某种汽车的购车费用是10万元,每年使用的保险费、养路费、汽油费约为0.9万元,年维修费用第一年是0.2万元,第二年是0.4万元,第三年是0.6万元,…,以后逐年递增0.2万元.汽车的购车费用、每年使用的保险费、养路费、汽油费、维修费用的和平均摊到每一年的费用叫做年平均费用.设这种汽车使用x(x∈N
*)年的维修费用为g(x),年平均费用为f(x).
(1)求出函数g(x),f(x)的解析式;
(2)这种汽车使用多少年时,它的年平均费用最小?最小值是多少?
考点分析:
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已知
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=(cosx,sinx),
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=(cosx,2
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cosx-sinx),f(x)=
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•
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+|
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|,x∈(
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,π].
(Ⅰ)求f(x)的最大值;
(Ⅱ)记△ABC的内角A、B、C的对边分别为a、b、c,若f(B)=-1,a=c=2,求
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•
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.
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已知函数f(x)=log
2x,设
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是首项和公差都等于1的等差数列.数列{b
n}满足
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.
(1)求数列{a
n}的通项公式,并证明数列{b
n}不是等比数列;
(2)令
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,S
n=c
1+c
2+c
3+…+c
n,求证:S
n<3.
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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/20131103101211442690341/SYS201311031012114426903015_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
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的值等于2.其中正确命题的序号是
.
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下表结出一个“直角三角形数阵”
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101211442690341/SYS201311031012114426903014_ST/0.png)
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103101211442690341/SYS201311031012114426903014_ST/1.png)
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…
满足每一列成等差数列,从第三行起,每一行的数成等比数列,且每一行的公比相等,记第i行第j列的数为a
ij(i≥j,i,j∈N
+),则a
83等于
.
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某所学校计划招聘男教师x名,女教师y名,x和y须满足约束条件
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则该校招聘的教师最多是
名.
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