mirror of https://gitee.com/XmacsLabs/planet.git
172 lines
216 KiB
Tcl
172 lines
216 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\>\<#65B0\>\<#9AD8\>\<#8003\>2\<#5377\>>>
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\<#4E00\>\<#3001\>\<#5355\>\<#9009\>\<#9898\>\<#FF08\>\<#672C\>\<#5927\>\<#9898\>\<#5171\>8\<#5C0F\>\<#9898\>\<#FF0C\>\<#5171\>40\<#5206\>\<#FF09\>
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<\enumerate-numeric>
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<item>\<#5DF2\>\<#77E5\>\<#96C6\>\<#5408\><math|A=<around|{|-1,1,2,4|}>>\<#FF0C\><math|B=<around|{|x\|<around|\||x-1|\|>\<leq\>1|}>>\<#FF0C\>\<#5219\><math|A\<cap\>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|<around|{|-1,2|}>>>|<cell|B. <math|<around|{|1,2|}>>>|<cell|C.
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<math|<around|{|1,4|}>>>|<cell|D. <math|<around|{|-1,4|}>>>>>>>
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<item><math|<around|(|2+2*i|)>*<around|(|1-2*i|)>=>
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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+4*i>>|<cell|B. <math|-2-4*i>>|<cell|C. <math|6+2*i>>|<cell|D.
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<math|6-2*i>>>>>>
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<item>\<#4E2D\>\<#56FD\>\<#7684\>\<#53E4\>\<#5EFA\>\<#7B51\>\<#4E0D\>\<#4EC5\>\<#662F\>\<#6321\>\<#98CE\>\<#906E\>\<#96E8\>\<#7684\>\<#4F4F\>\<#5904\>\<#FF0C\>\<#66F4\>\<#662F\>\<#7F8E\>\<#5B66\>\<#548C\>\<#54F2\>\<#5B66\>\<#7684\>\<#4F53\>\<#73B0\>.
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\<#5982\>\<#56FE\>\<#662F\>\<#67D0\>\<#53E4\>\<#5EFA\>\<#7B51\>\<#7269\>\<#7684\>\<#5256\>\<#9762\>\<#56FE\>\<#FF0C\>
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<math|A*A<rprime|'>>\<#FF0C\><math|B*B<rprime|'>>\<#FF0C\><math|C*C<rprime|'>>\<#FF0C\><math|D*D<rprime|'>>\<#662F\>\<#6841\>\<#FF0C\>
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<math|D*D<rsub|1>>\<#FF0C\><math|C*C<rsub|1>>\<#FF0C\><math|B*B<rsub|1>>\<#FF0C\><math|A*A<rsub|1>>\<#662F\>\<#810A\>\<#FF0C\>
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<math|O*D<rsub|1>>\<#FF0C\><math|D*C<rsub|1>>\<#FF0C\><math|C*B<rsub|1>>\<#FF0C\><math|B*A<rsub|1>>\<#662F\>\<#76F8\>\<#7B49\>\<#7684\>\<#6B65\>\<#FF0C\>
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\<#76F8\>\<#90BB\>\<#6841\>\<#7684\>\<#810A\>\<#6B65\>\<#7684\>\<#6BD4\>\<#5206\>\<#522B\>\<#4E3A\><math|<frac|D*D<rsub|1>|O*D<rsub|1>>=0.5>\<#FF0C\><math|<frac|C*C<rsub|1>|D*C<rsub|1>>=k<rsub|1>>\<#FF0C\><math|<frac|B*B<rsub|1>|C*B<rsub|1>>=k<rsub|2>>\<#FF0C\><math|<frac|A*A<rsub|1>|B*A<rsub|1>>=k<rsub|3>>\<#FF0C\>\<#82E5\><math|k<rsub|1>>\<#FF0C\><math|k<rsub|2>>\<#FF0C\><math|k<rsub|3>>\<#662F\>\<#516C\>\<#5DEE\>\<#4E3A\><math|0.1>\<#7684\>\<#7B49\>\<#5DEE\>\<#6570\>\<#5217\>\<#FF0C\>\<#76F4\>\<#7EBF\><math|O*A>\<#7684\>\<#659C\>\<#7387\>\<#4E3A\><math|0.725>\<#FF0C\>\<#5219\><math|k<rsub|3>=>
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|png>|121pt|87pt||>
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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|0.75>>|<cell|B. <math|0.8>>|<cell|C. <math|0.85>>|<cell|D.
