名校
1 . 已知
,则
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b951adb0efff962d44cf1075074706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9155b2f084a37d04703e2013b5813dc2.png)
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解题方法
2 . 定义区间
的长度为
,记函数
(其中
)的定义域
的长度为
,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31f158b30f049b709eab54a643c927bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/628560d39eeb0339fa00c9c15ab2c095.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71e45152c03cceffc5a0bfe22c0810d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e8a2c59e26d3a7305ac3b4b21803947.png)
A.![]() |
B.![]() ![]() |
C.![]() ![]() |
D.给定常数![]() ![]() ![]() ![]() |
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3 . 定义:双曲余弦函数
,双曲正弦函数
.
(1)求函数
的最小值;
(2)若函数
在
上的最小值为
,求正实数
的值;
(3)求证:对任意实数
,关于
的方程
总有实根.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f64d8edcac9fb4dc0cdc8c952596b722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f45428262907786c0f71f8233820ce2.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33c7df0ad98bbe77abb2c33ca85ea0a3.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e236b7c4a6651b7b88ae885b9ad3dddb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7da3a6d011679952771607b3a166676b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)求证:对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7f258ec6fed321bb9be780189249e6f.png)
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4 . 已知
,则
的值可以是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f0e9c04402a0ffdaa25c3e3c82c7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9929b4a95df4cb001be158a1600ae5e4.png)
A.4 | B.10 | C.![]() | D.3 |
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5 . 已知抛物线
与双曲线
的交点A的横坐标是1,则关于x的不等式
的解是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b629bea8e22de9bfc49158e2289871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07854693dd2e33f66030d6106eb6e0ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0bce5d244c8c4e504d66b27ce047a49.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/10/005a7ba9-231c-4b35-8c3b-0ca01debbcaa.png?resizew=154)
A.![]() ![]() | B.![]() |
C.![]() ![]() | D.![]() |
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6 . 如图1,抛物线
与x轴交于
,
两点.
(1)求该抛物线的解析式;
(2)设(1)中的抛物线交y轴于C点,在该抛物线的对称轴上是否存在点Q,使得
的周长最小?若存在,求出Q点的坐标;若不存在,请说明理由;
(3)如图2,在(1)中抛物线的第二象限部分是否存在一点P,使
的面积最大?若存在,求出点P的坐标及
的面积最大值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d88bbd34102b55fa928e8ff83f0d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8748dc55e2f45bc37fc4d84d7310f79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8314b1fdf7dcef270ac0a2567609242.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/21/23a1086c-0ebf-4918-9683-ec2ed38eaf7e.png?resizew=270)
(1)求该抛物线的解析式;
(2)设(1)中的抛物线交y轴于C点,在该抛物线的对称轴上是否存在点Q,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82bc4b926b29e58400df99ebf5771404.png)
(3)如图2,在(1)中抛物线的第二象限部分是否存在一点P,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f409b28f7cb97726646e79709ad25190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f409b28f7cb97726646e79709ad25190.png)
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7 . 在实数范围内定义一种运算“*”,其运算法则为
.根据这个法则,下列结论中正确的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44c3882335c9c93aacd2639b94f6023e.png)
A.![]() |
B.若![]() ![]() |
C.方程![]() ![]() ![]() |
D.若m,n是实数,则![]() |
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8 . 给出下列等式,其中因式分解正确的是( )
A.![]() | B.![]() |
C.![]() | D.![]() |
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9 . 在平面直角坐标系
中,对于点
和
,给出如下的定义:点
的横坐标差的绝对值和它们的纵坐标差的绝对值中较小的一个(若它们相等,则取其中任意一个)称为
两点的“近距”,记为
.即:若
,则
;若
,则
.
(1)请你直接写出
,
的“近距”
______﹔
(2)在条件(1)下,将线段
向右平移
个单位至线段
,其中点
分别对应点
.若在坐标轴上存在点
,使
,请求出点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bec550c01b4f075f22ab67f5e55ed5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee07c1f2f7b417036b79f165d4fe24c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/974f7120f0e29e71f4d918617456c1c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32286c3865f06865920816e7685c497a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b720248e85a39e7ecb4c9baf286e9ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7311691ce4a43c2b6ad1b656801d9c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/586c449d81bee2a8683a3cafef1d6c06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7b0182a19d683019a9153294fb7f8e9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/7/520b1b4b-f36b-499f-8760-9ac541aa8d12.png?resizew=223)
(1)请你直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a18a7caa080988802ba1145b4fe4203.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e9f2b482e8a8e0e1b5c720a3574af70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5267ff7ce5aa65879b770aa1990c0a7.png)
(2)在条件(1)下,将线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/921f77b35fefb43c706dc387ea23c5f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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10 . 如图,数轴上点
表示的数为
,化简![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e701c3c705089fa9a18b60d300bf6ad5.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e701c3c705089fa9a18b60d300bf6ad5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/9/dc906b4f-8e7b-4f0c-b9a8-5bc3cd70a6d2.png?resizew=176)
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