mirror of https://gitee.com/XmacsLabs/planet.git
331 lines
812 KiB
Tcl
331 lines
812 KiB
Tcl
<TeXmacs|2.1.3>
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<style|<tuple|generic|chinese>>
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<\body>
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<doc-data|<doc-title|2021年天津高考数学试题>>
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<with|font-series|bold|<with|font|Songti SC|一>、<with|font|Songti
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SC|单选题>>
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1<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
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SC|设集合><math|A=<around*|{|-1,0,1|}><with|font|Hiragino Kaku Gothic
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ProN|，>*B=<around*|{|1,3,5|}>,C=<around*|{|0,2,4|}>><with|font|Hiragino
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Kaku Gothic ProN|，><with|font|Songti SC|则><math|<around|(|A\<cap\>B|)>\<cup\>C=><with|font|Hiragino
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Kaku Gothic ProN|（ ）>
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<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A<with|font|Hiragino
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Kaku Gothic ProN|．><math|<around*|{|0|}>>>|<cell|B<with|font|Hiragino
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Kaku Gothic ProN|．><math|<around|{|0,1,3,5|}>>>|<cell|C<with|font|Hiragino
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Kaku Gothic ProN|．><math|<around|{|0,1,2,4|}>>>|<cell|D<with|font|Hiragino
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Kaku Gothic ProN|．><math|<around|{|0,2,3,4|}>>>>>>>\
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2<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
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SC|已知><math|a\<in\><math-bf|R>><with|font|Hiragino Kaku Gothic
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ProN|，><with|font|Songti SC|则>\P<math|a\<gtr\>6>\Q<with|font|Songti
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SC|是>\P<math|a<rsup|2>\<gtr\>36>\Q<with|font|Songti
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SC|的><with|font|Hiragino Kaku Gothic ProN|（ ）>
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<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A．充分而不必要条件>|<cell|B．必要而不充分条件>>|<row|<cell|C．充分必要条件>|<cell|D．既不充分也不必要条件>>>>>
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3<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
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SC|函数><math|y=<frac|ln <around|\||x|\|>|x<rsup|2>+2>><with|font|Songti
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SC|的图像大致为><with|font|Hiragino Kaku Gothic ProN|（ ）>
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A<with|font|Hiragino Kaku Gothic 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4<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
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SC|从某网络平台推荐的影视作品中抽取><math|400><with|font|Songti
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SC|部><with|font|Hiragino Kaku Gothic ProN|，><with|font|Songti
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SC|统计其评分数据><with|font|Hiragino Kaku Gothic