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<math|0.9>>>>>>
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<item>\<#5DF2\>\<#77E5\>\<#5411\>\<#91CF\><math|<wide|a|\<wide-varrightarrow\>>=<around|(|3,4|)>>\<#FF0C\><math|<wide|b|\<wide-varrightarrow\>>=<around|(|1,0|)>>\<#FF0C\><math|<wide|c|\<wide-varrightarrow\>>=<wide|a|\<wide-varrightarrow\>>+t<wide|b|\<wide-varrightarrow\>>>\<#FF0C\>\<#82E5\><math|\<less\><wide|a|\<wide-varrightarrow\>>,<wide|c|\<wide-varrightarrow\>>\<gtr\>=\<less\><wide|b|\<wide-varrightarrow\>>,<wide|c|\<wide-varrightarrow\>>\<gtr\>>\<#FF0C\>\<#5219\>\<#5B9E\>\<#6570\><math|t=>
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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|-6>>|<cell|B. <math|-5>>|<cell|C. <math|5>>|<cell|D. <math|6>>>>>>
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<item>\<#7532\>\<#4E59\>\<#4E19\>\<#4E01\>\<#620A\><math|5>\<#540D\>\<#540C\>\<#5B66\>\<#7AD9\>\<#6210\>\<#4E00\>\<#6392\>\<#53C2\>\<#52A0\>\<#6587\>\<#827A\>\<#6C47\>\<#6F14\>\<#FF0C\>\<#82E5\>\<#7532\>\<#4E0D\>\<#7AD9\>\<#5728\>\<#4E24\>\<#7AEF\>\<#FF0C\>\<#4E19\>\<#548C\>\<#4E01\>\<#76F8\>\<#90BB\>\<#7684\>\<#4E0D\>\<#540C\>\<#6392\>\<#5217\>\<#65B9\>\<#5F0F\>\<#6709\>
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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|12>\<#79CD\>>|<cell|B. <math|24>\<#79CD\>>|<cell|C.
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<math|36>\<#79CD\>>|<cell|D. <math|48>\<#79CD\>>>>>>
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<item>\<#82E5\><math|<math-up|sin><around|(|\<alpha\>+\<beta\>|)>+<math-up|cos><around|(|\<alpha\>+\<beta\>|)>=2*<sqrt|2><math-up|cos><around|(|\<alpha\>+<frac|\<pi\>|4>|)><math-up|sin>\<beta\>>\<#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|2|2|1|2|cell-valign|c>|<cwith|1|-1|1|-1|cell-halign|l>|<table|<row|<cell|A.
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<math|<math-up|tan><around|(|\<alpha\>+\<beta\>|)>=-1>>|<cell|B.
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<math|<math-up|tan><around|(|\<alpha\>+\<beta\>|)>=1>>>|<row|<cell|C.
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<math|<math-up|tan><around|(|\<alpha\>-\<beta\>|)>=-1>>|<cell|D.
