<#4E59\>\<#6BD4\>\<#8D5B\>\<#FF0C\><math|p>\<#6700\>\<#5927\>
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D. \<#8BE5\>\<#68CB\>\<#624B\>\<#5728\>\<#7B2C\>\<#4E8C\>\<#76D8\>\<#4E0E\>\<#4E19\>\<#6BD4\>\<#8D5B\>\<#FF0C\><math|p>\<#6700\>\<#5927\>
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<item>\<#5BF9\>\<#66F2\>\<#7EBF\><math|C>\<#7684\>\<#4E24\>\<#4E2A\>\<#7126\>\<#70B9\>\<#4E3A\><math|F<rsub|1>>\<#FF0C\><math|F<rsub|2>>\<#FF0C\>\<#4EE5\><math|C>\<#7684\>\<#5B9E\>\<#8F74\>\<#4E3A\>\<#76F4\>\<#5F84\>\<#7684\>\<#5706\>\<#8BB0\>\<#4E3A\><math|D>\<#FF0C\>\<#8FC7\><math|F<rsub|1>>\<#4F5C\><math|D>\<#7684\>\<#5207\>\<#7EBF\>\<#4E0E\><math|C>\<#4EA4\>\<#4E8E\><math|M>\<#FF0C\><math|N>\<#4E24\>\<#70B9\>\<#FF0C\>\<#4E14\><math|<math-up|cos>\<angle\>*F<rsub|1>*N*F<rsub|2>=<frac|3|5>>\<#FF0C\>\<#5219\><math|C>\<#7684\>\<#79BB\>\<#5FC3\>\<#7387\>\<#4E3A\>
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<tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-halign|l>|<table|<row|<cell|A.
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<math|<frac|<sqrt|5>|2>>>|<cell|B. <math|<frac|3|2>>>|<cell|C.
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<math|<frac|<sqrt|13>|2>>>|<cell|D. <math|<frac|<sqrt|17>|2>>>>>>>
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<item>\<#5DF2\>\<#77E5\>\<#51FD\>\<#6570\><math|f<around|(|x|)>>\<#FF0C\><math|g<around|(|x|)>>\<#7684\>\<#5B9A\>\<#4E49\>\<#57DF\>\<#5747\>\<#4E3A\><math|R>\<#FF0C\>\<#4E14\><math|f<around|(|x|)>+g*<around|(|2-x|)>=5>\<#FF0C\>
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<math|g<around|(|x|)>-f*<around|(|x-4|)>=7>\<#FF0C\>
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\<#82E5\><math|y=g<around|(|x|)>>\<#7684\>\<#56FE\>\<#50CF\>\<#5173\>\<#4E8E\>\<#76F4\>\<#7EBF\><math|x=2>\<#5BF9\>\<#79F0\>\<#FF0C\><math|g<around|(|2|)>=4>\<#FF0C\>
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\<#5219\><math|<big|sum><rsup|22><rsub|k=1>f<around|(|k|)>=>
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<tabular*|<tformat|<cwith|1|-1|1|-1|cell-valign|c>|<twith|table-width|1par>|<twith|table-hmode|exact>|<cwith|1|1|1|-1|cell-halign|l>|<table|<row|<cell|A.
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<math|-21>>|<cell|B. <math|-22>>|<cell|C. <math|-23>>|<cell|D.
