1 . 海岸上建有相距
海里的雷达站C,D,某一时刻接到海上B船因动力故障发出的求救信号后,调配附近的A船紧急前往救援,雷达站测得角度数据为
.
(2)求
之间的距离,并判断若A船以30海里每小时的速度前往B处,能否在3小时内赶到救援(说明理由)?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fd1766294dc48dd810a6ab4840703a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914a8b5f26d7ec9a180b1a15f5395a63.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6f48b9a53c0155a692509cf31f7e6.png)
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2 . 已知
是虚数单位,复数
,m为实数.
(1)当实数m满足什么条件时,
为纯虚数
(2)若复数
在复平面内对应的点位于实轴负半轴,求复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8518911c0598607ef6799bd4265b1b49.png)
(1)当实数m满足什么条件时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
(2)若复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
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解题方法
3 . 在
中,内角
的对边分别为
,且
.若
,
是边
的中点,且
,则
的内切圆的半径为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd63101d70caecb820056bf3ea0e76c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d75f67ac92faf413da3cf4aeaab9e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d35cbd9bb0385e6384107eb2183a136c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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4 . 已知复数
满足
,则复数
在复平面内对应点的集合所构成的图形面积为______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3f7970a806581eab4ea0845903d263.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
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5 . 下列命题错误的是( )
A.若向量![]() ![]() ![]() ![]() ![]() ![]() ![]() |
B.在![]() ![]() ![]() ![]() ![]() |
C.已知向量![]() ![]() ![]() ![]() ![]() |
D.平面向量![]() ![]() ![]() ![]() ![]() ![]() |
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6 . 若复数
满足
(
是虚数单位),则下列说法错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1b63802142b90e3353827482ff9bc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() |
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解题方法
7 . 已知平面向量
, 则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/322630eb737ee6c9af80933f9edafeb7.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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8 . 已知函数
的定义域是
,关于函数
给出下列命题:
①对于任意
,函数
是
上的减函数;
②对于任意
,函数
存在最小值;
③对于任意
,使得对于任意的
,都有
成立;
④对于任意
,函数
有两个零点.
其中正确命题的序号是______ .(写出所有正确命题的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd81eb7dc48fbacb0818ec936dd8426c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e20dd41998db5ca9e947fc50def74979.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
②对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f2c2e08101f22ffc56dcef37f64f632.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
③对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e20dd41998db5ca9e947fc50def74979.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
④对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f2c2e08101f22ffc56dcef37f64f632.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
其中正确命题的序号是
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解题方法
9 . 记
上的可导函数
的导函数为
,满足
的数列
称为函数
的“牛顿数列”.已知数列
为函数
的牛顿数列,且数列
满足
.
(1)证明数列
是等比数列并求
;
(2)设数列
的前
项和为
,若不等式
对任意的
恒成立,求t的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d11e3e7cd27440bbc6a93856c997b8d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2b53cd9892f6d174509740afbc69d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da8765813233a2c419d2d3bbc56f6670.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3d2f5b3ed3ee8ecce9a586f07244e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
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解题方法
10 . 已知函数
.
(1)当
时(
为大于0的常数),求
的最大值;
(2)若当
时,不等式
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0adee76b9907e6405940fb26a982aff7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b2d3722725e8293bb801a94e27389d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d6751cbb87b9740963138f9593b48db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c898787dd05d6f1f1d67b7a9b97ede5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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