名校
解题方法
1 . 高斯是德国著名的数学家,近代数学奠基者之一,享有“数学王子”的称号,他和阿基米德、牛顿并列为世界三大数学家,为了纪念他,人们把函数
(
)称为高斯函数,其中
表示不超过x的最大整数. 已知:
,(
,
)
,
,
,求
的值;
(2)若
,
,
,求证:
;
(3)设
,求S除以2023的余数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b7f26fe1977bda9de200debe99f020.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851eae00e3369068e33a7e6420483883.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f161c2a3717f1b6c62d0d7dae0b606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2382ddc29a4fec13b4d0a11deb2cfd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d290a4927c50661098e2fbea58d77b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167b43045b3297248e334c41c621b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0956ed974bee14fffcf9ada9cafe49d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/964a54ca7774d6fc04aaf8b85fda5fd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06ee581ca3282490206a8bc11dfb5ccf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81a45b5fe1fea8e19026d491596392fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f54e945ef81cf9c9d985aa6f2f72dc5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1972a6ab2655f4cb706f7dd379902a87.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03304e01039bd5039d463207d81ce65.png)
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名校
解题方法
2 . 已知函数
和
的定义域分别是A和B,若函数
和
同时满足下列两个条件:
①对任意的
,都有
或对任意的
,都有
;
②存在
,使得
.
则称
和
互为“依偎函数”,记作
,其中,
叫做“依偎点”.
(1)是否存在
有无数个“依偎点”?若存在,请举例说明;若不存在,请说明理由;
(2)若函数
,
,是否存在k,使得
如果存在,求出k的值;如果不存在,请说明理由;
(3)求证:
,其中
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
①对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a479511a50da604b2fc7398617db8387.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b4955c5adc717b7f6f0b975e0724ff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a479511a50da604b2fc7398617db8387.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43920f5171ed31db2520ef00e4c5fc24.png)
②存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18165b24e85935b2d036eb6ba4aa0125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/099adf32792e7334032a80084e0cb584.png)
则称
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a0e49c46c9fb222376736229da4e80b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(1)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a0e49c46c9fb222376736229da4e80b.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bacd6155ac43dbd8aa73d03740c24af5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914a49b0d7aedc593a3e87fbab7c31ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44f084386fd408381964398bf8c907a7.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a487acd081800a523a236a1337261e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
您最近一年使用:0次
2024-04-23更新
|
322次组卷
|
2卷引用:江苏省南京市南京师范大学附属中学2023-2024学年高二下学期期中考试数学试卷
解题方法
3 . 对于函数
,
和
,
,设
,若
,
,且
,皆有
成立,则称函数
与
“具有性质
”.
(1)判断函数
,
与
是否“具有性质
”,并说明理由;
(2)若函数
,
与
“具有性质
”,求
的取值范围;
(3)若函数
与
“具有性质
”,且函数
在区间
上存在两个零点
,
,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02059edf02fba0e7c62b7c2a48ef1184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bed7a0e7e7a3b49b4cd2e777a64e9061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a573996f5d4b27434a4491928b59f301.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28e384ba050b238e11f7c74d3002aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e450d0e48276909b7387fb576df4ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e93815f534a9ba003799aef2a53a242.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318a16f1950d06e5500c76d8f81a507f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53224898de85a85058ad336490bbbaa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49636685bca80ed0864d65d829973f8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/798548b5fbb631a0828621581a741f06.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a151adfdf0446b1ac074bca90076df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaae91ed6da60e86e3bb9b3eb7e03e60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ba0154a5c65b0b304c7e4df2e738f78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e93815f534a9ba003799aef2a53a242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb8ca1f5da558af68ebe76d985dbbe1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62b96ee0875a6bcaf9371fb9cfd7eae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04133adb6f1562d859510c9771b2e545.png)
您最近一年使用:0次
4 . 已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62559d143b4a977be9990eebcbec539e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79699156efecc21a555e63da6456031a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a551a88ac426439803f564a3bbee04a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
您最近一年使用:0次
昨日更新
|
7076次组卷
|
5卷引用:湖北省黄冈市浠水县第一中学2023-2024学年高二下学期期末质量检测数学试题
湖北省黄冈市浠水县第一中学2023-2024学年高二下学期期末质量检测数学试题2024年新课标全国Ⅰ卷数学真题(已下线)2024年高考数学真题完全解读(新高考Ⅰ卷)专题03导数及其应用(已下线)2024年新课标全国Ⅰ卷数学真题变式题16-19
名校
解题方法
5 . 拉格朗日中值定理是微积分学的基本定理之一,它与导数和函数的零点有关,其表达如下:若函数
在区间
连续,在区间
上可导,则存在
,使得
,我们将
称为函数
在
上的“中值点”.已知函数
,
,
.
(1)求
在
上的中值点的个数;
(2)若对于区间
内任意两个不相等的实数
,
,都有
成立,求实数t的取值范围.
(3)当
且
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee49cd415b686374189f90102d23ef7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdcb1944408a1f36d0123e093ea2f0ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff6838d84b68c6f0d3b93b196d9b08d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdbefd68d090abfa266cc874d4121f24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4633de9335d15d7685bdecb007a3678c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
(2)若对于区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e938b003ed30316afc6163e1f856c3c.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a369ce3949b2bd2747a48054f7b951c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa5572b8342e2c014a0cbdce7bd2dae.png)
您最近一年使用:0次
6 . 设函数
为定义在区间
上的可导函数,记
的导函数为
,若对
,都有
或
恒成立,则称
为区间
上的“原导同号函数”.
