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设集合A={x|-5<x<3},B={x|-2<x<4},则A∩B=
.
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已知数列{a
n}满足:
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024182933773867485/SYS201310241829337738674020_ST/0.png)
是公差为1的等差数列,且a
n+1=
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024182933773867485/SYS201310241829337738674020_ST/1.png)
+1.
(1)求数列{a
n}的通项公式a
n;
(2)设b
n=
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024182933773867485/SYS201310241829337738674020_ST/2.png)
),求证:b
1+b
2+…+b
n<2
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024182933773867485/SYS201310241829337738674020_ST/3.png)
-1.
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已知点
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024182933773867485/SYS201310241829337738674019_ST/0.png)
,椭圆
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024182933773867485/SYS201310241829337738674019_ST/1.png)
的右准线l
1+x=2与x轴相交于点D,右焦点F到上顶点的距离为
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024182933773867485/SYS201310241829337738674019_ST/2.png)
.
(1)求椭圆的方程;
(2)是否存在过点F且与x轴不垂直的直线l与椭圆交于A、B两点,使得
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024182933773867485/SYS201310241829337738674019_ST/3.png)
?若存在,求出直线l;若不存在,说明理由.
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函数f(x)=x
3+ax
2+bx-2的图象在与y轴交点的切线方程为y=x+a.
(1)求函数f(x)的解析式;
(2)设函数
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024182933773867485/SYS201310241829337738674018_ST/0.png)
存在极值,求实数m的取值范围.
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![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024182933773867485/SYS201310241829337738674017_ST/images0.png)
如图,已知ABCD是边长为2的正方形,DE⊥平面ABCD,BF⊥平面ABCD,且FB=2DE=2.
(1)求点E到平面FBC的距离;
(2)求证:平面AEC⊥平面AFC.
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