1 . 已知函数
(
)在
上的图象有且仅有3个最高点.下面四个结论:
①
在
上的图象有且仅有3个最低点;
②
在
至多有7个零点;
③
在
单调递增;
④
的取值范围是
;
则正确的结论是______ .(填写序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8046aa421d61d05da2f197f61c79ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bccd6a6e85bdf500218a3e75b31f3c.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8ec0ccdb6db6fbaeb1172e281ec22f.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8ec0ccdb6db6fbaeb1172e281ec22f.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0145c944dd3216b95c2fe55aa2fb17f.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b53b5494acfb30338683d64d35357a.png)
则正确的结论是
您最近一年使用:0次
2 . 已知函数
的定义域为
,将
的所有零点按照由小到大的顺序排列,记为:
,……,
……,对于正整数n有如下两个命题:甲:
;乙:
恒成立;则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4737bb32fbf29fa5dc389194bcff353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6acbd718031a4d6a5f4cb72052fd9f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09c7c7eefaf2a3b1a60d02b789343d8f.png)
A.甲正确,乙正确 | B.甲正确,乙错误 |
C.甲错误,乙正确 | D.甲错误,乙错误 |
您最近一年使用:0次
名校
3 . 已知函数
图象的一条对称轴为直线
,函数
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3af853d2ce30483fafa59ff9583b5da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de633b2c143b9f76b29cde1c6ffce71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/038f64de2d8a5b0677f48f3b97b27f75.png)
A.将![]() ![]() ![]() |
B.方程![]() ![]() |
C.函数![]() ![]() |
D.![]() ![]() ![]() |
您最近一年使用:0次
2024-04-07更新
|
1009次组卷
|
3卷引用:湖南省衡阳市衡阳县第一中学2023-2024学年高一下学期4月期中考试数学试题
解题方法
4 . 已知
为坐标原点,对于函数
,称向量
为函数
的相伴特征向量,同时称函数
为向量
的相伴函数.
(1)设函数
,试求
的相伴特征向量
;
(2)记向量
的相伴函数为
,当
时,求
的值域;
(3)已知
为
的相伴特征向量,
,请问在
的图象上是否存在一点
,使得
.若存在,求出
点坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66655b7a6825b124ce596197bf2aa14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b84dac41f87e939f6cc39f38dc59b78d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e723e57753f0a4fe1ef8ca1aee0e2117.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36bd5affcb55e254f5f71caf7ff2304b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e723e57753f0a4fe1ef8ca1aee0e2117.png)
(2)记向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fffe91c3b3290e5eb048b0028b0a5686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54df369856047a0133a25084ec4285d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff26491b344566f7bb04cbb7deb6baa1.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ef498f2668cdf0631c68fa309d9c5bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/771f16cb4827b8c57a3f5a1d241e8c31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd151d471f492ee2f847401dc5e8900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef1428037efcc8068ecc8b4cd2279568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b929fe0f9c13dd6dfabca91a1a4aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
名校
解题方法
5 . 设函数
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee57c3926fb6270949209069db695e67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7a634bee11fbfd85b812d559bcaa239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2270403ca1b733dc6a3344ce98143b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c765e0c21437d791423d7b328a0229b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a588de02d8a8e43ac3cca2a19e41b2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a60e77043cfa243c212f9e340c5f46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dafce249be1aeee0581417db4ce841db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71a9bae2d8a81286bc6e9dceb6f9d233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-05-19更新
|
1299次组卷
|
3卷引用:辽宁省六校协作体2022-2023学年高一下学期期中考试数学试题
辽宁省六校协作体2022-2023学年高一下学期期中考试数学试题江西省九江市德安县第一中学2022-2023学年高一下学期5月期中考试数学试题(已下线)第10章 三角恒等变换 单元综合测试(难点)-《重难点题型·高分突破》(苏教版2019必修第二册)
名校
解题方法
6 . 对于函数
,
,如果存在一组常数
,
,…,
(其中k为正整数,且
)使得当x取任意值时,有
则称函数
为“k级周天函数”.
(1)判断下列函数是否是“2级周天函数”,并说明理由:①
;②
;
(2)求证:当
时,
是“3级周天函数”;
(3)设函数
,其中b,c,d是不全为0的实数且存在
,使得
,证明:存在
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851eae00e3369068e33a7e6420483883.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c7eb49a823f757461cd5260757b088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd84a8f95166367063218ee03ffd5a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f7f4cc0837a4e6dcd0072887e4e2704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efe6d9f54a34762aadfdf8e2bac977cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01d28d20e26e8b1dee2848daf6baf0ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)判断下列函数是否是“2级周天函数”,并说明理由:①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/903ce67dc4e5bfb0dee630c072664bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddc833417345710524c29cf0d8a9384d.png)
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a91b27ee76da8dcec88eba1b230bfa19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbbcdfbc54530814e37819fc7c93cc07.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e159058cf3cbdf0dd54fa0ab50b58c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df307146ad61d4bf105370f65a3e742c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf90b80e784747a72920eb34d17ddbeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ddf844e3848b8bf52c0ec506fe749c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07534f9e1dc7abca543e655e05db1e50.png)
您最近一年使用:0次
7 . 已知函数
.
