名校
1 . 已知函数
,其中
.
(1)判断
的奇偶性(直接写出结论,不必说明理由);
(2)当
时,比较
与
的大小;
(3)若函数
有三个零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27cfd4498a1cc658b943061497345f5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57e23b3e7a3bae640c314bc9347ff67f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/123d2a9d1c04f94c4219ad15f6d6fdd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2 . 设a,b为正整数,且
是函数
的一个零点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92682840e2a230de346562b2032f8adb.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d0ac5e4a6ef4f217b2ffb08aea29489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/579a761c1d6caec68e40f196a9ce633e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92682840e2a230de346562b2032f8adb.png)
您最近一年使用:0次
解题方法
3 . 已知
是定义在
上且不恒为零的函数,对于任意实数
满足
,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d6aa5b51b3ff1469ee7a334543b6616.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66f16fcb06e100b7194a60852e151b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7558ff6e9d8b18314583dab83805bfb.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-12-05更新
|
764次组卷
|
2卷引用:广东省汕头市潮阳区棉城中学2023-2024学年高二上学期数学竞赛试题
名校
解题方法
4 . 在数学中,双曲函数是与三角函数类似的函数,最基本的双曲函数是双曲正弦函数与双曲余弦函数,其中双曲正弦函数:
,双曲余弦函数:
.(e是自然对数的底数,
).
(1)计算
的值;
(2)类比两角和的余弦公式,写出两角和的双曲余弦公式:
______,并加以证明;
(3)若对任意
,关于
的方程
有解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3321510a9eb73909a36c084a8630e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0099b9b80ed478824fa95677ebe9d5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11204e2fb6e560bf7a4ca26eaebfc526.png)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e694af0c9f990ecb8b54b1c08bcc578e.png)
(2)类比两角和的余弦公式,写出两角和的双曲余弦公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d92c32edc0e000405b7a6b9c48549959.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f78f05631a2ecb8bc3d379ca6c81f93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed807cc52eca7b462a3850b5e5e02b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-06-21更新
|
1013次组卷
|
8卷引用:山东省济南市山东师大附中2022-2023学年高一下学期数学竞赛选拔(初赛)试题
山东省济南市山东师大附中2022-2023学年高一下学期数学竞赛选拔(初赛)试题上海市宝山区2022-2023学年高一下学期期末数学试题(已下线)模块六 专题5 全真拔高模拟1(已下线)专题14 三角函数的图象与性质压轴题-【常考压轴题】(已下线)第10章 三角恒等变换单元综合能力测试卷-【帮课堂】(苏教版2019必修第二册)上海市闵行(文琦)中学2023-2024学年高一下学期3月月考数学试卷(已下线)专题06 期末解答压轴题-《期末真题分类汇编》(上海专用)上海市市西中学2023-2024学年高一下学期期末复习数学试卷
名校
5 . 已知三次函数
,且
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db966991f5c33aaed168f3c1424612c2.png)
__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa8b68e7afd95e024c29b908e9c8c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/509a0c0790dcf553abd63eb5c1658c39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6763b4c6f48b7962142218b8ea047b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c82634f3457b8dc8cd49544cfc48ad7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db966991f5c33aaed168f3c1424612c2.png)
您最近一年使用:0次
2022-10-27更新
|
843次组卷
|
3卷引用:河南省驻马店市确山县第一高级中学2022-2023学年高二上学期数学竞赛试题
6 . 已知函数
,
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef9183df9b3f276abc8a9b279ea35dc7.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce020353e4314fe1e1cfe2d84b91221.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41695a4b39b662183ebc8092c06bf034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b75b95500ecdd45377847255bcd5302.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d661ea1afb474d15f37b8a2378d764ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef9183df9b3f276abc8a9b279ea35dc7.png)
您最近一年使用:0次
7 . 已知函数
,满足:(ⅰ)对任意
,都有
;(ⅱ)对任意
都有
.则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d568f65771bdbbf9b5d6a4188546f92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/772c871658656926de9754ec28490155.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/958c91e0cc2cf4f17acb778de21846b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c199c596534dd80309fc1caf4c96b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ab37b80e606f9cbe65e3ec07fafe50.png)
A.54 | B.66 | C.81 | D.89 |
您最近一年使用:0次