在△ABC中,角A、B、C所对的边分别为a、b、c,向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222906681444150/SYS201311012229066814441015_ST/0.png)
,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222906681444150/SYS201311012229066814441015_ST/1.png)
,若
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∥
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222906681444150/SYS201311012229066814441015_ST/3.png)
.
(1)求角A、B、C的值;
(2)若
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,求函数f(x)=sinAsinx+cosBcosx的最大值与最小值.
考点分析:
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关于函数
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222906681444150/SYS201311012229066814441014_ST/0.png)
(a为常数,且a>0),对于下列命题:
①函数f(x)在每一点处都连续;
②若a=2,则函数f(x)在x=0处可导;
③函数f(x)在R上存在反函数;
④函数f(x)有最大值
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222906681444150/SYS201311012229066814441014_ST/1.png)
;
⑤对任意的实数x
1>x
2≥0,恒有f(
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)<
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222906681444150/SYS201311012229066814441014_ST/3.png)
;
其中正确命题的序号是
.
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已知函数f(x)=
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222906681444150/SYS201311012229066814441013_ST/0.png)
若数列{a
n}满a
1=
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222906681444150/SYS201311012229066814441013_ST/1.png)
,a
n+1=f(a
n),n∈N
*,则a
2006+a
2009+a
2010=
.
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已知函数f(x)=a
x+1-3(a>0且a≠1)的反函数的图象恒过定点A,且点A在直线mx+ny+1=0上,若m>0,n>0.则
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222906681444150/SYS201311012229066814441012_ST/0.png)
的最小值为
.
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已知函数f(x)=|x-2|,若a≠0,且a,b∈R,都有不等式|a+b|+|a-b|≥|a|•f(x)成立,则实数x的取值范围是
.
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下列图形中,若黑色三角形的个数依次构成一个数列的前4项,则这个数列的一个通项公式为
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