若复数z满足
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025124410291936128/SYS201310251244102919361000_ST/0.png)
,则z的值为
.
考点分析:
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已知函数f(x)=x
2-x,g(x)=lnx.
(1)求证:f(x)≥g(x);
(2)若f(x)≥ag(x)恒成立,求实数a的值;
(3)设F(x)=f(x)+mg(x)(m∈R)有两个极值点x
1、x
2(x
1<x
2);求实数m的取值范围,并证明:
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.
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定义:称
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025124410291934511/SYS201310251244102919345008_ST/0.png)
为n个正数p
1,p
2,…p
n的“均倒数”.若已知数列{a
n}的前n项的“均倒数”为
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.
(Ⅰ)求数列{a
n}的通项公式;
(Ⅱ)设
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,试求数列{d
n}的前n项和T
n.
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点集Q={(x,y)|x=x
1+x
2,y=y
1+y
2,(x
1,y
1)∈A,(x
2,y
2)∈B},其中A={(x,y)|x
2+y
2≤1},B={(x,y)|x≤4,y≥0,3x-4y≥0},所表示的区域的面积为
.
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设定义在[a,b](a≥-4)上的函数f(x),若函数
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025124410291934511/SYS201310251244102919345006_ST/0.png)
与f(x)的定义域与值域都相同,则实数m的取值范围为
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给出定义:若
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025124410291934511/SYS201310251244102919345005_ST/0.png)
(其中m为整数),则m叫做离实数x最近的整数,记作{x},即{x}=m.在此基础上给出下列关于函数f(x)=|x-{x}|的四个命题:
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![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025124410291934511/SYS201310251244102919345005_ST/1.png)
;
②函数y=f(x)的图象关于直线
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025124410291934511/SYS201310251244102919345005_ST/2.png)
对称;
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④函数y=f(x)在
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025124410291934511/SYS201310251244102919345005_ST/3.png)
上是增函数.
则其中真命题是( )
A.①②③
B.②③④
C.①②④
D.①③④
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