已知函数
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101225040684641483/SYS201311012250406846414020_ST/0.png)
.
(1)若函数f(x)在其定义域内为单调函数,求a的取值范围;
(2)若函数f(x)的图象在x=1处的切线的斜率为0,且
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101225040684641483/SYS201311012250406846414020_ST/1.png)
,已知a
1=4,求证:a
n≥2n+2;
(3)在(2)的条件下,试比较
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101225040684641483/SYS201311012250406846414020_ST/2.png)
与
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101225040684641483/SYS201311012250406846414020_ST/3.png)
的大小,并说明你的理由.
考点分析:
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某企业有一条价值为m万元的生产流水线,要提高其生产能力,提高产品的产值,就要对该流水线进行技术改造,假设产值y万元与投入的改造费用x万元之间的关系满足:①y与(m-x)x
2成正比;②当
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时,
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;③
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101225040684641483/SYS201311012250406846414019_ST/2.png)
,其中a为常数,且a∈[0,2]
(1)设y=f(x),求出f(x)的表达式;
(2)求产值y的最大值,并求出此时x的值.
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数列{a
n}满足a1=2,a
n+1=a
n2+6a
n+6(n∈N
×)
(Ⅰ)设C
n=log
5(a
n+3),求证{C
n}是等比数列;
(Ⅱ)求数列{a
n}的通项公式;
(Ⅲ)设
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101225040684641483/SYS201311012250406846414018_ST/0.png)
,数列{b
n}的前n项的和为T
n,求证:
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101225040684641483/SYS201311012250406846414018_ST/1.png)
.
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已知命题P:函数f(x)=x
2-4mx+4m
2+2在区间[-1,3]上的最小值等于2;命题Q:不等式x+|x-m|>1对任意x∈R恒成立.如果上述两个命题中有且仅有一个真命题,试求实数m的取值范围.
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在平面直角坐标系中,已知向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101225040684641483/SYS201311012250406846414016_ST/0.png)
=(-1,2),又点A(8,0),B(n,t),C(ksinθ,t)
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101225040684641483/SYS201311012250406846414016_ST/1.png)
.
(1)若
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101225040684641483/SYS201311012250406846414016_ST/2.png)
,且
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101225040684641483/SYS201311012250406846414016_ST/3.png)
为坐标原点),求向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101225040684641483/SYS201311012250406846414016_ST/4.png)
;
(2)若向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101225040684641483/SYS201311012250406846414016_ST/5.png)
与向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101225040684641483/SYS201311012250406846414016_ST/6.png)
共线,当k>4,且tsinθ取最大值4时,求
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101225040684641483/SYS201311012250406846414016_ST/7.png)
.
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已知函数
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101225040684641483/SYS201311012250406846414015_ST/0.png)
(1)求函数f(x)的最小正周期和最小值;
(2)在给出的直角坐标系中,用描点法画出函数y=f(x)在区间[0,π]上的图象.
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