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<math|<math-up|tan><around|(|\<alpha\>-\<beta\>|)>=1>>>>>>
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<item>\<#5DF2\>\<#77E5\>\<#6B63\>\<#4E09\>\<#68F1\>\<#53F0\>\<#7684\>\<#9AD8\>\<#4E3A\><math|1>\<#FF0C\>\<#4E0A\>\<#4E0B\>\<#5E95\>\<#9762\>\<#7684\>\<#8FB9\>\<#957F\>\<#5206\>\<#522B\>\<#4E3A\><math|3*<sqrt|3>>\<#548C\><math|4*<sqrt|3>>\<#FF0C\>\<#5176\>\<#9876\>\<#70B9\>\<#90FD\>\<#5728\>\<#540C\>\<#4E00\>\<#7403\>\<#9762\>\<#4E0A\>\<#FF0C\>\<#5219\>\<#8BE5\>\<#7403\>\<#7684\>\<#8868\>\<#9762\>\<#79EF\>\<#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|100*\<pi\>>>|<cell|B. <math|128*\<pi\>>>|<cell|C.
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<math|144*\<pi\>>>|<cell|D. <math|192*\<pi\>>>>>>>
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<item>\<#82E5\>\<#51FD\>\<#6570\><math|f<around|(|x|)>>\<#7684\>\<#5B9A\>\<#4E49\>\<#57DF\>\<#4E3A\><math|R>\<#FF0C\>\<#4E14\><math|f*<around|(|x+y|)>+f*<around|(|x-y|)>=f<around|(|x|)>*f<around|(|y|)>>\<#FF0C\><math|f=1>\<#FF0C\>\<#5219\><math|<big|int><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|-3>>|<cell|B. <math|-2>>|<cell|C. <math|0>>|<cell|D. <math|1>>>>>>
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</enumerate-numeric>
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\<#4E8C\>\<#3001\>\<#591A\>\<#9009\>\<#9898\>\<#FF08\>\<#672C\>\<#5927\>\<#9898\>\<#5171\>4\<#5C0F\>\<#9898\>\<#FF0C\>\<#5171\>20\<#5206\>\<#FF09\>
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<\enumerate-numeric>
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<assign|item-nr|8><item>\<#5DF2\>\<#77E5\>\<#51FD\>\<#6570\><math|f<around|(|x|)>=<math-up|sin><around|(|2*x+\<varphi\>|)>*<around|(|0\<less\>\<varphi\>\<less\>\<pi\>|)>>\<#7684\>\<#56FE\>\<#8C61\>\<#5173\>\<#4E8E\>\<#70B9\><math|<around|(|<frac|2*\<pi\>|3>,0|)>>\<#5BF9\>\<#79F0\>\<#FF0C\>\<#5219\>
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A. <math|f<around|(|x|)>>\<#5728\><math|<around|(|0,<frac|5*\<pi\>|12>|)>>\<#5355\>\<#8C03\>\<#9012\>\<#51CF\>
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B. <math|f<around|(|x|)>>\<#5728\><math|<around|(|-<frac|\<pi\>|12>,<frac|11*\<pi\>|12>|)>>\<#6709\>\<#4E24\>\<#4E2A\>\<#6781\>\<#503C\>\<#70B9\>
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C. \<#76F4\>\<#7EBF\><math|x=<frac|7*\<pi\>|6>>\<#662F\>\<#66F2\>\<#7EBF\><math|y=f<around|(|x|)>>\<#7684\>\<#4E00\>\<#6761\>\<#5BF9\>\<#79F0\>\<#8F74\>
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D. \<#76F4\>\<#7EBF\><math|y=<frac|<sqrt|3>|2>-x>\<#662F\>\<#66F2\>\<#7EBF\><math|y=f<around|(|x|)>>\<#7684\>\<#4E00\>\<#6761\>\<#5207\>\<#7EBF\>
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<item>\<#5DF2\>\<#77E5\><math|O>\<#4E3A\>\<#5750\>\<#6807\>\<#539F\>\<#70B9\>\<#FF0C\>\<#8FC7\>\<#629B\>\<#7269\>\<#7EBF\><math|C:y<rsup|2>=2*p*x*<around|(|p\<gtr\>0|)>>\<#7684\>\<#7126\>\<#70B9\><math|F>\<#7684\>\<#76F4\>\<#7EBF\>\<#4E0E\><math|C>\<#4EA4\>\<#4E8E\><math|A>\<#FF0C\><math|B>\<#4E24\>\<#70B9\>\<#FF0C\>\<#70B9\><math|A>\<#5728\>\<#7B2C\>\<#4E00\>\<#8C61\>\<#9650\>\<#FF0C\>\<#70B9\><math|M*<around|(|p,0|)>>\<#FF0C\>\<#82E5\><math|<around|\||A*F|\|>=<around|\||A*M|\|>>\<#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|2|2|1|2|cell-valign|c>|<cwith|1|-1|1|-1|cell-halign|l>|<table|<row|<cell|A.