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ProN|，><with|font|Songti SC|将所得><math|400><with|font|Songti
|
||
SC|个评分数据分为><math|8><with|font|Songti
|
||
SC|组><with|font|Hiragino Kaku Gothic ProN|：><math|<around*|\<nobracket\>|66,70|)>>、<math|<around*|\<nobracket\>|70,74|)>>、<math|\<cdots\>>、<math|<around|[|94,98|]>><with|font|Hiragino
|
||
Kaku Gothic ProN|，><with|font|Songti SC|并整理得到如下的频率分布直方图><with|font|Hiragino
|
||
Kaku Gothic ProN|，><with|font|Songti SC|则评分在区间><math|<around*|\<nobracket\>|82,86|)>><with|font|Songti
|
||
SC|内的影视作品数量是><with|font|Hiragino Kaku Gothic ProN|（
|
||
）>
|
||
|
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|png>|.2par|||>>
|
||
|
||
<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A<with|font|Hiragino
|
||
Kaku Gothic ProN|．><math|20>>|<cell|B<with|font|Hiragino Kaku Gothic
|
||
ProN|．><math|40>>|<cell|C<with|font|Hiragino Kaku Gothic
|
||
ProN|．><math|64>>|<cell|D<with|font|Hiragino Kaku Gothic
|
||
ProN|．><math|80>>>>>>\
|
||
|
||
5<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
|
||
SC|设><math|a=log <rsub|2>0.3,b=log<rsub|<frac|1|2>>
|
||
0.4,c=0.4<rsup|0.3>><with|font|Hiragino Kaku Gothic
|
||
ProN|，><with|font|Songti SC|则><em|a><with|font|Hiragino Kaku Gothic
|
||
ProN|，><em|b><with|font|Hiragino Kaku Gothic
|
||
ProN|，><em|c><with|font|Songti SC|的大小关系为><with|font|Hiragino
|
||
Kaku Gothic ProN|（ ）>
|
||
|
||
<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A<with|font|Hiragino
|
||
Kaku Gothic ProN|．><math|a\<less\>b\<less\>c>>|<cell|B<with|font|Hiragino
|
||
Kaku Gothic ProN|．><math|c\<less\>a\<less\>b>>|<cell|C<with|font|Hiragino
|
||
Kaku Gothic ProN|．><math|b\<less\>c\<less\>a>
|
||
>|<cell|D<with|font|Hiragino Kaku Gothic
|
||
ProN|．><math|a\<less\>c\<less\>b>>>>>>\
|
||
|
||
6<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
|
||
SC|两个圆锥的底面是一个球的同一截面><with|font|Hiragino
|
||
Kaku Gothic ProN|，><with|font|Songti SC|顶点均在球面上><with|font|Hiragino
|
||
Kaku Gothic ProN|，><with|font|Songti SC|若球的体积为><math|<frac|32*\<pi\>|3>><with|font|Hiragino
|
||
Kaku Gothic ProN|，><with|font|Songti SC|两个圆锥的高之比为><math|1:3><with|font|Hiragino
|
||
Kaku Gothic ProN|，><with|font|Songti SC|则这两个圆锥的体积之和为><with|font|Hiragino
|
||
Kaku Gothic ProN|（ ）>
|
||
|
||
<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A<with|font|Hiragino
|
||
Kaku Gothic ProN|．><math|3*\<pi\>>>|<cell|B<with|font|Hiragino Kaku
|
||
Gothic ProN|．><math|4*\<pi\>>>|<cell|C<with|font|Hiragino Kaku Gothic
|
||
ProN|．><math|9*\<pi\>>>|<cell|D<with|font|Hiragino Kaku Gothic
|
||
ProN|．><math|12*\<pi\>>>>>>>\
|
||
|
||
7<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
|
||
SC|若><math|2<rsup|a>=5<rsup|b>=10><with|font|Hiragino Kaku Gothic
|
||
ProN|，><with|font|Songti SC|则><math|<frac|1|a>+<frac|1|b>=><with|font|Hiragino
|
||
Kaku Gothic ProN|（ ）>
|
||
|
||
<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A<with|font|Hiragino
|
||
Kaku Gothic ProN|．><math|-1>>|<cell|B<with|font|Hiragino Kaku Gothic
|
||
ProN|．><math|lg 7>>|<cell|C<with|font|Hiragino Kaku Gothic
|
||
ProN|．>1>|<cell|D<with|font|Hiragino Kaku Gothic ProN|．><math|log
|
||
<rsub|7>10>>>>>>\
|
||
|
||
8<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
|
||
