考点分析:
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已知集合A={y|y=log
2x,
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<x<2},B={y|y=(
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)
x,0<x<1},则A∩B为( )
A.
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B.(0,2)
C.
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D.
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已知z=(1-2sinθ)+(2cosθ+
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)i(0<θ<π)是纯虚数,则θ=( )
A.
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B.
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C.
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D.
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或
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已知函数
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.
(I)当a=1时,求f(x)在x∈[1,+∞)最小值;
(Ⅱ)若f(x)存在单调递减区间,求a的取值范围;
(Ⅲ)求证:
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(n∈N
*).
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如图,平面EAD⊥平面ABFD,△AED为正三角形,四边形ABFD为直角梯形,且∠BAD=90°,
AB∥DF,AD=a,AB=
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a,DF=
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.
(I)求证:EF⊥FB;
(II)求二面角A-BF-E的大小;
(Ⅲ)点P是线段EB上的动点,当∠APF为直角时,求BP 的长度.
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抛物线y
2=2px(p>0)的准线方程为x=-2,该抛物线上的点到其准线的距离与到定点N的距离都相等,以N为圆心的圆与直线
l
1:y=x和l
2:y=-x都相切.
(Ⅰ)求圆N的方程;
(Ⅱ)是否存在直线l同时满足下列两个条件,若存在,求出的方程;若不存在请说明理由.
①l分别与直线l
1和l
2交于A、B两点,且AB中点为E(4,1);
②l被圆N截得的弦长为2.
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