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<math|-24>>>>>>
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</enumerate-numeric>
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\<#4E8C\>\<#3001\>\<#586B\>\<#7A7A\>\<#9898\>\<#FF08\>\<#672C\>\<#5927\>\<#9898\>\<#5171\>4\<#5C0F\>\<#9898\>\<#FF0C\>\<#5171\>20.0\<#5206\>\<#FF09\>
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<\enumerate-numeric>
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<assign|item-nr|12><item>\<#4ECE\>\<#7532\>\<#3001\>\<#4E59\>\<#7B49\><math|5>\<#540D\>\<#540C\>\<#5B66\>\<#4E2D\>\<#968F\>\<#673A\>\<#9009\><math|3>\<#540D\>\<#53C2\>\<#52A0\>\<#793E\>\<#533A\>\<#670D\>\<#52A1\>\<#5DE5\>\<#4F5C\>\<#FF0C\>\<#5219\>\<#7532\>\<#3001\>\<#4E59\>\<#90FD\>\<#5165\>\<#9009\>\<#7684\>\<#6982\>\<#7387\>\<#4E3A\><underline|<space|2cm>>\<#FF0E\>
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<item>\<#8FC7\>\<#56DB\>\<#70B9\><math|<around|(|0,0|)>>\<#FF0C\><math|<around|(|4,0|)>>\<#FF0C\><math|<around|(|-1,1|)>>\<#FF0C\><math|<around|(|4,2|)>>\<#4E2D\>\<#7684\>\<#4E09\>\<#70B9\>\<#7684\>\<#4E00\>\<#4E2A\>\<#5706\>\<#7684\>\<#65B9\>\<#7A0B\>\<#4E3A\><underline|<space|2cm>>\<#FF0E\>
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<item>\<#8BB0\>\<#51FD\>\<#6570\><math|f<around|(|x|)>=<math-up|cos><around|(|\<omega\>*x+\<varphi\>|)>*<around|(|\<omega\>\<gtr\>0,0\<less\>\<varphi\>\<less\>\<pi\>|)>>\<#7684\>\<#6700\>\<#5C0F\>\<#6B63\>\<#5468\>\<#671F\>\<#4E3A\><math|T>\<#FF0C\>\<#82E5\><math|f<around|(|T|)>=<frac|<sqrt|3>|2>>\<#FF0C\><math|x=<frac|\<pi\>|9>>\<#4E3A\><math|f<around|(|x|)>>\<#7684\>\<#96F6\>\<#70B9\>\<#FF0C\>\<#5219\><math|\<omega\>>\<#7684\>\<#6700\>\<#5C0F\>\<#503C\>\<#4E3A\><underline|<space|2cm>>\<#FF0E\>
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<item>\<#5DF2\>\<#77E5\><math|x=x<rsub|1>>\<#548C\><math|x=x<rsub|2>>\<#5206\>\<#522B\>\<#662F\>\<#51FD\>\<#6570\><math|f<around|(|x|)>=2*a<rsup|x>-e*x<rsup|2>(a\<gtr\>0>\<#4E14\><math|a\<neq\>1)>\<#7684\>\<#6781\>\<#5C0F\>\<#503C\>\<#70B9\>\<#548C\>\<#6781\>\<#5927\>\<#503C\>\<#70B9\>\<#FF0C\>\<#82E5\><math|x<rsub|1>\<less\>x<rsub|2>>\<#FF0C\>\<#5219\><math|a>\<#7684\>\<#53D6\>\<#503C\>\<#8303\>\<#56F4\>\<#662F\><underline|<space|2cm>>.
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</enumerate-numeric>
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|
\<#4E09\>\<#3001\>\<#89E3\>\<#7B54\>\<#9898\>\<#FF08\>\<#672C\>\<#5927\>\<#9898\>\<#5171\>7\<#5C0F\>\<#9898\>\<#FF0C\>\<#5171\>80\<#5206\>\<#FF09\>
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\ (\<#4E00\>) \ \<#5FC5\>\<#8003\>\<#9898\>\<#FF1A\>\<#5171\> 60 \<#5206\>.
