解题方法
1 . 海水受日月的引力,在一定的时候发生涨落的现象叫潮.一般地,早潮叫潮,晚潮叫汐.由于受潮汐的影响,某港口一天中各时刻的水位高低相差很大.如图,已知该港口某天从8时至14时的水深
(单位:
)与时刻
的关系可用函数
近似刻画,其中
,
,
.据此可估计该港口当天9时的水深为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89ba73ba2a2a4744eb19b5ae33f032ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13378be06b6b01bcad1d261ff14e87cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4130bb0cb60f3e356e99d21fae8a166.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/67f5b5b7-7330-43d9-8b31-a37986f051b7.png?resizew=171)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
2 . 若函数
有最小值,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d079eb4509a31a461775601f7655d7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
3 . 函数
的图象如图所示,则
的解析式可能是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/2/8431f3e7-8f10-47db-946b-60138a445554.png?resizew=188)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/2/8431f3e7-8f10-47db-946b-60138a445554.png?resizew=188)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
4 . 已知
,函数
.
(1)当
时,求函数
的定义域;
(2)若关于
的方程
的解集中有且只有一个元素,求实数
的取值范围;
(3)设
,若
,使得函数
在区间
上的最大值与最小值的差不超过1,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c76ef2d9b6ad8530682811ada6c1e4.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a19f229fae6b755b76bdacf200c4d7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c1326beb4653dd170d1d7878e351598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf8682c07954e4ba88e5766b1e005f03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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5 . 已知函数
.
(ⅰ)函数
的定义域为______ ;
(ⅱ)若
是斜三角形的一个内角,则使不等式
成立的
的集合为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c111ae39998037ad9c2eef5a892b3e6.png)
(ⅰ)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2aeda5c6f101566159dd4c460b943b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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6 . 已知集合
或
,
,其中
.
(ⅰ)当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e60375f97ff7854f4d3a8b1108d2e3.png)
______ ;
(ⅱ)若
,则实数
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b6036b5f9fcc6f245ee1f0ff218839f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa3022e7435b36f3b4b088d0820a700.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88592a427b6845d3d4c821218b3e2171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e60375f97ff7854f4d3a8b1108d2e3.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b05d2be27e8f53e4de3071846dffb41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
7 . 已知二次函数
,
.
(1)若函数
是偶函数,求实数
的值;
(2)若
,求不等式
的解集;
(3)若函数
在区间
上具有单调性,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4bc22c9795dd0dc317cc6ab96550f9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7a1d739890a8951586e23b78b035bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0530e48690edc3429da2d23c25151296.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
8 . 2023年10月26日神舟十七号载人飞船在长征二号F遥十七运载火箭的托举下点火升空,成功进入预定轨道.我国在航天领域取得的巨大成就,得益于我国先进的运载火箭技术.根据火箭理想速度公式
,可以计算理想状态下火箭的最大速度
,其中
是喷流相对速度,
是火箭(除推进剂外)的质量,
是推进剂与火箭质量的总和,
称为总质比.已知甲型火箭喷流相对速度为
.
(ⅰ)当总质比为9时,甲型火箭的最大速度为______
;
(ⅱ)若经过材料更新和技术改进后,甲型火箭的喷流相对速度提高到原来的
倍,总质比变为原来的
.若要使火箭的最大速度至少增加
,则在材料更新和技术改进前总质比的最小值为______ .
(所有结果保留整数,参考数据:
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/801fb850c497a5e833e8c4b7c6035f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55e90016eded560b57a129f28d03aee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df0e5de30429c62a5febe61fe45ef24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebee00d8ff03814d153038706ebd7943.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7524718b9f699c26c3ff742bfc8675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/467f61f8d38c71fcb30f3f16d88650d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc73529ef6d4431646ca0bdbca09f608.png)
(ⅰ)当总质比为9时,甲型火箭的最大速度为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22964de2a093c97a8755dbe70487735e.png)
(ⅱ)若经过材料更新和技术改进后,甲型火箭的喷流相对速度提高到原来的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4836d554eed2e9b666ba934090c2bd77.png)
(所有结果保留整数,参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a50101047632b94dcd5cf8035b093cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4afc32b1084af96113b5cd239607d8ce.png)
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解题方法
9 . “
”是“
”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9ca0fc5c9300932f5fcc85af1a0745a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
A.必要不充分条件 | B.充分不必要条件 |
C.充要条件 | D.既不充分也不必要条件 |
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10 . 已知
,
,则用
,
表示![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40da37f9dc8f3e3b5790e9d67da1be15.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a08a2a5540efcdb5a77aa4ea3049884.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/850df3e299d9b1ecbda7e3a59e2a255e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40da37f9dc8f3e3b5790e9d67da1be15.png)
您最近一年使用:0次