解题方法
1 . 已知函数
.
(1)若
,求实数
的值;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da3209dff6bbdde2d918e9a8451ec7bf.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05a7285dc5997e188d4ab024c29383e7.png)
您最近一年使用:0次
2 . 已知数列
的通项公式为
,
,记
.
(1)求
,
的值;
(2)是否存在实数
,使得对任意
,
恒成立?若存在,求出实数
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8acf45c78d24aa54c26c8aa1c95c0c46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee1fe089a854b729eb5178416d2bd64.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e70f9d75c7f5403b05bbd571bbc09a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
3 . 在四边形
中,
,
,
,则四边形
的对角线
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b8b98b2f83279a49e94d9f48c5e6f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/503c035fc57fb25aede1445af9aa2747.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
您最近一年使用:0次
2020-03-04更新
|
2026次组卷
|
5卷引用:2020届江西省南昌县莲塘第一中学高三上学期月考数学(理)试题
解题方法
4 . 规定:对于任意实数
,若存在数列
和实数
,使
,则称
可以表示成
进制形式,简记为:
;如:
,表示
是一个2进制形式的数,且
;
(1)已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dff740b3b15a876e6de4e1a2783bcdf.png)
,试将
表示成
进制的简记形式;
(2)若数列
满足
,
,
,
,
,求证:
;
(3)若常数
满足
且
,
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db02c520989da5adce55d84410a644b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c5827acadcb93523ae7fa25204ebcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f49fb140af76ff062c908e96e9dab466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69946ed268a024eca1cf522acee6985a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0328bf462207065c2e0eaaba1002ef1.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dff740b3b15a876e6de4e1a2783bcdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aebf62d230cbee1781de6c1d73a7ff6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c7f1ce82982b8385d78e8e77c8f1e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b6d151d3f864bae873987f6db9327a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb701fb5c95b3612e64712d836754860.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed6ef8ef7af86ebdca4f34a36989a63.png)
(3)若常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823ab696d27d40920c39b8c910789380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33e12b644318c5c276a086a82982b8dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e909ffa98363a211839d0b1338afbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137510e8bcf483cdb40a0592140a800a.png)
您最近一年使用:0次
名校
解题方法
5 . 如图,某景区内有一半圆形花圃,其直径AB为6,O是圆心,且OC⊥AB.在OC上有一座观赏亭Q,其中∠AQC=
,.计划在
上再建一座观赏亭P,记∠POB=θ
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/28/712eec87-b04e-4efc-ad55-39063ca159d4.png?resizew=161)
(1)当θ=
时,求∠OPQ的大小;
(2)当∠OPQ越大时,游客在观赏亭P处的观赏效果越佳,求游客在观赏亭P处的观赏效果最佳时,角θ的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44917f942c3fd36614f58d47b5fe1821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed41d321f4c0717ac5b443aad942d9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c243ab07091b102ee4f57a2e8de20622.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/28/712eec87-b04e-4efc-ad55-39063ca159d4.png?resizew=161)
(1)当θ=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
(2)当∠OPQ越大时,游客在观赏亭P处的观赏效果越佳,求游客在观赏亭P处的观赏效果最佳时,角θ的正弦值.
您最近一年使用:0次
2020-02-25更新
|
2613次组卷
|
7卷引用:江苏省苏锡常镇2018届高三3月教学情况调研(一)数学试题
江苏省苏锡常镇2018届高三3月教学情况调研(一)数学试题专题17 以三角函数为背景的应用题-《巅峰冲刺2020年高考之二轮专项提升》[江苏](已下线)考点24 正弦定理、余弦定理(考点专练)-备战2021年新高考数学一轮复习考点微专题广东省普宁市勤建学校2024届高三上学期第二次调研数学试题重庆市第八中学2021届高三下学期第五次模拟数学试题(已下线)专题4-4 三角函数与解三角形大题归类-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)江苏省徐州市睢宁县2021-2022学年高一下学期(线上)期中数学试题
解题方法
6 . 已知函数
,设
,其中
,方程
和方程
根的个数分别为
.
