已知矩阵
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231537909158566/SYS201311012315379091585021_ST/0.png)
,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231537909158566/SYS201311012315379091585021_ST/1.png)
,求满足AX=B的二阶矩阵X.
考点分析:
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(几何证明选讲选做题)已知AD是△ABC的外角∠EAC的平分线,交BC的延长线于点D,延长DA交△ABC的外接圆于点F,连接FB,FC.
(1)求证:FB=FC;
(2)若AB是△ABC外接圆的直径,∠EAC=120°,BC=3
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231537909158566/SYS201311012315379091585020_ST/0.png)
,求AD的长.
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已知数列{a
n},对于任意n≥2,在a
n-1与a
n之间插入n个数,构成的新数列{b
n}成等差数列,并记在a
n-1与a
n之间插入的这n个数均值为C
n-1.
(1)若a
n=
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231537909158566/SYS201311012315379091585019_ST/0.png)
,求C
1,C
2,C
3;
(2)在(1)的条件下是否存在常数λ,使{C
n-1-λC
n}是等差数列?如果存在,求出满足条件的λ,如果不存在,请说明理由;
(3)求出所有的满足条件的数列{a
n}.
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已知函数f(x)=
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231537909158566/SYS201311012315379091585018_ST/0.png)
(1)当
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231537909158566/SYS201311012315379091585018_ST/1.png)
时,求f(x)的极值点;
(2)若f(x)在f′(x)的单调区间上也是单调的,求实数a的范围.
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如图,已知椭圆
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231537909158566/SYS201311012315379091585017_ST/0.png)
,左、右焦点分别为F
1,F
2,右顶点为A,上顶点为B,P为椭圆上在第一象限内一点.
(1)若
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231537909158566/SYS201311012315379091585017_ST/1.png)
,求椭圆的离心率;
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![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231537909158566/SYS201311012315379091585017_ST/2.png)
=
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231537909158566/SYS201311012315379091585017_ST/3.png)
,求直线PF
1的斜率k;
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![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231537909158566/SYS201311012315379091585017_ST/4.png)
成等差数列,椭圆的离心率e
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231537909158566/SYS201311012315379091585017_ST/5.png)
,求直线PF
1的斜率k的取值范围.
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如图,半径为1圆心角为
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231537909158566/SYS201311012315379091585016_ST/0.png)
圆弧
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231537909158566/SYS201311012315379091585016_ST/1.png)
上有一点C.
(1)当C为圆弧
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231537909158566/SYS201311012315379091585016_ST/2.png)
中点时,D为线段OA上任一点,求
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231537909158566/SYS201311012315379091585016_ST/3.png)
的最小值.
(2)当C在圆弧
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231537909158566/SYS201311012315379091585016_ST/4.png)
上运动时,D、E分别为线段OA、OB的中点,求
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231537909158566/SYS201311012315379091585016_ST/5.png)
的取值范围.
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