|
|
\<#76F4\>\<#7EBF\><math|A*B>\<#7684\>\<#659C\>\<#7387\>\<#4E3A\><math|2*<sqrt|6>>>|<cell|B.
|
|
<math|<around|\||O*B|\|>=<around|\||O*F|\|>>>>|<row|<cell|C.
|
|
<math|<around|\||A*B|\|>\<gtr\>4*<around|\||O*F|\|>>>|<cell|D.
|
|
<math|\<angle\>*O*A*M+\<angle\>*O*B*M\<less\>180*\<degree\>>>>>>>
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<item>\<#5982\>\<#56FE\>\<#FF0C\>\<#56DB\>\<#8FB9\>\<#5F62\><math|A*B*C*D>\<#4E3A\>\<#6B63\>\<#65B9\>\<#5F62\>\<#FF0C\><math|E*D*\<bot\>>\<#5E73\>\<#9762\><math|A*B*C*D>\<#FF0C\><math|F*B//E*D>\<#FF0C\>
|
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<math|A*B=E*D=2*F*B>\<#FF0C\>\<#8BB0\>\<#4E09\>\<#68F1\>\<#9525\><math|E-A*B*C>\<#FF0C\><math|E-A*C*F>\<#FF0C\><math|F-A*B*C>\<#7684\>\<#4F53\>\<#79EF\>\<#5206\>\<#522B\>\<#4E3A\><math|V<rsub|1>>\<#FF0C\><math|V<rsub|2>>\<#FF0C\><math|V<rsub|3>>\<#FF0C\>\<#5219\>
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|png>|90pt|87pt||>
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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.
|
|
<math|V<rsub|3>=2*V<rsub|2>>>|<cell|B.
|
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<math|V<rsub|3>=2*V<rsub|1>>>|<cell|C.
|
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<math|V<rsub|3>=V<rsub|1>+V<rsub|2>>>|<cell|D.
|
|
<math|2*V<rsub|3>=3*V<rsub|1>>>>>>>
|
|
|
|
<item>\<#82E5\>\<#5B9E\>\<#6570\><math|x>\<#FF0C\><math|y>\<#6EE1\>\<#8DB3\><math|x<rsup|2>+y<rsup|2>-x*y=1>\<#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.
|
|
<math|x+y\<leq\>1>>|<cell|B. <math|x+y\<geq\>-2>>|<cell|C.
|
|
<math|x<rsup|2>+y<rsup|2>\<geq\>1>>|<cell|D.