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|
<\enumerate-numeric>
|
|
<assign|item-nr|16><item>\<#8BB0\><math|\<Delta\>*A*B*C>\<#7684\>\<#5185\>\<#89D2\><math|A>\<#3001\><math|B>\<#3001\><math|C>\<#7684\>\<#5BF9\>\<#8FB9\>\<#5206\>\<#522B\>\<#4E3A\><math|a>\<#3001\><math|b>\<#3001\><math|c>\<#FF0C\>\<#5DF2\>\<#77E5\><math|<math-up|sin>C<math-up|sin><around|(|A-B|)>=<math-up|sin>B<math-up|sin><around|(|C-A|)>>\<#FF0E\>
|
|
|
|
(1)\<#8BC1\>\<#660E\>\<#FF1A\><math|2*a<rsup|2>=b<rsup|2>+c<rsup|2>>;
|
|
|
|
(2)\<#82E5\><math|a=5>\<#FF0C\><math|<math-up|cos>A=<frac|25|31>>\<#FF0C\>\<#6C42\><math|\<Delta\>*A*B*C>\<#7684\>\<#5468\>\<#957F\>\<#FF0E\><vspace|5cm>
|
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|
|
<item>\<#5982\>\<#56FE\>\<#FF0C\>\<#56DB\>\<#9762\>\<#4F53\><math|A*B*C*D>\<#4E2D\><math|A*D*\<bot\>*C*D>\<#FF0C\><math|A*D=C*D>\<#FF0C\><math|\<angle\>*A*D*B=\<angle\>*B*D*C>\<#FF0C\><math|E>\<#4E3A\><math|A*C>\<#4E2D\>\<#70B9\>\<#FF0E\>
|
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|
|
(1)\<#8BC1\>\<#660E\>\<#FF1A\>\<#5E73\>\<#9762\><math|B*E*D*\<bot\>>\<#5E73\>\<#9762\><math|A*C*D>;
|
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|
(2)\<#8BBE\><math|A*B=B*D=2>\<#FF0C\><math|\<angle\>*A*C*B=60<rsup|\<circ\>>>\<#FF0C\>\<#70B9\><math|F>\<#5728\><math|B*D>\<#4E0A\>\<#FF0C\>\<#5F53\><math|\<bigtriangleup\>*A*F*C>\<#7684\>\<#9762\>\<#79EF\>\<#6700\>\<#5C0F\>\<#65F6\>\<#FF0C\>\<#6C42\><math|C*F>\<#4E0E\>\<#5E73\>\<#9762\><math|A*B*D>\<#6240\>\<#6210\>\<#89D2\>\<#7684\>\<#6B63\>\<#5F26\>\<#503C\>\<#FF0E\>
|
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<item>\<#67D0\>\<#5730\>\<#7ECF\>\<#8FC7\>\<#591A\>\<#5E74\>\<#7684\>\<#73AF\>\<#586B\>\<#6CBB\>\<#7406\>\<#FF0C\>\<#5DF2\>\<#5C06\>\<#5C31\>\<#5C71\>\<#6539\>\<#9020\>\<#6210\>\<#4E86\>\<#7EFF\>\<#6C34\>\<#9752\>\<#5C71\>.\<#4E3A\>\<#4F30\>\<#8BA1\>\<#4E00\>\<#6797\>\<#533A\>\<#67D0\>\<#79CD\>\<#6811\>\<#6728\>\<#7684\>\<#603B\>\<#6750\>\<#79EF\>\<#91CF\>\<#FF0C\>\<#968F\>\<#673A\>\<#9009\>\<#53D6\>\<#4E86\><math|10>\<#68F5\>\<#8FD9\>\<#79CD\>\<#6751\>\<#6728\>\<#FF0C\>\<#6D4B\>\<#91CF\>\<#6BCF\>\<#68F5\>\<#6751\>\<#7684\>\<#6839\>\<#90E8\>\<#6A2A\>\<#622A\>\<#800C\>\<#79EF\>(\<#5FC3\>\<#4F4D\>\<#FF1A\><math|m<rsup|2>>)\<#548C\>\<#6750\>\<#79EF\>\<#91CF\><math|<around|(|m<rsup|3>|)>>\<#FF0C\>\<#5F97\>\<#5230\>\<#5982\>\<#4E0B\>\<#6570\>\<#636E\>\<#FF1A\>
