planet/高考数学/2021年全国新高考II卷数学试题.tm

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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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  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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  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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  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\>

  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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  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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  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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  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\>

  A\<#FF0E\>\<#82E5\>\<#70B9\><em|A>\<#5728\>\<#5706\><em|C>\<#4E0A\>\<#FF0C\>\<#5219\>\<#76F4\>\<#7EBF\><em|l>\<#4E0E\>\<#5706\><em|C>\<#76F8\>\<#5207\>\ 

  B\<#FF0E\>\<#82E5\>\<#70B9\><em|A>\<#5728\>\<#5706\><em|C>\<#5185\>\<#FF0C\>\<#5219\>\<#76F4\>\<#7EBF\><em|l>\<#4E0E\>\<#5706\><em|C>\<#76F8\>\<#79BB\>

  C\<#FF0E\>\<#82E5\>\<#70B9\><em|A>\<#5728\>\<#5706\><em|C>\<#5916\>\<#FF0C\>\<#5219\>\<#76F4\>\<#7EBF\><em|l>\<#4E0E\>\<#5706\><em|C>\<#76F8\>\<#79BB\>\ 

  D\<#FF0E\>\<#82E5\>\<#70B9\><em|A>\<#5728\>\<#76F4\>\<#7EBF\><em|l>\<#4E0A\>\<#FF0C\>\<#5219\>\<#76F4\>\<#7EBF\><em|l>\<#4E0E\>\<#5706\><em|C>\<#76F8\>\<#5207\>

  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\>

  <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>>>>>>\ 

  <with|font-series|bold|\<#4E09\>\<#3001\>\<#586B\>\<#7A7A\>\<#9898\>>

  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\>

  14\<#FF0E\>\<#5199\>\<#51FA\>\<#4E00\>\<#4E2A\>\<#540C\>\<#65F6\>\<#5177\>\<#6709\>\<#4E0B\>\<#5217\>\<#6027\>\<#8D28\>\<#2460\>\<#2461\>\<#2462\>\<#7684\>\<#51FD\>\<#6570\><math|f<around|(|x|)>>:
  <underline|<space|2cm>>\<#FF0E\>

  \<#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\>
  <around*|(|0,+\<infty\>|)>>\<#65F6\>\<#FF0C\><math|f<rprime|'><around|(|x|)>\<gtr\>0>\<#FF1B\>\<#2462\><math|f<rprime|'><around|(|x|)>>\<#662F\>\<#5947\>\<#51FD\>\<#6570\>\<#FF0E\>

  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\>

  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\>

  <with|font-series|bold|\<#56DB\>\<#3001\>\<#89E3\>\<#7B54\>\<#9898\>>

  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\>

  \<#FF08\>1\<#FF09\>\<#6C42\>\<#6570\>\<#5217\><math|<around*|{|a<rsub|n>|}>>\<#7684\>\<#901A\>\<#9879\>\<#516C\>\<#5F0F\><math|a<rsub|n>>\<#FF1B\>

  \<#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>

  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>.

  \<#FF08\>1\<#FF09\>\<#82E5\><math|2*sin C=3*sin
  A>\<#FF0C\>\<#6C42\><math|\<triangle\>A*B*C>\<#7684\>\<#9762\>\<#79EF\>\<#FF1B\>

  \<#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>

  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\>

  <center|<image|<tuple|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

  \<#FF08\>1\<#FF09\>\<#8BC1\>\<#660E\>\<#FF1A\>\<#5E73\>\<#9762\><math|Q*A*D*\<bot\>>\<#5E73\>\<#9762\><math|A*B*C*D>\<#FF1B\>

  \<#FF08\>2\<#FF09\>\<#6C42\>\<#4E8C\>\<#9762\>\<#89D2\><math|B-Q*D-A>\<#7684\>\<#5E73\>\<#9762\>\<#89D2\>\<#7684\>\<#4F59\>\<#5F26\>\<#503C\>\<#FF0E\><vspace|3cm>

  20\<#FF0E\>\<#5DF2\>\<#77E5\>\<#692D\>\<#5706\><em|C>\<#7684\>\<#65B9\>\<#7A0B\>\<#4E3A\><math|<frac|x<rsup|2>|a<rsup|2>>+<frac|y<rsup|2>|b<rsup|2>>=1*<around|(|a\<gtr\>b\<gtr\>0|)>>\<#FF0C\>\<#53F3\>\<#7126\>\<#70B9\>\<#4E3A\><math|F<around|(|<sqrt|2>,0|)>>\<#FF0C\>\<#4E14\>\<#79BB\>\<#5FC3\>\<#7387\>\<#4E3A\><math|<frac|<sqrt|6>|3>>\<#FF0E\>

  \<#FF08\>1\<#FF09\>\<#6C42\>\<#692D\>\<#5706\><em|C>\<#7684\>\<#65B9\>\<#7A0B\>\<#FF1B\>

  \<#FF08\>2\<#FF09\>\<#8BBE\><em|M>\<#FF0C\><em|N>\<#662F\>\<#692D\>\<#5706\><em|C>\<#4E0A\>\<#7684\>\<#4E24\>\<#70B9\>\<#FF0C\>\<#76F4\>\<#7EBF\><math|M*N>\<#4E0E\>\<#66F2\>\<#7EBF\><math|x<rsup|2>+y<rsup|2>=b<rsup|2>*<around|(|x\<gtr\>0|)>>\<#76F8\>\<#5207\>\<#FF0E\>\<#8BC1\>\<#660E\>\<#FF1A\><em|M>\<#FF0C\><em|N>\<#FF0C\><em|F>\<#4E09\>\<#70B9\>\<#5171\>\<#7EBF\>\<#7684\>\<#5145\>\<#8981\>\<#6761\>\<#4EF6\>\<#662F\><math|<around|\||M*N|\|>=<sqrt|3>>\<#FF0E\><vspace|3cm>

  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\>

  \<#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\>

  \<#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\>

  \<#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>

  22\<#FF0E\>\<#5DF2\>\<#77E5\>\<#51FD\>\<#6570\><math|f<around|(|x|)>=<around|(|x-1|)>*e<rsup|x>-a*x<rsup|2>+b>\<#FF0E\>

  \<#FF08\>1\<#FF09\>\<#8BA8\>\<#8BBA\><math|f<around|(|x|)>>\<#7684\>\<#5355\>\<#8C03\>\<#6027\>\<#FF1B\>

  \<#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\>.

  \<#2460\><math|<frac|1|2>\<less\>a\<leq\><frac|e<rsup|2>|2>,b\<gtr\>2*a>\<#FF1B\>

  \<#2461\><math|0\<less\>a\<less\><frac|1|2>,b\<leq\>2*a>\<#FF0E\><vspace|3cm>
</body>

<initial|<\collection>
</collection>>