|
|
<math|x<rsup|2>+y<rsup|2>\<leq\>2>>>>>>
|
|
</enumerate-numeric>
|
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|
|
\<#4E09\>\<#3001\>\<#586B\>\<#7A7A\>\<#9898\>\<#FF08\>\<#672C\>\<#5927\>\<#9898\>\<#5171\>4\<#5C0F\>\<#9898\>\<#FF0C\>\<#5171\>20\<#5206\>\<#FF09\>
|
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|
<\enumerate-numeric>
|
|
<assign|item-nr|12><item>\<#968F\>\<#673A\>\<#53D8\>\<#91CF\><math|X>\<#670D\>\<#4ECE\>\<#6B63\>\<#6001\>\<#5206\>\<#5E03\><math|N*<around|(|2,\<sigma\><rsup|2>|)>>\<#FF0C\>\<#82E5\><math|P*<around|(|2\<less\>x\<leq\>2.5|)>=0.36>\<#FF0C\>\<#5219\><math|P*<around|(|X\<gtr\>2.5|)>=><underline|<space|2cm>>\<#FF0E\>
|
|
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|
<item>\<#66F2\>\<#7EBF\><math|y=<math-up|ln><around|\||x|\|>>\<#7ECF\>\<#8FC7\>\<#5750\>\<#6807\>\<#539F\>\<#70B9\>\<#7684\>\<#4E24\>\<#6761\>\<#5207\>\<#7EBF\>\<#65B9\>\<#7A0B\>\<#5206\>\<#522B\>\<#4E3A\><underline|<space|1cm>>\<#FF0C\><underline|<space|1cm>>\<#FF0E\>
|
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|
<item>\<#8BBE\>\<#70B9\><math|A*<around|(|-2,3|)>>\<#FF0C\><math|B*<around|(|0,a|)>>\<#FF0C\>\<#76F4\>\<#7EBF\><math|A*B>\<#5173\>\<#4E8E\>\<#76F4\>\<#7EBF\><math|y=a>\<#7684\>\<#5BF9\>\<#79F0\>\<#76F4\>\<#7EBF\>\<#4E3A\><math|l>\<#FF0C\>\<#5DF2\>\<#77E5\><math|l>\<#4E0E\>\<#5706\><math|C:<around|(|x+3|)><rsup|2>+<around|(|y+2|)><rsup|2>=1>\<#6709\>\<#516C\>\<#5171\>\<#70B9\>\<#FF0C\>\<#5219\><math|a>\<#7684\>\<#53D6\>\<#503C\>\<#8303\>\<#56F4\>\<#4E3A\><underline|<space|2cm>>\<#FF0E\>
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<item>\<#5DF2\>\<#77E5\>\<#76F4\>\<#7EBF\><math|l>\<#4E0E\>\<#692D\>\<#5706\><math|<frac|x<rsup|2>|6>+<frac|y<rsup|2>|3>=1>\<#5728\>\<#7B2C\>\<#4E00\>\<#8C61\>\<#9650\>\<#4EA4\>\<#4E8E\><math|A>\<#FF0C\><math|B>\<#4E24\>\<#70B9\>\<#FF0C\><math|l>\<#4E0E\><math|x>\<#8F74\><math|y>\<#8F74\>\<#5206\>\<#522B\>\<#76F8\>\<#4EA4\>\<#4E8E\><math|M>\<#FF0C\><math|N>\<#4E24\>\<#70B9\>\<#FF0C\>\<#4E14\><math|<around|\||M*A|\|>=<around|\||N*B|\|>>\<#FF0C\><math|<around|\||M*N|\|>=2*<sqrt|3>>\<#FF0C\>\<#5219\>\<#76F4\>\<#7EBF\><math|l>\<#7684\>\<#65B9\>\<#7A0B\>\<#4E3A\><underline|<space|2cm>>\<#FF0E\>
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</enumerate-numeric>
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\<#56DB\>\<#3001\>\<#89E3\>\<#7B54\>\<#9898\>\<#FF08\>\<#672C\>\<#5927\>\<#9898\>\<#5171\>6\<#5C0F\>\<#9898\>\<#FF0C\>\<#5171\>70\<#5206\>\<#FF09\>