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<block*|<tformat|<table|<row|<cell|\<#6837\>\<#672C\>\<#53F7\><math|i>>|<cell|1>|<cell|2>|<cell|3>|<cell|4>|<cell|5>|<cell|6>|<cell|7>|<cell|8>|<cell|9>|<cell|10>|<cell|\<#603B\>\<#548C\>>>|<row|<cell|\<#6839\>\<#90E8\>\<#6A2A\>\<#622A\>\<#9762\>\<#79EF\><math|x
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<rsub|i>>>|<cell|0.04>|<cell|0.06>|<cell|0.04>|<cell|0.08>|<cell|0.08>|<cell|0.05>|<cell|0.05>|<cell|0.07>|<cell|0.07>|<cell|0.06>|<cell|0.6>>|<row|<cell|\<#6750\>\<#79EF\>\<#91CF\><math|y<rsub|i>>>|<cell|0.25>|<cell|0.40>|<cell|0.22>|<cell|0.54>|<cell|0.51>|<cell|0.34>|<cell|0.36>|<cell|0.46>|<cell|0.42>|<cell|0.40>|<cell|3.9>>>>>
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\<#5E76\>\<#8BA1\>\<#7B97\>\<#5F97\><math|<big|sum><rsup|10><rsub|i=1>x<rsub|i><rsup|2>=0.038>\<#FF0C\><math|<big|sum><rsup|10><rsub|i=1>y<rsup|2><rsub|i>=1.6158>\<#FF0C\><math|<big|sum><rsup|10><rsub|i=1>x<rsub|i>*y<rsub|i>=0.2474>\<#FF0E\>
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(1)\<#4F30\>\<#8BA1\>\<#8BE5\>\<#6797\>\<#533A\>\<#8FD9\>\<#79CD\>\<#6811\>\<#6728\>\<#5E73\>\<#5747\>\<#4E00\>\<#68F5\>\<#7684\>\<#6839\>\<#90E8\>\<#6A2A\>\<#622A\>\<#9762\>\<#79EF\>\<#4E0E\>\<#5E73\>\<#5747\>\<#4E00\>\<#68F5\>\<#7684\>\<#6750\>\<#79EF\>\<#91CF\>\<#FF1A\>
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(2)\<#6C42\>\<#8BE5\>\<#6797\>\<#533A\>\<#8FD9\>\<#79CD\>\<#6811\>\<#6728\>\<#7684\>\<#6839\>\<#90E8\>\<#6A2A\>\<#622A\>\<#9762\>\<#79EF\>\<#4E0E\>\<#6750\>\<#79EF\>\<#91CF\>\<#7684\>\<#6837\>\<#672C\>\<#76F8\>\<#5173\>\<#7CFB\>\<#6570\>(\<#7CBE\>\<#786E\>\<#5230\>0.01);
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(3)\<#73B0\>\<#6D4B\>\<#91CF\>\<#4E86\>\<#8BE5\>\<#6797\>\<#533A\>\<#6240\>\<#6709\>\<#8FD9\>\<#79CD\>\<#6811\>\<#6728\>\<#7684\>\<#6839\>\<#90E8\>\<#6A2A\>\<#622A\>\<#9762\>\<#79EF\>\<#FF0C\>\<#5E76\>\<#5F97\>\<#5230\>\<#6240\>\<#6709\>\<#8FD9\>\<#79CD\>\<#6811\>\<#6728\>\<#7684\>\<#6839\>\<#90E8\>\<#6A2A\>\<#622A\>\<#9762\>\<#79EF\>\<#603B\>\<#548C\>\<#4E3A\><math|186*m<rsup|2>>.\<#5DF2\>\<#77E5\>\<#6811\>\<#6728\>\<#7684\>\<#6750\>\<#79EF\>\<#91CF\>\<#4E0E\>\<#5176\>\<#6839\>\<#90E8\>\<#6A2A\>\<#622A\>\<#9762\>\<#79EF\>\<#8FD1\>\<#4F3C\>\<#6210\>\<#6B63\>\<#6BD4\>.\<#5229\>\<#7528\>\<#4EE5\>\<#4E0A\>\<#6570\>\<#636E\>\<#7ED9\>\<#51FA\>\<#8BE5\>\<#6797\>\<#533A\>\<#8FD9\>\<#79CD\>\<#6811\>\<#6728\>\<#7684\>\<#603B\>\<#6750\>\<#79EF\>\<#91CF\>\<#7684\>\<#4F30\>\<#8BA1\>\<#503C\>\<#FF0E\>