(1)求
的值;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662efab1df249abe7d6054ccd16e3d63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21420dd916b32e2cc08ab1eac348bb29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9ab7bb40f58f28c9799b20f91d15d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57a1d99e29458005cece4efb2d7349ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b3c9c43aabf2d057c539740b081f07a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65baa63a788455c2106aa8285ecb2a7d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7473709ab426b4d6e05a28d03ac97d39.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e69ddddaeda0a61e69224357cc3bbf.png)
您最近一年使用:0次
2020-02-25更新
|
606次组卷
|
3卷引用:江苏省扬州市高邮市第一中学2020-2021学年高三上学期10月测试数学试题
7 . 设
,
为正整数,一个正整数数列
满足
.对
,定义集合
.数列
中的
是集合
中元素的个数.
(1)若数列
为5,3,3,2,1,1,写出数列
;
(2)若
,
,
为公比为
的等比数列,求
;
(3)对
,定义集合
,令
是集合
中元素数的个数.求证:对
,均有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c827decbf8ca42797b3ab43562d8a834.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f59d39259c5b099998c3641814be99a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81bcfc388fc9c63e3a32c7627e40688a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0deee56cdb3d71a61f33763d350845a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be20b1d65c27647a1cd88d1657f3ae40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdc5c895153932c3e827a464664cef90.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f33d18f3387b7e1301c9b213bd218157.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0deee56cdb3d71a61f33763d350845a9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/334f8809e0f6e2a995f034b86f6c5501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/527093b2ec760913d0dccff8a099248b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0deee56cdb3d71a61f33763d350845a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/831ed34d8c6d99fdd0b94688ef03bfcb.png)
(3)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2429b6a233ef2f66677b15bc11a13294.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff36e6cade860eafd0ba3a0f960a88cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12161550d951e17f4eb3de58496cd6e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e19dd2f5dd5c782fc17b44ad2d68a450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2429b6a233ef2f66677b15bc11a13294.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b554bc1451068f8a8d7f2432ef545ff.png)
您最近一年使用:0次
2020-02-15更新
|
697次组卷
|
2卷引用:2020届北京市陈经纶学校高三上学期数学10月份月考试卷
8 . 设集合
的元素均为实数,若对任意
,存在
,
,使得
且
,则称元素个数最少的
和
为
的“孪生集”;称
的“孪生集”的“孪生集”为
的“2级孪生集”;称
的“2级孪生集”的“孪生集”为
的“3级孪生集”,依此类推……
(1)设
,直接写出集合
的“孪生集”;
(2)设元素个数为
的集合
的“孪生集”分别为
和
,若使集合
中元素个数最少且所有元素之和为2,证明:
中所有元素之和为
;
(3)若
,请直接写出
的“
级孪生集”的个数,及
所有“
级孪生集”的并集
的元素个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc020b0997a2f37b214718112b79d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2317480af8719266bb92ee59d6b2c3b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44f502064e70176f25ed0e1c29c979a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cbd9271372676f33ffe81bbd9dde52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb573197384b9410cb951a4d1e301b3c.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d72bc3ebd480e761d156ae995abc1153.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)设元素个数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.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/2e3efe261376149359971ac137d88f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c00ab72facda02139df8dadc8dbea3a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
您最近一年使用:0次
9 . 设n∈N*且n≥2,集合
(1)写出集合
中的所有元素;
(2)设(
,···,
),(
,···,
)∈
,证明“
=
”的充要条件是
=
(i=1,2,3,···,n);
(3)设集合
={
︳(
,···,
)∈
},求
中所有正数之和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/748cbeae327ab853b3d648b1e539925c.png)
(1)写出集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
(2)设(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9039d926c1f24d3a00596a405570ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c0704b318a88a83adbe29f33e3e160d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216325d35da32daa063e3e0021a44e1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8fe26774c21aa0cf4b6cdf518ba1cec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1602c6064af12eed3fd1291f8272d93c.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb237a6331d0f965c0d25e18e5bf6858.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be07753eab86fa9c439a65db51c9a9e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2020-02-15更新
|
966次组卷
|
3卷引用:2019年北京市丰台区高三(3月)模拟数学(理)
10 . 已知函数
,
(其中
为常数).
(1)如果函数
和
有相同的极值点,求
的值;
(2)当
,
恒成立,求
的取值范围;
(3)记函数
,若函数
有
个不同的零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85cab2fdee1f759d9fe9b528d4c4e4f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5553c9a5fca394bc8fad9a3435cd9dd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)如果函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc6e69ad1a27916fb5c3d5901ded134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/599b100243599b6dc57c333a829c129f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f18ebac881089041c232b1679d7d994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)记函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc2e5608a4114ff1baa102c53c60b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66973c3d1a3b832ace4d19d75df4bbc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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