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<\enumerate-numeric>
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<assign|item-nr|16><item>\<#5DF2\>\<#77E5\><math|<around|{|a<rsub|n>|}>>\<#4E3A\>\<#7B49\>\<#5DEE\>\<#6570\>\<#5217\>\<#FF0C\><math|<around|{|b<rsub|n>|}>>\<#4E3A\>\<#516C\>\<#6BD4\>\<#4E3A\><math|2>\<#7684\>\<#7B49\>\<#6BD4\>\<#6570\>\<#5217\>\<#FF0C\>\<#4E14\><math|a<rsub|2>-b<rsub|2>=a<rsub|3>-b<rsub|3>=b<rsub|4>-a<rsub|4>>\<#FF0E\>
|
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(1)\<#8BC1\>\<#660E\>\<#FF1A\><math|a<rsub|1>=b<rsub|1>>;
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(2)\<#6C42\>\<#96C6\>\<#5408\><math|<around|{|k\|b<rsub|k>=a<rsub|m>+a<rsub|1>,1\<leq\>m\<leq\>500|}>>\<#4E2D\>\<#5143\>\<#7D20\>\<#4E2A\>\<#6570\>\<#FF0E\><vspace|5cm>
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<item>\<#8BB0\><math|\<bigtriangleup\>*A*B*C>\<#7684\>\<#4E09\>\<#4E2A\>\<#5185\>\<#89D2\>\<#5206\>\<#522B\>\<#4E3A\><math|A>\<#FF0C\><math|B>\<#FF0C\><math|C>\<#FF0C\>\<#5176\>\<#5BF9\>\<#8FB9\>\<#5206\>\<#522B\>\<#4E3A\><math|a>\<#FF0C\><math|b>\<#FF0C\><math|c>\<#FF0C\>\<#5206\>\<#522B\>\<#4EE5\><math|a>\<#FF0C\><math|b>\<#FF0C\><math|c>\<#4E3A\>\<#8FB9\>\<#957F\>\<#7684\>\<#4E09\>\<#4E2A\>\<#6B63\>\<#4E09\>\<#89D2\>\<#5F62\>\<#7684\>\<#9762\>\<#79EF\>\<#4F9D\>\<#6B21\>\<#4E3A\><math|S<rsub|1>>\<#FF0C\><math|S<rsub|2>>\<#FF0C\><math|S<rsub|3>>\<#FF0C\>\<#4E14\><math|S<rsub|1>-S<rsub|2>+S<rsub|3>=<frac|<sqrt|3>|2>>\<#FF0C\><math|<math-up|sin>B=<frac|1|3>>\<#FF0E\>
|
|
|
|
(1)\<#6C42\><math|\<bigtriangleup\>*A*B*C>\<#7684\>\<#9762\>\<#79EF\>;
|
|
|
|
(2)\<#82E5\><math|<math-up|sin>A<math-up|sin>C=<frac|<sqrt|2>|3>>\<#FF0C\>\<#6C42\><math|b>\<#FF0E\><vspace|5cm>
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|
<item>\<#5728\>\<#67D0\>\<#5730\>\<#533A\>\<#8FDB\>\<#884C\>\<#67D0\>\<#79CD\>\<#75BE\>\<#75C5\>\<#8C03\>\<#67E5\>\<#FF0C\>\<#968F\>\<#673A\>\<#8C03\>\<#67E5\>\<#4E86\><math|100>\<#4F4D\>\<#8FD9\>\<#79CD\>\<#75BE\>\<#75C5\>\<#60A3\>\<#8005\>\<#7684\>\<#5E74\>\<#9F84\>\<#FF0C\>\<#5F97\>\<#5230\>\<#5982\>\<#4E0B\>\<#6837\>\<#672C\>\<#6570\>\<#636E\>\<#9891\>\<#7387\>\<#5206\>\<#5E03\>\<#76F4\>\<#65B9\>\<#56FE\>\<#FF0E\>
