函数f(x)=
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的值域是
.
考点分析:
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若集合A={x|2x+1>0},B={x||x-1|<2},则A∩B=
.
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设集合P
n={1,2,…,n},n∈N
*.记f(n)为同时满足下列条件的集合A的个数:
①A⊆P
n;②若x∈A,则2x∉A;③若x∈
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A,则2x∉
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A.
(1)求f(4);
(2)求f(n)的解析式(用n表示).
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设ξ为随机变量,从棱长为1的正方体的12条棱中任取两条,当两条棱相交时,ξ=0;当两条棱平行时,ξ的值为两条棱之间的距离;当两条棱异面时,ξ=1.
(1)求概率P(ξ=0);
(2)求ξ的分布列,并求其数学期望E(ξ).
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A.[选修4-1:几何证明选讲]
如图,AB是圆O的直径,D,E为圆上位于AB异侧的两点,连接BD并延长至点C,使BD=DC,连接AC,AE,DE.
求证:∠E=∠C.
B.[选修4-2:矩阵与变换]
已知矩阵A的逆矩阵
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,求矩阵A的特征值.
C.[选修4-4:坐标系与参数方程]
在极坐标中,已知圆C经过点P(
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024190122796417966/SYS201310241901227964179020_ST/1.png)
,
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),圆心为直线ρsin(θ-
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)=-
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与极轴的交点,求圆C的极坐标方程.
D.[选修4-5:不等式选讲]
已知实数x,y满足:|x+y|<
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024190122796417966/SYS201310241901227964179020_ST/5.png)
,|2x-y|<
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,求证:|y|<
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.
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