函数f(x)=a
x-(k-1)a
-x(a>0且≠1)是定义域为R的奇函数.
(1)求k值;
(2)若f(1)<0,试判断函数单调性并求使不等式f(x
2+tx)+f(4-x)<0恒成立的取值范围.
考点分析:
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各项均为正数的数列{a
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(1)求数列{a
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恒成立,求k的取值范围.
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已知向量
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=(cosωx-sinωx,sinωx),
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=(-cosωx-sinωx,2
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cosωx),设函数f(x)=
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930743711/SYS201311031024209307437016_ST/3.png)
•
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+λ(x∈R)的图象关于直线x=π对称,其中ω,λ为常数,且ω∈(
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930743711/SYS201311031024209307437016_ST/5.png)
,1)
(1)求函数f(x)的最小正周期;
(2)若y=f(x)的图象经过点(
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930743711/SYS201311031024209307437016_ST/6.png)
,0)求函数f(x)在区间[0,
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]上的取值范围.
查看答案
给出以下五个命题:
①命题“∀x∈R,x
2+x+1>0”的否定是:“∃x∈R,x
2+x+1<0”.
②已知函数f(x)=k•cosx的图象经过点P(
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930743711/SYS201311031024209307437015_ST/0.png)
,1),则函数图象上过点P的切线斜率等于
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930743711/SYS201311031024209307437015_ST/1.png)
③a=1是直线y=ax+1和直线y=(a-2)x-1垂直的充要条件.
④函数
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930743711/SYS201311031024209307437015_ST/2.png)
在区间(0,1)上存在零点.
⑤已知向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930743711/SYS201311031024209307437015_ST/3.png)
与向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102420930743711/SYS201311031024209307437015_ST/4.png)
的夹角为锐角,那么实数m的取值范围是(
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)
其中正确命题的序号是
.
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已知正四棱柱ABCD-A
1B
1C
1D
1的高为
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,外接球的体积是
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,则A、B两点的球面距离为
.
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若函数
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在[-1,1]上是单调增函数,则实数a的取值范围是
.
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