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(1)\<#4F30\>\<#8BA1\>\<#8BE5\>\<#5730\>\<#533A\>\<#8FD9\>\<#79CD\>\<#75BE\>\<#75C5\>\<#60A3\>\<#8005\>\<#7684\>\<#5E73\>\<#5747\>\<#5E74\>\<#9F84\>;(\<#540C\>\<#4E00\>\<#7EC4\>\<#6570\>\<#636E\>\<#7528\>\<#8BE5\>\<#533A\>\<#95F4\>\<#7684\>\<#4E2D\>\<#70B9\>\<#503C\>\<#4F5C\>\<#4EE3\>\<#8868\><math|)>;
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(2)\<#4F30\>\<#8BA1\>\<#8BE5\>\<#5730\>\<#533A\>\<#4EE5\>\<#4E3A\>\<#8FD9\>\<#79CD\>\<#75BE\>\<#75C5\>\<#60A3\>\<#8005\>\<#5E74\>\<#9F84\>\<#4F4D\>\<#4E8E\>\<#533A\>\<#95F4\><math|<around|[|20,70|)>>\<#7684\>\<#6982\>\<#7387\>;
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(3)\<#5DF2\>\<#77E5\>\<#8BE5\>\<#5730\>\<#533A\>\<#8FD9\>\<#79CD\>\<#75BE\>\<#75C5\>\<#60A3\>\<#8005\>\<#7684\>\<#60A3\>\<#75C5\>\<#7387\>\<#4E3A\><math|0.1%>\<#FF0C\>\<#8BE5\>\<#5730\>\<#533A\>\<#5E74\>\<#9F84\>\<#4F4D\>\<#4E8E\>\<#533A\>\<#95F4\><math|<around|[|40,50|)>>\<#7684\>\<#4EBA\>\<#53E3\>\<#6570\>\<#5360\>\<#8BE5\>\<#5730\>\<#533A\>\<#603B\>\<#4EBA\>\<#53E3\>\<#6570\>\<#7684\><math|16%>\<#FF0C\>\<#4ECE\>\<#8BE5\>\<#5730\>\<#533A\>\<#9009\>\<#51FA\><math|1>\<#4EBA\>\<#FF0C\>\<#82E5\>\<#6B64\>\<#4EBA\>\<#7684\>\<#5E74\>\<#9F84\>\<#4F4D\>\<#4E8E\>\<#533A\>\<#95F4\><math|<around|[|40,50|)>>\<#FF0C\>\<#6C42\>\<#6B64\>\<#4EBA\>\<#60A3\>\<#8FD9\>\<#79CD\>\<#75BE\>\<#75C5\>\<#7684\>\<#6982\>\<#7387\><math|(>\<#7CBE\>\<#786E\>\<#5230\><math|0.0001)>\<#FF0E\><vspace|5cm>
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<item>\<#5982\>\<#56FE\>\<#FF0C\><math|P*O>\<#662F\>\<#4E09\>\<#68F1\>\<#9525\><math|P-A*B*C>\<#7684\>\<#9AD8\>\<#FF0C\><math|P*A=P*B>\<#FF0C\><math|A*B*\<bot\>*A*C>\<#FF0C\><math|E>\<#662F\><math|P*B>\<#7684\>\<#4E2D\>\<#70B9\>\<#FF0E\>
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(1)\<#8BC1\>\<#660E\>\<#FF1A\><math|O*E//>\<#5E73\>\<#9762\><math|P*A*C>;
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(2)\<#82E5\><math|\<angle\>*A*B*O=\<angle\>*C*B*O=30*\<degree\>>\<#FF0C\><math|P*O=3>\<#FF0C\><math|P*A=5>\<#FF0C\>\<#6C42\>\<#4E8C\>\<#9762\>\<#89D2\><math|C-A*E-B>\<#6B63\>\<#5F26\>\<#503C\>\<#FF0E\>
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<vspace|5cm>
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<item>\<#8BBE\>\<#53CC\>\<#66F2\>\<#7EBF\><math|C:<frac|x<rsup|2>|a<rsup|2>>-<frac|y<rsup|2>|b<rsup|2>>=1*<around|(|a\<gtr\>0,b\<gtr\>0|)>>\<#7684\>\<#53F3\>\<#7126\>\<#70B9\>\<#4E3A\><math|F*<around|(|2,0|)>>\<#FF0C\>\<#6E10\>\<#8FD1\>\<#7EBF\>\<#65B9\>\<#7A0B\>\<#4E3A\><math|y=<sqrt|3>*x>.
