名校
解题方法
1 . 已知函数
(
且
)的图象过点
.
(1)若
,求
的定义域并判断其奇偶性;
(2)解关于x的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a04546d92fd165fc1ad2cc82c2dbb25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e0d8b8e3f765d602f579b5d0730ba7e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62508b473e2104cc9536447ac9c03396.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)解关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b1acb50156198ce922576b86e83f9e8.png)
您最近一年使用:0次
名校
解题方法
2 . 为了求一个棱长为
的正四面体的体积,某同学设计如下解法.
解:构造一个棱长为1的正方体,如图1:则四面体
为棱长是
的正四面体,且有
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/16/6db5d8bf-a942-4eb1-b74e-0d41be5b6734.png?resizew=583)
(1)类似此解法,如图2,一个相对棱长都相等的四面体,其三组棱长分别为
,
,
,求此四面体的体积;
(2)对棱分别相等的四面体
中,
,
,
.求证:这个四面体的四个面都是锐角三角形;
(3)有4条长为2的线段和2条长为
的线段,用这6条线段作为棱且长度为
的线段不相邻,构成一个三棱锥,问
为何值时,构成三棱锥体积最大,最大值为多少?
[参考公式:三元均值不等式
及变形
,当且仅当
时取得等号]
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
解:构造一个棱长为1的正方体,如图1:则四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68ac02c2f91cadb1e328bc6ab9b9c491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6f878ffcff2ca25a434cbeea7d5c841.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/16/6db5d8bf-a942-4eb1-b74e-0d41be5b6734.png?resizew=583)
(1)类似此解法,如图2,一个相对棱长都相等的四面体,其三组棱长分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50690dab38f4512eb72e18b7f86cf6f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4056761b8f826eeb6ad8c9a151d3c9c.png)
(2)对棱分别相等的四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c220eadc312101e2fb89dfe920f7b30d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de966c316db1013defc56372fcf814e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d2530e7023b2345c651e8f53629ff1.png)
(3)有4条长为2的线段和2条长为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
[参考公式:三元均值不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ffb6b373d2e672bb2afc8de547861a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4849ff71159df2bb9099b26065d81e1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44acc0ee22dc4b7750e8be825e7c1355.png)
您最近一年使用:0次
2021-07-15更新
|
814次组卷
|
2卷引用:重庆市西南大学附属中学2020-2021学年高一下学期期末数学试题
名校
3 . 已知函数
.
(1)当
时,求关于
的不等式
的解集;
(2)关于
的方程
的解集中恰有一个元素,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab5c53352f3eafd25b5dbf4ee5bbbd6.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b61adc4745f283e4072ddd762f92ffe.png)
(2)关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcabfd34bc2f6ae5f0ca547aa2a8f043.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2019-12-16更新
|
246次组卷
|
2卷引用:重庆市西南大学附中2018-2019学年高一上学期期末数学试题
名校
解题方法
4 . 已知正实数a满足不等式
.
(1)解关于x的不等式
.
(2)若函数
在区间
上有最大值
,求实数a的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a21b21b1f5616546b8ba08fd43bce26.png)
(1)解关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2503d595c99ad629ab6a7cd4f331316a.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e709a77c478f99fd629ca781784c1c26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
您最近一年使用:0次
2020-02-15更新
|
362次组卷
|
3卷引用:重庆市西南大学附属中学2019-2020学年高一上学期期末数学试题
解题方法
5 . 函数
(
为自然对数的底数).
(1)若
,求
;
(2)若关于
的方程
有三个不相等的实数解
.求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ceff26a3c71729b5da2edffbd3a8767.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b4bf4b8f5797abd8e8a0950ec647604.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6af5c76ec9d1f28ff48b91adfa279f9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/894e50c6e3243ed66ab2d08f3b20ba92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8893a79d3bcd230b7f7eb02a6e0664dc.png)
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