已知点A(-3,0),B(3,0),动点P到A的距离与到B的距离之比为2.
(1)求P点的轨迹E的方程;
(2)当m为何值时,直线l:mx+(2m-1)y-5m+1=0被曲线E截得的弦最短.
考点分析:
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已知函数f(x)=e
x,其图象在点P(2,f(2))处的切线为l.
(1)求y=f(x)、直线x=2及两坐标轴围成的图形绕x轴旋转一周所得几何体的体积;
(2)求y=f(x)、直线l及y轴围成图形的面积.
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用0~5六个数字组成四位数,求:
(1)能组成多少个四位数; (2)能组成多少个没有重复数字的四位奇数.
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已知下列四个命题:
①若函数y=f(x)在x
°处的导数f'(x
°)=0,则它在x=x
°处有极值;
②不论m为何值,直线y=mx+1均与曲线
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222934305719861/SYS201311012229343057198014_ST/0.png)
有公共点,则b≥1;
③设直线l
1、l
2的倾斜角分别为α、β,且1+tanβ-tanα+tanαtanβ=0,则l
1和l
2的夹角为45°;
④若命题“存在x∈R,使得|x-a|+|x+1|≤2”是假命题,则|a+1|>2;
以上四个命题正确的是
(填入相应序号).
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观察下列等式:观察下列等式:
C
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222934305719861/SYS201311012229343057198013_ST/0.png)
+C
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222934305719861/SYS201311012229343057198013_ST/1.png)
=2
3-2,
C
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222934305719861/SYS201311012229343057198013_ST/2.png)
+C
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222934305719861/SYS201311012229343057198013_ST/3.png)
+C
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222934305719861/SYS201311012229343057198013_ST/4.png)
=2
7+2
3,
C
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222934305719861/SYS201311012229343057198013_ST/5.png)
+C
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222934305719861/SYS201311012229343057198013_ST/6.png)
+C
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222934305719861/SYS201311012229343057198013_ST/7.png)
+C
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222934305719861/SYS201311012229343057198013_ST/8.png)
=2
11-2
5,
C
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222934305719861/SYS201311012229343057198013_ST/9.png)
+C
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222934305719861/SYS201311012229343057198013_ST/10.png)
+C
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+C
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222934305719861/SYS201311012229343057198013_ST/12.png)
+C
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222934305719861/SYS201311012229343057198013_ST/13.png)
=2
15+2
7,
…
由以上等式推测到一个一般结论:
对于n∈N
*,C
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+C
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+C
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+…+C
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222934305719861/SYS201311012229343057198013_ST/17.png)
=
.
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已知复数
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222934305719861/SYS201311012229343057198012_ST/0.png)
对应的向量为
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,复数ω
2对应的向量为
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222934305719861/SYS201311012229343057198012_ST/2.png)
,那么向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222934305719861/SYS201311012229343057198012_ST/3.png)
对应的复数为
.
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