已知函数f(x)=[2sin(x+
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)+sinx]cosx-
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sin
2x,x∈R.
(1)求函数f(x)的最小正周期;
(2)若任意x∈[0,
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],使不等式恒f(x)>m成立,求实数m的取值范围.
考点分析:
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下列命题:
①函数y=sinx在第一象限是增函数;
②函数y=|cosx+
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102756334215940/SYS201311031027563342159013_ST/0.png)
|的最小正周期是π;
③函数y=tn
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102756334215940/SYS201311031027563342159013_ST/1.png)
x的图象的对称中心是(kπ,0),k∈Z;
④函数y=ln(1+2cos2x)的递减区间是[kπ,kπ+
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102756334215940/SYS201311031027563342159013_ST/2.png)
),k∈Z;
⑤函数y=3sin(2x+
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102756334215940/SYS201311031027563342159013_ST/3.png)
)的图象可由函数y=3sin2x的图象向右平移
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102756334215940/SYS201311031027563342159013_ST/4.png)
平移得到.
其中正确的命题序号是
.
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若向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102756334215940/SYS201311031027563342159012_ST/0.png)
=(1,3),
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102756334215940/SYS201311031027563342159012_ST/1.png)
=(-x,-1)的夹角为钝角,则实数x的取值范围为
.
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已知sin(
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102756334215940/SYS201311031027563342159010_ST/0.png)
+α)=
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102756334215940/SYS201311031027563342159010_ST/1.png)
,则cos(
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102756334215940/SYS201311031027563342159010_ST/2.png)
)=
.
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已知函数f(x)是(-∞,+∞)上的偶函数,若对于x≥0,都有f(x+2)=-f(x),且当x∈[0,2)时,f(x)=log
2(x+1),则f(-2011)+f(2012)=
.
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