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(1)\<#6C42\><math|C>\<#7684\>\<#65B9\>\<#7A0B\>;
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(2)\<#7ECF\>\<#8FC7\><math|F>\<#7684\>\<#76F4\>\<#7EBF\>\<#4E0E\><math|C>\<#7684\>\<#6E10\>\<#8FD1\>\<#7EBF\>\<#5206\>\<#522B\>\<#4EA4\>\<#4E8E\><math|A>\<#FF0C\><math|B>\<#4E24\>\<#70B9\>\<#FF0C\>\<#70B9\><math|P*<around|(|x<rsub|1>,y<rsub|1>|)>>\<#FF0C\><math|Q<around|(|x<rsub|2>,y<rsub|2>|)>>\<#5728\><math|C>\<#4E0A\>\<#FF0C\>\<#4E14\><math|x<rsub|1>\<gtr\>x<rsub|2>\<gtr\>0>\<#FF0C\><math|y<rsub|1>\<gtr\>0>.\<#8FC7\><math|P>\<#4E14\>\<#659C\>\<#7387\>\<#4E3A\><math|-<sqrt|3>>\<#7684\>\<#76F4\>\<#7EBF\>\<#4E0E\>\<#8FC7\><math|Q>\<#4E14\>\<#659C\>\<#7387\>\<#4E3A\><math|<sqrt|3>>\<#7684\>\<#76F4\>\<#7EBF\>\<#4EA4\>\<#4E8E\>\<#70B9\><math|M>\<#FF0C\>\<#4ECE\>\<#4E0B\>\<#9762\>\<#4E09\>\<#4E2A\>\<#6761\>\<#4EF6\>\<#2460\>\<#2461\>\<#2462\>\<#4E2D\>\<#9009\>\<#62E9\>\<#4E24\>\<#4E2A\>\<#6761\>\<#4EF6\>\<#FF0C\>\<#8BC1\>\<#660E\>\<#53E6\>\<#4E00\>\<#4E2A\>\<#6761\>\<#4EF6\>\<#6210\>\<#7ACB\>\<#FF1A\><math-up|\<#2460\>><math|M>\<#5728\><math|A*B>\<#4E0A\><math|;<math-up|\<#2461\>>P*Q//A*B;<math-up|\<#2462\>><around|\||A*M|\|>=<around|\||B*M|\|>>\<#FF0E\><vspace|5cm>
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<item>\<#5DF2\>\<#77E5\>\<#51FD\>\<#6570\><math|f<around|(|x|)>=x*e<rsup|a*x>-e<rsup|x>>\<#FF0E\>
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(1)\<#5F53\><math|a=1>\<#65F6\>\<#FF0C\>\<#8BA8\>\<#8BBA\><math|f<around|(|x|)>>\<#7684\>\<#5355\>\<#8C03\>\<#6027\>;
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(2)\<#5F53\><math|x\<gtr\>0>\<#65F6\>\<#FF0C\><math|f<around|(|x|)>\<less\>-1>\<#FF0C\>\<#6C42\>\<#5B9E\>\<#6570\><math|a>\<#7684\>\<#53D6\>\<#503C\>\<#8303\>\<#56F4\>;
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(3)\<#8BBE\><math|n\<in\>N<rsup|\<ast\>>>\<#FF0C\>\<#8BC1\>\<#660E\>\<#FF1A\><math|<frac|1|<sqrt|1<rsup|2>+1>>+<frac|1|<sqrt|2<rsup|2>+2>>+\<cdots\>+<frac|1|<sqrt|n<rsup|2>+n>>\<gtr\><math-up|ln><around|(|n+1|)>>\<#FF0E\><vspace|5cm>
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</enumerate-numeric>
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</body>
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<initial|<\collection>
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</collection>> |