SC|已知双曲线><math|<frac|x<rsup|2>|a<rsup|2>>-<frac|y<rsup|2>|b<rsup|2>>=1*<around|(|a\<gtr\>0,b\<gtr\>0|)>><with|font|Songti
|
||
SC|的右焦点与抛物线><math|y<rsup|2>=2*p*x*<around|(|p\<gtr\>0|)>><with|font|Songti
|
||
SC|的焦点重合><with|font|Hiragino Kaku Gothic
|
||
ProN|，><with|font|Songti SC|抛物线的准线交双曲线于><em|A><with|font|Hiragino
|
||
Kaku Gothic ProN|，><em|B><with|font|Songti SC|两点><with|font|Hiragino
|
||
Kaku Gothic ProN|，><with|font|Songti SC|交双曲线的渐近线于><em|C>、<em|D><with|font|Songti
|
||
SC|两点><with|font|Hiragino Kaku Gothic ProN|，><with|font|Songti
|
||
SC|若><math|<around|\||C*D|\|>=<sqrt|2>*<around|\||A*B|\|>><with|font|Hiragino
|
||
Kaku Gothic ProN|．><with|font|Songti SC|则双曲线的离心率为><with|font|Hiragino
|
||
Kaku Gothic ProN|（ ）>
|
||
|
||
<tabular|<tformat|<twith|table-width|1par>|<twith|table-hmode|exact>|<table|<row|<cell|A<with|font|Hiragino
|
||
Kaku Gothic ProN|．><math|<sqrt|2>>>|<cell|B<with|font|Hiragino Kaku
|
||
Gothic ProN|．><math|<sqrt|3>>>|<cell|C<with|font|Hiragino Kaku Gothic
|
||
ProN|．>2>|<cell|D<with|font|Hiragino Kaku Gothic ProN|．>3>>>>>\
|
||
|
||
9<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
|
||
SC|设><math|a\<in\><math-bf|R>><with|font|Hiragino Kaku Gothic
|
||
ProN|，><with|font|Songti SC|函数><math|f<around*|(|x|)>=><choice|<tformat|<table|<row|<cell|<math|cos
|
||
<around|(|2*\<pi\>*x-2*\<pi\>*a|)>.>>|<cell|<math|x\<less\>a>>>|<row|<cell|<math|x<rsup|2>-2*<around|(|a+1|)>*x+a<rsup|2>+5,>>|<cell|<math|x\<geqslant\>a>>>>>><with|font|Hiragino
|
||
Kaku Gothic ProN|，><with|font|Songti SC|若><math|f<around|(|x|)>><with|font|Songti
|
||
SC|在区间><math|<around|(|0,+\<infty\>|)>><with|font|Songti
|
||
SC|内恰有>6<with|font|Songti SC|个零点><with|font|Hiragino Kaku
|
||
Gothic ProN|，><with|font|Songti SC|则><em|a><with|font|Songti
|
||
SC|的取值范围是><with|font|Hiragino Kaku Gothic ProN|（ ）>
|
||
|
||
<\wide-tabular>
|
||
<tformat|<table|<row|<\cell>
|
||
A. <math|<around*|(|2,<frac|9|4>|]>\<cup\><around*|(|<frac|5|2>,<frac|11|4>|]>>
|
||
</cell>|<\cell>
|
||
B. <math|<around*|(|<frac|7|4>,2|)>\<cup\><around*|(|<frac|5|2>,<frac|11|4>|]>>
|
||
</cell>|<\cell>
|
||
C. <math|<around*|(|2,<frac|9|4>|]>\<cup\><around*|[|<frac|11|4>,3|)>>
|
||
</cell>|<\cell>
|
||
D. <math|<around*|(|<frac|7|4>,2|)>\<cup\><around*|[|<frac|11|4>,3|)>>
|
||
</cell>>>>
|
||
</wide-tabular>
|
||
|
||
\
|
||
|
||
<with|font-series|bold|<with|font|Songti SC|二>、<with|font|Songti
|
||
SC|填空题>>
|
||
|
||
10<with|font|Hiragino Kaku Gothic ProN|．><math|i><with|font|Songti
|
||
SC|是虚数单位><with|font|Hiragino Kaku Gothic
|
||
ProN|，><with|font|Songti SC|复数><math|<frac|9+2*i|2+i>=><underline|<space|2cm>>．
|
||
|
||
11<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
|
||
SC|在><math|<around*|(|2*x<rsup|3>+<frac|1|x>|)><rsup|6>><with|font|Songti
|
||
SC|的展开式中><with|font|Hiragino Kaku Gothic
|
||
ProN|，><math|x<rsup|6>><with|font|Songti
|
||
SC|的系数是><underline|<space|2cm>>．
|
||
|
||
12<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
|
||
SC|若斜率为><math|<sqrt|3>><with|font|Songti
|
||
SC|的直线与><math|y><with|font|Songti
|
||
SC|轴交于点><math|A><with|font|Hiragino Kaku Gothic
|
||
ProN|，><with|font|Songti SC|与圆><math|x<rsup|2>+<around|(|y-1|)><rsup|2>=1><with|font|Songti
|
||
SC|相切于点><math|B><with|font|Hiragino Kaku Gothic
|
||
ProN|，><with|font|Songti SC|则><math|<around|\||A*B|\|>=><underline|<space|2cm>>．
