已知△ABC的顶点为A(7,8),B(3,5),C(4,3),若
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222351920132307/SYS201311012223519201323016_ST/0.png)
且
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222351920132307/SYS201311012223519201323016_ST/1.png)
,CM与BN交于点G,求向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222351920132307/SYS201311012223519201323016_ST/2.png)
.
考点分析:
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已知|
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222351920132307/SYS201311012223519201323015_ST/0.png)
|=3,|
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222351920132307/SYS201311012223519201323015_ST/1.png)
|=4,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222351920132307/SYS201311012223519201323015_ST/2.png)
与
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222351920132307/SYS201311012223519201323015_ST/3.png)
的夹角为60°,试求:
(1)|
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222351920132307/SYS201311012223519201323015_ST/4.png)
+
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222351920132307/SYS201311012223519201323015_ST/5.png)
|;
(2)
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222351920132307/SYS201311012223519201323015_ST/6.png)
+
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222351920132307/SYS201311012223519201323015_ST/7.png)
与
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222351920132307/SYS201311012223519201323015_ST/8.png)
-
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222351920132307/SYS201311012223519201323015_ST/9.png)
的夹角θ的余弦值.
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已知集合A={x||x|≤3},B={x|m-1<x<2m+1},m∈R.
(1)若m=3,求(C
UA)∩B;
(2)若A∪B=A,求实数m的取值范围.
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下列命题:
①若
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222351920132307/SYS201311012223519201323013_ST/0.png)
,则
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222351920132307/SYS201311012223519201323013_ST/1.png)
或
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222351920132307/SYS201311012223519201323013_ST/2.png)
;②若
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222351920132307/SYS201311012223519201323013_ST/3.png)
,则
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222351920132307/SYS201311012223519201323013_ST/4.png)
或
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222351920132307/SYS201311012223519201323013_ST/5.png)
;③
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222351920132307/SYS201311012223519201323013_ST/6.png)
;④
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222351920132307/SYS201311012223519201323013_ST/7.png)
.
其中,正确命题的序号是
.(把所有正确的序号都填上)
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将函数y=f(x)的图象沿x轴向左平移
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222351920132307/SYS201311012223519201323012_ST/0.png)
个单位,再使图象上所有的点的纵坐标不变,横坐标变为原来的2倍,得到函数y=cosx的图象,则f(x)的解析式可能是
.
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设f(x)是定义域为R,最小正周期为
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222351920132307/SYS201311012223519201323011_ST/0.png)
的函数,若
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222351920132307/SYS201311012223519201323011_ST/1.png)
,则
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222351920132307/SYS201311012223519201323011_ST/2.png)
等于
.
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