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\<#9644\>\<#FF1A\>\<#76F8\>\<#5173\>\<#7CFB\>\<#6570\><math|r=<frac|<big|sum><rsup|n><rsub|i=1><around*|(|x<rsub|i>-<wide|x|\<bar\>>|)>*<around*|(|y<rsub|i>-<wide|y|\<bar\>>|)>|<sqrt|<big|sum><rsup|n><rsub|i=1><around*|(|x<rsub|i>-<wide|x|\<bar\>>|)><rsup|2>*<big|sum><rsup|n><rsub|i=1><around*|(|y<rsub|i>-<wide|y|\<bar\>>|)><rsup|2>>>>\<#FF0C\><math|<sqrt|1.896>\<approx\>1.377>\<#FF0E\><vspace|5cm>
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<item>\<#5DF2\>\<#77E5\>\<#692D\>\<#5706\><math|E>\<#7684\>\<#4E2D\>\<#5FC3\>\<#4E3A\>\<#5750\>\<#6807\>\<#539F\>\<#70B9\>\<#FF0C\>\<#5BF9\>\<#79F0\>\<#8F74\>\<#4E3A\><math|x>\<#8F74\>\<#FF0C\><math|y>\<#8F74\>\<#FF0C\>\<#4E14\>\<#8FC7\><math|A*<around|(|0,-2|)>>\<#FF0C\>
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<math|B*<around|(|<frac|3|2>,-1|)>> \<#4E24\>\<#70B9\>.
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(1)\<#6C42\><math|E>\<#7684\>\<#65B9\>\<#7A0B\>;
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(2)\<#8BBE\>\<#8FC7\>\<#70B9\><math|P<around|(|1,-2|)>>\<#7684\>\<#76F4\>\<#7EBF\>\<#4EA4\><math|E>\<#4E8E\><math|M>\<#FF0C\><math|N>\<#4E24\>\<#70B9\>\<#FF0C\>\<#8FC7\><math|M>\<#4E14\>\<#5E73\>\<#884C\>\<#4E8E\><math|x>\<#7684\>\<#76F4\>\<#7EBF\>\<#4E0E\>\<#7EBF\>\<#6BB5\><math|A*B>\<#4EA4\>\<#4E8E\>\<#70B9\><math|T>\<#FF0C\>\<#70B9\><math|H>\<#6EE1\>\<#8DB3\><math|<wide|M*T|\<wide-varrightarrow\>>=<wide|T*H|\<wide-varrightarrow\>>>\<#FF0C\>\<#8BC1\>\<#660E\>\<#FF1A\>\<#76F4\>\<#7EBF\><math|H*N>\<#8FC7\>\<#5B9A\>\<#70B9\>\<#FF0E\><vspace|5cm>
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<item>\<#5DF2\>\<#77E5\>\<#51FD\>\<#6570\><math|f<around|(|x|)>=<math-up|ln><around|(|1+x|)>+a*x*e<rsup|-x>>\<#FF0E\>
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(1)\<#5F53\><math|a=1>\<#65F6\>\<#FF0C\>\<#6C42\>\<#66F2\>\<#7EBF\><math|f<around|(|x|)>>\<#5728\>\<#70B9\><math|<around|(|0,f<around|(|0|)>|)>>\<#5904\>\<#7684\>\<#5207\>\<#7EBF\>\<#65B9\>\<#7A0B\>\<#FF1A\>
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(2)\<#82E5\><math|f<around|(|x|)>>\<#5728\>\<#533A\>\<#95F4\><math|<around|(|-1,0|)>>\<#FF0C\><math|<around|(|0,+\<infty\>|)>>\<#5404\>\<#6070\>\<#6709\>\<#4E00\>\<#4E2A\>\<#96F6\>\<#70B9\>\<#FF0C\>\<#6C42\><math|a>\<#7684\>\<#53D6\>\<#503C\>\<#8303\>\<#56F4\>\<#FF0E\><vspace|5cm>
