若实数x、y、m满足|x-m|<|y-m|,则称x比y接近m.
(1)若2x-1比3接近0,求x的取值范围;
(2)对任意两个不相等的正数a、b,证明:a
2b+ab
2比a
3+b
3接近
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.
考点分析:
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在△ABC中,角A、B、C的对边分别为a、b、c,且满足(2b-c)cosA-acosC=0,
(Ⅰ)求角A的大小;
(Ⅱ)若
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,试判断△ABC的形状,并说明理由.
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已知
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231426650268958/SYS201311012314266502689015_ST/0.png)
=(1,x),
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=(x
2+x,-x)m为常数且m≤-2,求使不等式
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•
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+2>m
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231426650268958/SYS201311012314266502689015_ST/4.png)
成立的x的范围.
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给出下列四个命题:
①已知a,b,m都是正数,且
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,则a<b;
②若函数f(x)=lg(ax+1)的定义域是{x|x<1},则a<-1;
③已知x∈(0,π),则y=sinx+
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231426650268958/SYS201311012314266502689014_ST/1.png)
的最小值为
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;
④已知a、b、c成等比数列,a、x、b成等差数列,b、y、c也成等差数列,则
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231426650268958/SYS201311012314266502689014_ST/3.png)
的值等于2.其中正确命题的序号是
.
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已知
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231426650268958/SYS201311012314266502689013_ST/0.png)
⊥
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231426650268958/SYS201311012314266502689013_ST/1.png)
,|
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231426650268958/SYS201311012314266502689013_ST/2.png)
|=2,|
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231426650268958/SYS201311012314266502689013_ST/3.png)
|=3,且3
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231426650268958/SYS201311012314266502689013_ST/4.png)
+2
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231426650268958/SYS201311012314266502689013_ST/5.png)
与λ
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231426650268958/SYS201311012314266502689013_ST/6.png)
-
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垂直,则实数λ的值为
.
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规定符号“*”表示一种两个正实数之间的运算,即a*b=
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101231426650268958/SYS201311012314266502689012_ST/0.png)
+a+b,,已知1*k=3,则函数f(x)=k*x的值域是
.
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