|
||
|
||
13<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
|
||
SC|若><math|a\<gtr\>0,b\<gtr\>0><with|font|Hiragino Kaku Gothic
|
||
ProN|，><with|font|Songti SC|则><math|<frac|1|a>+<frac|a|b<rsup|2>>+b><with|font|Songti
|
||
SC|的最小值为><underline|<space|2cm>>．
|
||
|
||
<with|font-series|bold|<with|font|Songti SC|三>、<with|font|Songti
|
||
SC|双空题>>
|
||
|
||
14<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
|
||
SC|甲>、<with|font|Songti SC|乙两人在每次猜谜活动中各猜一个谜语><with|font|Hiragino
|
||
Kaku Gothic ProN|，><with|font|Songti SC|若一方猜对且另一方猜错><with|font|Hiragino
|
||
Kaku Gothic ProN|，><with|font|Songti SC|则猜对的一方获胜><with|font|Hiragino
|
||
Kaku Gothic ProN|，><with|font|Songti SC|否则本次平局><with|font|Hiragino
|
||
Kaku Gothic ProN|，><with|font|Songti SC|已知每次活动中><with|font|Hiragino
|
||
Kaku Gothic ProN|，><with|font|Songti SC|甲>、<with|font|Songti
|
||
SC|乙猜对的概率分别为><math|<frac|5|6>><with|font|Songti
|
||
SC|和><math|<frac|1|5>><with|font|Hiragino Kaku Gothic
|
||
ProN|，><with|font|Songti SC|且每次活动中甲>、<with|font|Songti
|
||
SC|乙猜对与否互不影响><with|font|Hiragino Kaku Gothic
|
||
ProN|，><with|font|Songti SC|各次活动也互不影响><with|font|Hiragino
|
||
Kaku Gothic ProN|，><with|font|Songti SC|则一次活动中><with|font|Hiragino
|
||
Kaku Gothic ProN|，><with|font|Songti SC|甲获胜的概率为><underline|<space|2cm>><with|font|Hiragino
|
||
Kaku Gothic ProN|，>3<with|font|Songti SC|次活动中><with|font|Hiragino
|
||
Kaku Gothic ProN|，><with|font|Songti SC|甲至少获胜>2<with|font|Songti
|
||
SC|次的概率为><underline|<space|2cm>>．
|
||
|
||
15<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
|
||
SC|在边长为>1<with|font|Songti SC|的等边三角形><em|ABC><with|font|Songti
|
||
SC|中><with|font|Hiragino Kaku Gothic ProN|，><em|D><with|font|Songti
|
||
SC|为线段><em|BC><with|font|Songti SC|上的动点><with|font|Hiragino
|
||
Kaku Gothic ProN|，><math|D*E*\<bot\>*A*B><with|font|Songti
|
||
SC|且交><em|AB><with|font|Songti SC|于点><em|E><with|font|Hiragino Kaku
|
||
Gothic ProN|．> <math|D*F*<text|//>A*B><with|font|Songti
|
||
SC|且交><em|AC><with|font|Songti SC|于点><em|F>,<with|font|Songti
|
||
SC|则><math|<around|\||2*<wide|B*E|\<wide-varrightarrow\>>+<wide|D*F|\<wide-varrightarrow\>>|\|>><with|font|Songti
|
||
SC|的值为><underline|<space|2cm>><with|font|Hiragino Kaku Gothic
|
||
ProN|；><math|<around|(|<wide|D*E|\<wide-varrightarrow\>>+<wide|D*F|\<wide-varrightarrow\>>|)>\<cdot\><wide|D*A|\<wide-varrightarrow\>>><with|font|Songti
|
||
SC|的最小值为><underline|<space|2cm>>．
|
||
|
||
<with|font-series|bold|<with|font|Songti SC|四>、<with|font|Songti
|
||
SC|解答题>>
|
||
|
||
16<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
|
||
SC|在><math|\<triangle\>A*B*C><with|font|Hiragino Kaku Gothic
|
||
ProN|，><with|font|Songti SC|角><math|A,B,C><with|font|Songti
|
||
SC|所对的边分别为><math|a,b,c><with|font|Hiragino Kaku Gothic
|
||
ProN|，><with|font|Songti SC|已知><math|sin A:sin B:sin
|
||
C=2:1:<sqrt|2>><with|font|Hiragino Kaku Gothic
|
||
ProN|，><math|b=<sqrt|2>><with|font|Hiragino Kaku Gothic ProN|．>
|
||
|
||
<with|font|Hiragino Kaku Gothic ProN|（>I<with|font|Hiragino Kaku Gothic
|
||
ProN|）><with|font|Songti SC|求><em|a><with|font|Songti
|
||
SC|的值><with|font|Hiragino Kaku Gothic ProN|；>
|
||
|
||
<with|font|Hiragino Kaku Gothic ProN|（>II<with|font|Hiragino Kaku Gothic
|
||
ProN|）><with|font|Songti SC|求><math|cos C><with|font|Songti
|
||