(1)当
,
时,求函数
的单调增区间;
(2)当
,
时,设
,且函数
的图像关于直线
对称,将函数
的图像向右平移
个单位,得到函数
,求解不等式
;
(3)当
,
,
时,若实数m,n,p使得
对任意实数x恒成立,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/117f7de645564f5a28a1e2f3c0a33689.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657435e1fda84118e7f63c97505c8b75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a783088120d67cc98936081e80fb7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9998f27aca8e31ba479b96858b509c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c6cb0cc172657611e286e7fa669584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e915b67f8f747698b8b46d37bc453667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5de89467e97506fbd3f79833900c203.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a783088120d67cc98936081e80fb7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90de59980f26e4456ff705ca6842400b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b2ea0a0cae3148268b0e977b27ff824.png)
您最近一年使用:0次
名校
解题方法
8 . 十字测天仪广泛应用于欧洲中世纪晚期的航海领域,主要用于测量太阳等星体的方位,便于船员确定位置.如图1所示,十字测天仪由杆AB和横档CD构成,并且E是CD的中点,横档与杆垂直并且可在杆上滑动.十字测天仪的使用方法如下:如图2,手持十字测天仪,使得眼睛可以从A点观察.滑动横档CD使得A,C在同一水平面上,并且眼睛恰好能观察到太阳,此时视线恰好经过点D,DE的影子恰好是AE.然后,通过测量AE的长度,可计算出视线和水平面的夹角
(称为太阳高度角),最后通过查阅地图来确定船员所在的位置.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/2/f340736c-a23f-4b3e-a3ef-710244b4e922.png?resizew=359)
(1)若在某次测量中,横档
的长度为20,测得太阳高度角
,求影子AE的长;
(2)若在另一次测量中,
,横档
的长度为20,求太阳高度角的正弦值;
(3)在杆AB上有两点
,
满足
.当横档CD的中点E位于
时,记太阳高度角为
,其中
,
都是锐角.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5157b42da58d55daad27d98b2fec15ff.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/2/f340736c-a23f-4b3e-a3ef-710244b4e922.png?resizew=359)
(1)若在某次测量中,横档
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b528818e98c5c2ddf301048b4228d2.png)
(2)若在另一次测量中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af0e847821c95966efc534f26fbe4f6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(3)在杆AB上有两点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2059d1b10017e04aa35812c0354049b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cafc046509e3ca71090d8a1de862efa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943b765718479c160ba61ec5c6f8c5f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e29bf5652f0d4f764c3606efcdb445f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dadb2357b7a648d3a69c7a84dbdffcc0.png)
您最近一年使用:0次
2023-04-26更新
|
1471次组卷
|
6卷引用:四川省成都市第七中学2022-2023学年高一下学期期中考试数学试题
名校
解题方法
9 . 已知函数
的图象如图所示, 点
为
与
轴的交点, 点
分别为
的最高点和最低点, 而函数
的相邻两条对称轴之间的距离为
, 且其在
处取得最小值.
和
的值;
(2)若
,求向量
与向量
夹角的余弦值;
(3)若点P为
函数图象上的动点,当点
在
之间运动时,
恒成立,求A的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e0831ede3dd847d9ab6f919900b4d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/007817eb1a73c5a4f8b0493c4405d456.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662a33b9677e5a92e98cfd4fffcf4e3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c98a7f3a8bf384b1dfc1d34aebd46d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cab12359ab934c34ef538d26ba946001.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/241c79af2ffef371608d1b0d13442947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce61f84f16bcb280a0e7bf762255c3b4.png)
(3)若点P为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662a33b9677e5a92e98cfd4fffcf4e3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/541804a860732c41f47c087ff257c38f.png)
您最近一年使用:0次
2022-05-16更新
|
2467次组卷
|
13卷引用:湖北省宜昌市部分学校2021-2022学年高一下学期期中数学试题
湖北省宜昌市部分学校2021-2022学年高一下学期期中数学试题北京市第三十五中学2023-2024学年高一下学期期中测试数学试卷湖北省华中师范大学第一附属中学2021-2022学年高一下学期5月月考数学试题北京市海淀区教师进修学校2021-2022学年高一6月份数学月考试题广东省深圳市福田区福田中学2023届高三上学期第二次月考数学试题江苏省南通市海安高级中学2022-2023学年高一下学期阶段检测(一)数学试题重庆市第一中学校2022-2023学年高一下学期第一次月考(3月)数学试题江苏省镇江市丹阳高级中学2022-2023学年高一下学期3月月考数学试题黑龙江省哈尔滨市第六中学校2022-2023学年高一下学期4月考试数学试题湖北省武汉市部分中学2021-2022学年高一下学期5月联考数学试题湖北省襄阳市第三中学2022-2023学年高一下学期5月月考数学试题江苏省苏州市桃坞高级中学校2023-2024学年高一下学期3月自学能力测试数学试卷山东省临沂市第二中学2023-2024学年高一下学期第一次阶段性测试数学试题
10 . 已知函数
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d7328802a661ae7d90c0830db0581c.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() | D.![]() ![]() |
您最近一年使用:0次
2022-03-16更新
|
2059次组卷
|
5卷引用:浙江省杭州学军中学西溪校区2021-2022学年高二下学期4月期中数学试题
浙江省杭州学军中学西溪校区2021-2022学年高二下学期4月期中数学试题(已下线)高中数学 高二下-4湖北省八市2022届高三下学期3月联考数学试题(已下线)考点07 三角函数的图像与性质-2-(核心考点讲与练)-2023年高考数学一轮复习核心考点讲与练(新高考专用)(已下线)微考点3-1 新高考中三角函数的图像与性质应用中的九大核心考点-2