(1)证明:
为
上的“原导同号函数”;
(2)是否存在实数
,使
为
上的“原导同号函数”,若存在,求出
的取值范围;若不存在,请说明理由;
(3)若
为
上的“原导同号函数”,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1da2db85b44ae9ced8c09cd19593e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/126f7f1e8cdd38225803c6ec59968660.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22a935456da83aed9c3f485152e541f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36489856ced75bf35dea7b12c2b6bcd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14ce24da9de20311832866834d78a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6146c34c9aad4d49938e086d3b18c774.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8845c0d06613fabb0358d5392cca38b3.png)
您最近一年使用:0次
名校
7 . 已知
与
都是定义在
上的函数,若对任意
,
,当
时,都有
,则称
是
的一个“控制函数”.
(1)判断
是否为函数
的一个控制函数,并说明理由;
(2)设
的导数为
,求证:关于
的方程
在区间
上有实数解;
(3)设
,函数
是否存在控制函数?若存在,请求出
的控制函数;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7493c0fcdc634aa03efb6be277e23769.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f937c7606a3ab00e17e34b39144a0ad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23afc43a8c5b8cfe6bf2a1caed920c01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68e79a9937ad71a65a3bceca7eff82a8.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6263576e5c3f2324a8dac311476bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78c65058951db06fff9020ed2e65656e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7a9a783d62f5967e662a562211e2d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc1b193aa193153eb402df8560778e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
您最近一年使用:0次
名校
8 . 已知
与
都是定义在
上的函数,函数
图像上任意两点
,记
表示此两点连线的斜率.当
时,都有
,则称
是
的一个“T函数”.
(1)判断
是否为函数
的一个
函数,并说明理由;
(2)设
的导数为
,求证:关于
的方程
在区间
上有实数解;
(3)函数
的导函数存在记为
,即
导函数存在记为
,当
都有
,函数
是否存在T函数?若存在,请求出
的所有
函数;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3a1467ecf286e3cadaf5aa006606f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c1dc007e36c78ab98df4cd2383b4c5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3861f863fc3d8703abf9e5bf97ef6117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95a43b43650ed3473888a95607908644.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5ff3dc91272a2244b4d76056967e9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/591c5b712dc14517e369be2345526fc7.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff6838d84b68c6f0d3b93b196d9b08d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4c513ef355a637fff90a3371dc5328a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa852120429d7db38eb6266cf9d0d152.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
(3)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d98da166934830f1cfdbcd48dbfea6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2287352f6b9c1ef9e35d2ac6670fcbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e82f423c1c5d304766d1a22d72f042.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34367bca1e9f02459dc301e4881edbe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/591c5b712dc14517e369be2345526fc7.png)
您最近一年使用:0次
名校
9 . 如图,在四棱锥
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2234205f80829a5bbc6ae3a675fe4f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28155ab6f06636cae7e5a4eb07e580d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/836ac3d625647007c99532bac34a6f92.png)
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a8911f5302c0a65c1d28c0ed1c939e.png)
为
的中点.
平面
;
(2)求平面
与平面
的夹角的余弦值的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2234205f80829a5bbc6ae3a675fe4f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28155ab6f06636cae7e5a4eb07e580d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/836ac3d625647007c99532bac34a6f92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d618f2f945043c0fc4b2bb492206d4cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a8911f5302c0a65c1d28c0ed1c939e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c372d059202ec388960b125d4a87dc84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4d781525777c7b5284dffc70b2a28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
您最近一年使用:0次
名校
解题方法
10 . 帕德近似是法国数学家亨利
帕德发明的用有理多项式近似特定函数的方法.给定两个正整数
,
,函数
在
处的
阶帕德近似定义为:
,且满足:
,
,
,
,
,注:
,
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee7bb49247387a9028602315729f8d7.png)
已知函数
.
(1)求函数
在
处的
阶帕德近似
,并求
的近似数
精确到![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7e2a6b3944261bb5b2e0244d05af639.png)
(2)在(1)的条件下:
①求证:
;
②若
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c97ec04a1aa7ac6fce72d589864940a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16563cfb206d0394cac2a0c2595dda6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adcb8c6a69df1a0deaba265e204d5f99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047a8c1ed551fccee1c1848746c5f282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72029562177dfc99a171c9013eb90227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee7bb49247387a9028602315729f8d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4573475f70860a3d99b92a329d0d07f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca214aa6276b96d67a451c3fdbc59b3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cba6d8d56270fc72edd1af793542c036.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/030c5fc27fb5c07e4d6c913653af07ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f8f07548edb2d114804fbfca1eee55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee7bb49247387a9028602315729f8d7.png)
已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35dd621776dee688a0175a1abe39c258.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35dd621776dee688a0175a1abe39c258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40765d09390381658d5b4dc0160366cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9966dfe9109671c587892bd32f0b6699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5c1ae8ac7a70fcab9a5daca65ccd99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7e2a6b3944261bb5b2e0244d05af639.png)
(2)在(1)的条件下:
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec667cb20a6d670c47adfca4e4f5dd5.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dad7d4b49b53e6d1aae16e515cf0975.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2024-04-13更新
|
1072次组卷
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7卷引用:重庆市万州第二高级中学2023-2024学年高二下学期期中质量监测数学试题
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