SC|的值><with|font|Hiragino Kaku Gothic ProN|；>
|
||
|
||
<with|font|Hiragino Kaku Gothic ProN|（>III<with|font|Hiragino Kaku Gothic
|
||
ProN|）><with|font|Songti SC|求><math|sin
|
||
<around*|(|2*C-<frac|\<pi\>|6>|)>><with|font|Songti
|
||
SC|的值><with|font|Hiragino Kaku Gothic ProN|．><vspace|3cm>
|
||
|
||
17<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
|
||
SC|如图><with|font|Hiragino Kaku Gothic ProN|，><with|font|Songti
|
||
SC|在棱长为>2<with|font|Songti SC|的正方体><math|A*B*C*D-A<rsub|1>*B<rsub|1>*C<rsub|1>*D<rsub|1>><with|font|Songti
|
||
SC|中><with|font|Hiragino Kaku Gothic ProN|，><em|E><with|font|Songti
|
||
SC|为棱><em|BC><with|font|Songti SC|的中点><with|font|Hiragino Kaku
|
||
Gothic ProN|，><em|F><with|font|Songti SC|为棱><em|CD><with|font|Songti
|
||
SC|的中点><with|font|Hiragino Kaku Gothic ProN|．>
|
||
|
||
<\center>
|
||
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</center>
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<with|font|Hiragino Kaku Gothic ProN|（>I<with|font|Hiragino Kaku Gothic
|
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ProN|）><with|font|Songti SC|求证><with|font|Hiragino Kaku Gothic
|
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ProN|：><math|D<rsub|1>*F//><with|font|Songti
|
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SC|平面><math|A<rsub|1>*E*C<rsub|1>><with|font|Hiragino Kaku Gothic
|
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ProN|；>
|
||
|
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<with|font|Hiragino Kaku Gothic ProN|（>II<with|font|Hiragino Kaku Gothic
|
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ProN|）><with|font|Songti SC|求直线><math|A*C<rsub|1>><with|font|Songti
|
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SC|与平面><math|A<rsub|1>*E*C<rsub|1>><with|font|Songti
|
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SC|所成角的正弦值><with|font|Hiragino Kaku Gothic ProN|．>
|
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|
||
<with|font|Hiragino Kaku Gothic ProN|（>III<with|font|Hiragino Kaku Gothic
|
||
ProN|）><with|font|Songti SC|求二面角><math|A-A<rsub|1>*C<rsub|1>-E><with|font|Songti
|
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SC|的正弦值><with|font|Hiragino Kaku Gothic ProN|．<vspace|3cm>>
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|
||
18<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
|
||
SC|已知椭圆><math|<frac|x<rsup|2>|a<rsup|2>>+<frac|y<rsup|2>|b<rsup|2>>=1*<around|(|a\<gtr\>b\<gtr\>0|)>><with|font|Songti
|
||
SC|的右焦点为><math|F><with|font|Hiragino Kaku Gothic
|
||
ProN|，><with|font|Songti SC|上顶点为><math|B><with|font|Hiragino Kaku
|
||
Gothic ProN|，><with|font|Songti SC|离心率为><math|<frac|2*<sqrt|5>|5>><with|font|Hiragino
|
||
Kaku Gothic ProN|，><with|font|Songti SC|且><math|<around|\||B*F|\|>=<sqrt|5>><with|font|Hiragino
|
||
Kaku Gothic ProN|．>
|
||
|
||
<with|font|Hiragino Kaku Gothic ProN|（>1<with|font|Hiragino Kaku Gothic
|
||
ProN|）><with|font|Songti SC|求椭圆的方程><with|font|Hiragino Kaku
|
||
Gothic ProN|；>
|
||
|
||
<with|font|Hiragino Kaku Gothic ProN|（>2<with|font|Hiragino Kaku Gothic
|
||
ProN|）><with|font|Songti SC|直线><math|l><with|font|Songti
|
||
SC|与椭圆有唯一的公共点><math|M><with|font|Hiragino Kaku Gothic
|
||
ProN|，><with|font|Songti SC|与><math|y><with|font|Songti
|
||
SC|轴的正半轴交于点><math|N><with|font|Hiragino Kaku Gothic
