已知函数f(x)的定义域是
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024183115792032694/SYS201310241831157920326021_ST/0.png)
且f(x)+f(2-x)=0,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024183115792032694/SYS201310241831157920326021_ST/1.png)
,当
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024183115792032694/SYS201310241831157920326021_ST/2.png)
时,f(x)=3
x.
(1)求证:f(x)是奇函数;
(2)求f(x)在区间
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024183115792032694/SYS201310241831157920326021_ST/3.png)
Z)上的解析式;
(3)是否存在正整数k,使得当x∈
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024183115792032694/SYS201310241831157920326021_ST/4.png)
时,不等式log
3f(x)>x
2-kx-2k有解?证明你的结论.
考点分析:
相关试题推荐
设
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024183115792032694/SYS201310241831157920326020_ST/0.png)
,其中a
ik(1≤i≤n,1≤k≤n)表示该数阵中位于第i行第k列的数,已知该数阵每一行的数成等差数列,每一列的数成公比为2的等比数列,且a
23=8,a
34=20.
(1)求a
11和a
ik;
(2)设数阵第i行的公差为d
i(i=1,2,…,n),f(n)=d
1+d
2+…+d
n,求f(n);
(3)设A
n=a
1n+a
2(n-1)+a
3(n-2)+…+a
n1,证明:当n是3的倍数时,A
n+n能被21整除.
查看答案
图1是某种称为“凹槽”的机械部件的示意图,图2是凹槽的横截面(阴影部分)示意图,其中四边形ABCD是矩形,弧CmD是半圆,凹槽的横截面的周长为4.已知凹槽的强度与横截面的面积成正比,比例系数为
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024183115792032694/SYS201310241831157920326019_ST/0.png)
,设AB=2x,BC=y.
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024183115792032694/SYS201310241831157920326019_ST/images1.png)
(1)写出y关于x函数表达式,并指出x的取值范围;
(2)求当x取何值时,凹槽的强度最大.
查看答案
已知向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024183115792032694/SYS201310241831157920326018_ST/0.png)
=(
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024183115792032694/SYS201310241831157920326018_ST/1.png)
sin2x-1,cosx),
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024183115792032694/SYS201310241831157920326018_ST/2.png)
=(1,2cosx),设函数
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024183115792032694/SYS201310241831157920326018_ST/3.png)
.
(1)求函数 f(x)的最小正周期及
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024183115792032694/SYS201310241831157920326018_ST/4.png)
时的最大值;
(2)把函数f(x)的图象向左平移φ(φ>0)个单位,所得到的图象对应的函数为奇函数,求φ的最小值.
查看答案
在直三棱柱ABC-A
1B
1C
1中,∠ACB=90°,BC=CC
1=a,AC=2a,
(1)求多面体B
1-AA
1C
1C的体积;
(2)求异面直线AB
1与CC
1所成角的大小.
查看答案
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131024183115792032694/SYS201310241831157920326016_ST/images0.png)
某程序框图如图所示,该程序运行后输出的k的值是( )
A.4
B.5
C.6
D.7
查看答案