1 . 设
是给定的正整数.对于数列
,
,…,
,令集合
.
(1)对于数列
,
,
,直接写出集合
;(用列举法表示)
(2)设常数
.若
,
,…,
是以
为首项,
为公差的等差数列,求证:集合
的元素个数为
;
(3)若
,
,…,
是等比数列,且
,公比
.求集合
的元素个数,并求集合
中所有元素之和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8715a3f984d2627afd7c40c61347b7cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80ea510c81ac4540b401e4ddaf75bdd4.png)
(1)对于数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(2)设常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ce64685821c3e55c07f151996ca8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627a57cd9fdb1f586f35d9825b6bcc0b.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d9b6c86435e0ceff94d8ad1cd03737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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2 . 设
,
.已知函数
的图像关于直线
成轴对称.
(1)求函数
的表达式;
(2)若
,且
为锐角,求
;
(3)设
,
.若函数
在区间
上恰有奇数个零点,求
的值以及零点的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a3fa587a9b2e1c9fe82750db0ec22fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1032f84bd8fe83f23a9dae6919c8ab5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec25b105130d71d3d529524671b6218.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2331c755ff3034217ea3d9f45b25f62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3728ff1d39b6603a7a058cd603a6e1fe.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a34d6f60032718820c3da2b07786b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b239212220b63455456f53831c97e38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e693dfd7263845592f49f5f6f3bedb1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
3 . 在
中,角
、
、
的对边分别为
、
、
.若
是
、
的等比中项,则角
的最大值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b1936b35d7998bbae3f299c4e42fb76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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4 . 已知函数
,
,
,若函数
的所有零点依次记为
,且
,
若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/024ae20c7e4202c32f8af3e55bedcaa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4320d335ff4b89ae76aebcad1665715.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745b580e4b155ff4f931fbaa7fde55f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8787195c89953c9a25db95c41a4bd9d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0494c6d226729dd902a2940ab7228fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efe4aaa53a7a9a582b9c68bc2c06ec28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b14c78bbc6e3142533110098ef498d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9126123e86bfb5eda20aeb025875f099.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
5 . 已知函数
,其中
.
(1)若
,求
的值;
(2)若
,函数
图像向右平移
个单位,得到函数
的图像,
是
的一个零点,若函数
在
且
上恰好有4个零点,求
的最小值;
(3)令
,对任意实数
,当
时,有
成立.将函数
的图像向左平移
个单位得到函数
,已知函数
的最大值为10,求满足条件的
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46bd76719285e060ec49ec0f50697d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b6a03bf07751c3d6f2fd26c3c20c67a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83f95e85ce6707ff4161cc675665c557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9895bf4192f5c55c16f8270d53c49b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/325d003b77e1fcd87643ccf44b27edcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03735bb51c68d7c57fdefd724efc12ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dec619e74bfe8fb0e661e16e70a4f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433691481d2e5a7a5fb8653221ac7943.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda96c08c50e3495200bb200175732e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74eb7b0102cd1255713df18ecc7d171a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1143be2991e07bdc61d453c4cfc71e45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abe84f65c9c4345ae5ddcdafa89e7273.png)
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6 . 设
是正实数,将函数
的图象绕坐标原点逆时针方向旋转角
,得到的曲线仍然是某个函数的图象,则
的最大值______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b37b9e50c0f74b76d478a98f137f84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92806cb5030be634088dd5a18588a14f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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解题方法
7 . (1)已知P是直线
上一点,
(
为实数,且
),点
的坐标分别为
,求点P的坐标
.
(2)已知平面上三点A、B、C的坐标分别是
,小明在点B处休憩,有只机器狗沿着
所在直线来回跑动.当机器狗在什么位置时,离小明最近?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a949c00526fddf435423272cf10f25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b5bb87687b19fbc48be9068db60da7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c87f4c40e50504adaface510404dbfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594fa9a4bce1ed5fd27e4cb55d63cf0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf8be368791da55817b64a14a89fcf24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0203b006524305c3d8ee0b6c34cd872b.png)
(2)已知平面上三点A、B、C的坐标分别是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de9c2a68bb128cdd92cdd103b0fedc03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
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8 . 已知函数
,将
图像上所有点的横坐标伸长到原来的2倍,而纵坐标保持不变,得到函数
的部分图像如图所示,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9448bf1d6136b3a108e7ea60506ad39.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8b2e285758984e8613fa1b52d674c8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2faa63899873813748f6a28b8a92e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a6460400186f2b74ece79c861ceb063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9448bf1d6136b3a108e7ea60506ad39.png)
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9 . 已知平面非零向量
的模均为
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799ad95449b4135dee2890ac31c43706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc983f1bad03411ae64d84ff7bdf2551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a16710403d8a87b858d92647ebaa1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
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解题方法
10 . 在
中,角
的对边分别为
,已知
且
,则下列结论正确的是( )
![](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/6de1d395e6c48c0676a1488a299479d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31f29690b1da5f72f9aa34de977aab55.png)
A.![]() | B.![]() ![]() |
C.![]() | D.若![]() ![]() ![]() ![]() |
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