|
||
ProN|，><with|font|Songti SC|过><math|N><with|font|Songti
|
||
SC|与><math|B*F><with|font|Songti SC|垂直的直线交><math|x><with|font|Songti
|
||
SC|轴于点><math|P><with|font|Hiragino Kaku Gothic
|
||
ProN|．><with|font|Songti SC|若><math|M*P*<text|//>B*F><with|font|Hiragino
|
||
Kaku Gothic ProN|，><with|font|Songti SC|求直线><math|l><with|font|Songti
|
||
SC|的方程><with|font|Hiragino Kaku Gothic ProN|．><vspace|3cm>
|
||
|
||
19<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
|
||
SC|已知><math|<around*|{|a<rsub|n>|}>><with|font|Songti
|
||
SC|是公差为>2<with|font|Songti SC|的等差数列><with|font|Hiragino
|
||
Kaku Gothic ProN|，><with|font|Songti SC|其前>8<with|font|Songti
|
||
SC|项和为>64<with|font|Hiragino Kaku Gothic
|
||
ProN|．><math|<around*|{|b<rsub|n>|}>><with|font|Songti
|
||
SC|是公比大于>0<with|font|Songti SC|的等比数列><with|font|Hiragino
|
||
Kaku Gothic ProN|，><math|b<rsub|1>=4,b<rsub|3>-b<rsub|2>=48><with|font|Hiragino
|
||
Kaku Gothic ProN|．>
|
||
|
||
<with|font|Hiragino Kaku Gothic ProN|（>I<with|font|Hiragino Kaku Gothic
|
||
ProN|）><with|font|Songti SC|求><math|<around*|{|a<rsub|n>|}>><with|font|Songti
|
||
SC|和><math|<around*|{|b<rsub|n>|}>><with|font|Songti
|
||
SC|的通项公式><with|font|Hiragino Kaku Gothic ProN|；>
|
||
|
||
<with|font|Hiragino Kaku Gothic ProN|（>II<with|font|Hiragino Kaku Gothic
|
||
ProN|）><with|font|Songti SC|记><math|c<rsub|n>=b<rsub|2*n>+<frac|1|b<rsub|n>>,n\<in\>N<rsup|\<ast\>>><with|font|Hiragino
|
||
Kaku Gothic ProN|，>
|
||
|
||
<with|font|Hiragino Kaku Gothic ProN|（>i<with|font|Hiragino Kaku Gothic
|
||
ProN|）><with|font|Songti SC|证明><math|<around*|{|c<rsub|n><rsup|2>-c<rsub|2*n>|}>><with|font|Songti
|
||
SC|是等比数列><with|font|Hiragino Kaku Gothic ProN|；>
|
||
|
||
<with|font|Hiragino Kaku Gothic ProN|（>ii<with|font|Hiragino Kaku Gothic
|
||
ProN|）><with|font|Songti SC|证明><math|<big|sum><rsub|k=1><rsup|n><sqrt|<frac|a<rsub|k>*a<rsub|k+1>|c<rsub|k><rsup|2>-c<rsub|2*k>>>\<less\>2*<sqrt|2>*<around*|(|n\<in\>N<rsup|\<ast\>>|)>>.<vspace|3cm>
|
||
|
||
20<with|font|Hiragino Kaku Gothic ProN|．><with|font|Songti
|
||
SC|已知><math|a\<gtr\>0><with|font|Hiragino Kaku Gothic
|
||
ProN|，><with|font|Songti SC|函数><math|f<around|(|x|)>=a*x-x*e<rsup|x>><with|font|Hiragino
|
||
Kaku Gothic ProN|．>
|
||
|
||
<with|font|Hiragino Kaku Gothic ProN|（>I<with|font|Hiragino Kaku Gothic
|
||
ProN|）><with|font|Songti SC|求曲线><math|y=f<around|(|x|)>><with|font|Songti
|
||
SC|在点><math|<around*|(|0,f<around*|(|0|)>|)>><with|font|Songti
|
||
SC|处的切线方程><with|font|Hiragino Kaku Gothic ProN|：>
|
||
|
||
<with|font|Hiragino Kaku Gothic ProN|（>II<with|font|Hiragino Kaku Gothic
|
||
ProN|）><with|font|Songti SC|证明><math|f<around|(|x|)>><with|font|Songti
|
||
SC|存在唯一的极值点>
|
||
|
||
<with|font|Hiragino Kaku Gothic ProN|（>III<with|font|Hiragino Kaku Gothic
|
||
ProN|）><with|font|Songti SC|若存在><em|a><with|font|Hiragino Kaku
|
||
Gothic ProN|，><with|font|Songti SC|使得><math|f<around|(|x|)>\<leq\>a+b><with|font|Songti
|
||
SC|对任意><math|x\<in\>R><with|font|Songti SC|成立><with|font|Hiragino
|
||
Kaku Gothic ProN|，><with|font|Songti SC|求实数><em|b><with|font|Songti
|
||
SC|的取值范围><with|font|Hiragino Kaku Gothic ProN|． ><vspace|3cm>
|
||
</body>
|
||
|
||
<\initial>
|
||
<\collection>
|
||
<associate|page-medium|paper>
|
||
</collection>
|
||
</initial> |