名校
1 . 如图,是一座“双塔钢结构自锚式悬索桥”,悬索的形状是平面几何中的悬链线,悬链线方程为
(c为参数,
),当
时,该方程就是双曲余弦函数
类似的有双曲正弦函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b383983da73f97c0ec7922556b84c49.png)
和
的值;
(2)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70dfa06870da52663bbb4c7e18217dd9.png)
(3)
不等式
恒成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ad2f5a11d7437f506adab0996961269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594663e98b797cdc4efbd098cc15854f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d712038d937090679d0e8cee56b47a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b383983da73f97c0ec7922556b84c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7b3d6bb49565cf01620a0259431d7ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1272e4f338038b3b9468cb9ecc06fe26.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70dfa06870da52663bbb4c7e18217dd9.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8d489d153159fcf945322bf0c6761a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3120403a25e9fc836f06a7781d23c6ec.png)
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2 . 已知函数
.
(1)若
,求
在区间
上的最大值和最小值;
(2)若
在
上恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e569275b72bb0ccd25959dea844035f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e354f44c5841806fdc363073abdd052.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58196b9e63ec00aa1119052b6de6ae12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825094a0d5c41dcb90880b3a5f27e435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
3 . 设
,若在区间
上,关于x的不等式
有意义且能恒成立,则t的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51159984b2cb00f30b3986315019623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4359d13ea0544aeaa81a79d83fcf758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ca382d448a37942c3ee536525da6abc.png)
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4 . 已知函数
.
(1)若
,求
的取值范围;
(2)若
有两个不相等的实根
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
①求
的取值范围;
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bfe72da09a3c70855e5481e5c8eaf80.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a1b101171cf52faf2e3e53d6725aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a18ca67c2770b98f36dbfd802595a95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd25b0aac17082018e89b67803cd6a1.png)
您最近一年使用:0次
2024·全国·模拟预测
解题方法
5 . 设函数
,若
在
上恒成立,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93fb291a6a262747af8fa821e19ea91d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2edd8edcb21bd41584daf9bb95a5c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
6 . 固定项链的两端,在重力的作用下项链所形成的曲线是悬链线,1691年,莱布尼茨等得出“悬链线”方程
,其中
为参数.当
时,就是双曲余弦函数
,类似的我们可以定义双曲正弦函数
.它们与正、余弦函数有许多类似的性质.
(1)求证:
;
(2)对
,不等式
恒成立,求实数
的取值范围;
(3)若
,试比较
与
的大小关系,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08144630f70f5bba0c73252569d97841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d848439a448faa1d4cd9fa20ca206215.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe0a24e9c7616bf8afac5a0ffb0aa1fb.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bdd3fb4f930b309f261929ba7a1f055.png)
(2)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe9f3099ed9429dc5b4e38a350e524a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24464f0ea26038d85cc22a1786257605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a83c8948a168ff2c567aee048cabff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a2cebaab3423dfb2f2c944dfc43df8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb966b7b2dd6581640bcee2d97dacf77.png)
您最近一年使用:0次
名校
解题方法
7 . 已知定义在
上的偶函数
和奇函数
满足
,且
在
上恒成立,则实数
的取值范围为__________ .
![](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/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df412ae6aa217d7eaa8dd3b88faa9b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f8d3b07eda359f229378c4597ccedb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
8 . 已知函数
定义域为
.
(1)求
的取值范围;
(2)当
时,函数
的图象始终在函数
的图象上方,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/703c5f5f5316f7e3461550262b057275.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f1a939f4c755490d52484c7fcaf98b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80b5e9031206ff27e2c7fd41593601ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
9 . 已知函数
,
.
(1)若
的最小值为
,求实数
的值;
(2)当
时,若
,
,都有
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37d731c58d6aae3a7feff8fdb8b94d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf95eab8ecee97f99978e83b0c8f0d19.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/703c71e301b4bdaef96da0c9769adbe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287e397fd53dc63328299a520281facc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6cd6de7210a634d1a083ca941c741ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2024-02-17更新
|
708次组卷
|
5卷引用:福建省三明市2023-2024学年高一上学期期末质量检测数学试题
福建省三明市2023-2024学年高一上学期期末质量检测数学试题广西南宁市第二中学2023-2024学年高一下学期开学考试数学试卷湖北省宜荆荆随恩重点高中教研协作体2023-2024学年高一下学期3月联考数学试卷B卷重庆市璧山来凤中学校2023-2024学年高一下学期3月月考数学试题(已下线)专题02三角函数的图像与性质期末10种常考题型归类-《期末真题分类汇编》(人教B版2019必修第三册)
名校
10 . 定义在
上的奇函数,当
时,
,其中
,且
,其中
是自然对数的底,
.
(1)求
的值;
(2)当
时,求函数
的解析式;
(3)若存在
,满足
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7da3a6d011679952771607b3a166676b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/401fac6e7c32d142a86a7afa828e4b2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/810949b76573ccd9d43af3815299d443.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57d57d6918060460b61f4b3448bb03a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dcd143a57a268a5a8ef486e2a4d5c0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e0cc202753558c28d925d782b27198a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(3)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79cc799ccaa3e4c85094780b520a68cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3caba8eddb5dbb5940db14f837f39450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f21117c3a658c09a019b47e492fbe3.png)
您最近一年使用:0次
2024-01-22更新
|
158次组卷
|
2卷引用:广东省广州市天河区2023-2024学年高一上学期期末考试数学试卷