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</enumerate-numeric>
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(\<#4E8C\>) \<#9009\>\<#8003\>\<#9898\>\<#FF1A\>\<#5171\> 10 \<#5206\>
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<\enumerate>
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<assign|item-nr|21><item>\<#5728\>\<#76F4\>\<#89D2\>\<#5750\>\<#6807\>\<#7CFB\><math|x*O*y>\<#4E2D\>\<#FF0C\>\<#66F2\>\<#7EBF\><math|C>\<#7684\>\<#65B9\>\<#7A0B\>\<#4E3A\><math|<around*|{|<tabular*|<tformat|<cwith|1|-1|1|1|cell-halign|l>|<cwith|1|-1|1|1|cell-lborder|0ln>|<cwith|1|-1|1|1|cell-rborder|0ln>|<table|<row|<cell|x=<sqrt|3><math-up|cos>2*t>>|<row|<cell|y=2<math-up|sin>t>>>>>|\<nobracket\>>(t>\<#4E3A\>\<#53C2\>\<#6570\><math|)>.\<#4EE5\>\<#5750\>\<#6807\>\<#539F\>\<#70B9\>\<#4E3A\>\<#6781\>\<#70B9\>\<#FF0C\><math|x>\<#8F74\>\<#6B63\>\<#534A\>\<#8F74\>\<#4E3A\>\<#6781\>\<#8F74\>\<#5EFA\>\<#7ACB\>\<#6781\>\<#5750\>\<#6807\>\<#7CFB\>\<#FF0C\>\<#5DF2\>\<#77E5\>\<#76F4\>\<#7EBF\><math|l>\<#7684\>\<#6781\>\<#5750\>\<#6807\>\<#65B9\>\<#7A0B\>\<#4E3A\><math|\<rho\><math-up|sin><around|(|\<theta\>+<frac|\<pi\>|3>|)>+m=0>\<#FF0E\>
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(1)\<#5199\>\<#51FA\><math|l>\<#7684\>\<#76F4\>\<#89D2\>\<#5750\>\<#6807\>\<#65B9\>\<#7A0B\>\<#FF1A\>
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(2)\<#82E5\><math|l>\<#4E0E\><math|C>\<#6709\>\<#516C\>\<#5171\>\<#70B9\>\<#FF0C\>\<#6C42\><math|m>\<#7684\>\<#53D6\>\<#503C\>\<#8303\>\<#56F4\>\<#FF0E\><vspace|5cm>
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<item>\<#5DF2\>\<#77E5\><math|a.*b.*c>\<#4E3A\>\<#6B63\>\<#6570\>\<#FF0C\>\<#4E14\><math|a<rsup|<frac|3|2>>+b<rsup|<frac|3|2>>+c<rsup|<frac|3|2>>=1>\<#FF0C\>\<#8BC1\>\<#660E\>\<#FF1A\>
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\ <math|<around|(|1|)>*a*b*c\<leq\><frac|1|9>>;
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<math|<around|(|2|)><frac|a|b+c>+<frac|b|a+c>+<frac|c|a+b>\<leq\><frac|1|2*<sqrt|a*b*c>>>.<vspace|5cm>
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</enumerate>
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\;
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\;
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</body>
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<initial|<\collection>
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</collection>> |