2024高三下·全国·专题练习
1 . 已知函数
,
.
(1)若关于
的方程
只有一个实数解,实数
的取值范围为___________ ;
(2)若当
时,不等式
恒成立,求实数
的取值范围为_________ ;
(3)函数
在区间
上的最大值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f496911266e86ff15d128b01657838cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38b8ee0eda4e045c51b2fb6518dc7457.png)
(1)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e48d083295a18dbf2ba261145bd37fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43920f5171ed31db2520ef00e4c5fc24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fe958fdf039b2e2c47d685b7b5bb0ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ead3fdcb8fe8f5eb3dbe7d96cabc28b.png)
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名校
解题方法
2 . 在现实生活中,一个符合实际的函数模型经常是将不同的函数组合得到的,如听音乐家演奏音乐时,我们听到的声音常常就是多种不同乐器产生的声波叠加的结果.在学习了向量和三角函数后,人大附中某研学小组利用所学知识研究若干振幅相同,同频同向的简谐波叠加后,得到新的简谐波的振幅和初相规律,该小组把
(N为正整数)叠加,研究
中的
和
,其中
.
(1)当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46626b75bd7bc420bf32b66e3253b40b.png)
______ .
(2)当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46626b75bd7bc420bf32b66e3253b40b.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2073aefa188a89d515b9d32de5d89c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e289d2f03b9a42c8f61858f1c3b32e1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d52d236ed8d14f8135a0a63d41a351fe.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb55d413f1ab722e17747c8e99f6c59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46626b75bd7bc420bf32b66e3253b40b.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/722068b39032dd59c01afdba985d65be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46626b75bd7bc420bf32b66e3253b40b.png)
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3 . 已知抛物线
交x轴于
,
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/c9bfb006-0827-4b39-9b0e-0873015fee88.png?resizew=162)
(1)m的值为______ ;
(2)已知点
,
,P,Q均在抛物线上,且
,
时,均有
,则a的取值范围是______ ;
(3)有点
,抛物线交y轴于点C,过B,D作直线
交y轴于E.M为线段
上一点,当
时,则M的横坐标为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ec8e5d8786ef56d44bf535551a09f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe3c48e6f4858150888d0995a0cb8e1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b02568a2d65f35225e190b68e8a5ca4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/428c2271836a8e28ccf66dd06738c273.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/c9bfb006-0827-4b39-9b0e-0873015fee88.png?resizew=162)
(1)m的值为
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/545046110e0a7d4df4f1cfcdf4fe40ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53861973282c55a43feb1ab034a55f62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/958d4cb5c007188bda41687ee1286e47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d70d194e7bb8b86fc5db975d19192c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1acc35371a619b9ae9beb0de6e966e1.png)
(3)有点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7c198d5e7103bd6f1f1c9ee02b8b04b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99d76f8f6c9f0432958ff23ea87364c7.png)
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