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
(
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
.
______.(用
,
表示)
(2)
,不等式
恒成立,求实数
的取值范围;
(3)设
,证明:
有唯一的正零点
,并比较
和
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98be08efebc64ff0fbc8d0ef819b0290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.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/2705e42f28cd5e415655cb1fbecf728b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bd6153986cc8b26dd0e58cf92abc00e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/740eb38441fe1cc663275e9f84bacb26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/515599523e72afd87bb9f2929425f35c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ff0b4309f7e59ab9c65410bdee9485.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c745eb108da3e42138a93d1ce780317f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a197403d3d4d35f97c483db6a95a1db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a4ba376c9dfa67cc027d683476368f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a858b8c19d4627c256c8fd524051221a.png)
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解题方法
2 . 已知
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/027ae44ac7aab22863610036c016bb65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28b495cee32b2debec62a621185f91e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19a3fccbc87e08e94a90695a848c0902.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 已知函数
(
是自然对数的底数),则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c715d433b58fea1e74049279cbbd17f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a82d68ed3c2ae422e6b0a312f0bf5523.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
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4 . 已知函数
,
.下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af865aabfaa584ce3e7b2abad78d7e9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a88294f9b8f086fc2ff31f5347a4afa0.png)
A.![]() |
B.![]() ![]() |
C.对任意![]() ![]() |
D.对任意![]() ![]() |
您最近一年使用:0次
2024-04-29更新
|
743次组卷
|
4卷引用:浙江省绍兴市第一中学2024届高三下学期5月模拟数学试题
名校
5 . 设全集为
,定义域为
的函数
是关于x的函数“函数组”,当n取
中不同的数值时可以得到不同的函数.例如:定义域为
的函数
,当
时,有
若存在非空集合
满足当且仅当
时,函数
在
上存在零点,则称
是
上的“跳跃函数”.
(1)设
,若函数
是
上的“跳跃函数”,求集合
;
(2)设
,若不存在集合
使
为
上的“跳跃函数”,求所有满足条件的集合
的并集;
(3)设
,
为
上的“跳跃函数”,
.已知
,且对任意正整数n,均有
.
(i)证明:
;
(ii)求实数
的最大值,使得对于任意
,均有
的零点
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b4f24969673c863b5aff4fb6751ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2425552313d50a253bfb3cb4e9974ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b4f24969673c863b5aff4fb6751ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5182856db60fa5cfda34c97b5748197a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02670179163cffe5070d209066b7aa12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d18ae300954e363c2637120f4f3ef82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45020afb5156159ad42add5537797ee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b05f8bcb38a5c47e2e8fe9889717fc88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2e77ed55488688257efc354fad8875c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c853fd24a33bd11fbf2d5dba50806d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00108abe0b3ee27e7549f6cc0d86c36f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b4f24969673c863b5aff4fb6751ce.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02670179163cffe5070d209066b7aa12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3946552f0f9f048a916879402e4d315a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47efc68941a3be03f5bebbabfbe388fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e94f0ab8e7418164e0c7481150e6b5.png)
(i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d80a81e375bf3c3bdc3603ef7a2a37.png)
(ii)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b05f8bcb38a5c47e2e8fe9889717fc88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9fbab6e1a7963d26e1265e1686cba40.png)
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解题方法
6 . 已知
,
,
则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da40791c8490a6a0012389c1cb5b7a81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cf88c0b30fda73aeebc05758ab28d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770e1b508165df25802f9c63ddc51ac9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
7 . 函数
,有
且
,则下列选项成立的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e863ea4f1e8af63d06ad88a235a48f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e14206c7d228a7c2259a7b27da8813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff39b4890d0c471065f7e6348301ab27.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 在平面直角坐标系中,如果将函数
的图象绕坐标原点逆时针旋转
(
为弧度)后,所得曲线仍然是某个函数的图象,则称
为“
旋转函数”,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e623b581b1ced2534a478748bd03816e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
A.![]() ![]() ![]() |
B.若函数![]() ![]() ![]() |
C.若函数![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
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解题方法
9 . 二次函数
的最大值为
,且满足
,
,函数
.
(1)求函数
的解析式;
(2)若存在
,使得
,且
的所有零点构成的集合为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f9fe3333dcebb2427d3e9952c688c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/733b65d6c53f97ec82aace63f45f9203.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e524ced0b845fbe86ae37ae621148799.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28bb47982e7ef47c982071a70ffa60d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/099adf32792e7334032a80084e0cb584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/138472ac217ce3f838b18ce39b39b869.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf8b4eaba49a70bc86fc37ff869b2d05.png)
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解题方法
10 . 已知函数
为奇函数.
(1)求a的值;
(2)设函数
,
i.证明:
有且只有一个零点;
ii.记函数
的零点为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9b073296a8d31514d8b394331df70c2.png)
(1)求a的值;
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6625dd55e79c5115e6e7299cb83600.png)
i.证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2faa63899873813748f6a28b8a92e9.png)
ii.记函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2faa63899873813748f6a28b8a92e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be0b46f954f3590a00fe5a074e8e931b.png)
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2024-02-23更新
|
584次组卷
|
3卷引用:浙江省温州市浙南名校联盟2023-2024学年高一下学期寒假返校联考数学试题
浙江省温州市浙南名校联盟2023-2024学年高一下学期寒假返校联考数学试题(已下线)浙江省宁波市鄞州中学2023-2024学年高二下学期期中考试数学试题广东省广州市铁一中学2023-2024学年高一下学期3月月考数学试题