1 . 给出以下两个数学运算(符号)定义:
①若函数
,则
,其中
称为函数
的
次迭代.如:
.
②对于正整数
,若
被
除得的余数为
,则称
同余于
,记为
.如:
.
(1)若函数
,求
;
(2)设
是一个给定的正整数,函数
记集合
.
①证明:当
时,
;
②求
并猜想
.
①若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac36cc9de2d52fa81b310df3c137559f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbc5dcd0b5d4e94cb92e52ca31f0cfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b956f95d6cdcded732751d6d74c14cab.png)
②对于正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0ace40e2e209924905e48bf00df631f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8b539bc9386988afc25da70e13ae899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/706057125d5d481d23b0319e10e2d936.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e08e564833f8450a876460a6db43dad1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e91f1470cecf7c4da36644e5244775bf.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b44a1741d645756e39740a0818412e75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/208bd4b35f6be79500cdf5d8e433e449.png)
①证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b94f6525788e512dbc8121c49b46bc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/502416314c8c26f8442e639ea6a5db13.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
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解题方法
2 . 定义:函数
满足对于任意不同的
,都有
,则称
为
上的“
类函数”.
(1)若
,判断
是否为
上的“2类函数”;
(2)若
为
上的“3类函数”,求实数a的取值范围;
(3)若
为
上的“2类函数”,且
,证明:
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d6fe21d6ed78bfc1d2b9cc41a766c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2a699f43d6836c18eaced5758a37a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6ece875296333d786d8a671b2749255.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2ec965488c7e1cea085463c7731285.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93ed0f3a123e0e3b1c08db887fa1697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47e734b17201fe992be7775714e9558.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9210e75c35fb455d0446eb7ddba7d79c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2db4bd08a64c7ceefac83e2fce50b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/673207f6b77b8192d25463d071737b7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ea6e1bfbda5c4f6421ed18e802aba04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b1ab2e5e3dd3a1c768a88eb182b44d9.png)
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2024-06-04更新
|
378次组卷
|
2卷引用:重庆市求精中学校2023-2024学年高二下学期第二阶段考试数学试题
名校
3 . 阅读材料一:“装错信封问题”是由数学家约翰·伯努利(Johann Bernoulli,1667~1748)的儿子丹尼尔·伯努利提出来的,大意如下:一个人写了
封不同的信及相应的
个不同的信封,他把这
封信都装错了信封,问都装错信封的这一情况有多少种?后来瑞士数学家欧拉(Leonhard Euler,1707~1783)给出了解答:记都装错
封信的情况为
种,可以用全排列
减去有装正确的情况种数,结合容斥原理可得公式:
,其中
.
阅读材料二:英国数学家泰勒发现的泰勒公式有如下特殊形式:当
在
处
阶可导,则有:
,注
表示
的
阶导数,该公式也称麦克劳林公式.阅读以上材料后请完成以下问题:
(1)求出
的值;
(2)估算
的大小(保留小数点后2位),并给出用
和
表示
的估计公式;
(3)求证:
,其中
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66d4e8502106802f1485c3b0f28f2664.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a8412f5256b2b370e421c07f18cc732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4403d632f9a81e52c6cd135c6834bc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
阅读材料二:英国数学家泰勒发现的泰勒公式有如下特殊形式:当
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ce152ca98ac7e21237e00667f005b62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35993bd1db970330494665d925c0be7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/395c6efaa63dcd4ee513323d51c6a7eb.png)
(2)估算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2598975ac1edb754817eada15b9a473e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66d4e8502106802f1485c3b0f28f2664.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca08ded0d1136421f0a81517f5c2fc9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
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解题方法
4 . T性质是一类重要的函数性质,具有T性质的函数被称为T函数,它可以从不同角度定义与研究.人们探究发现,当
的图像是一条连续不断的曲线时,下列两个关于T函数的定义是等价关系.
定义一:若
为区间
上的可导函数,且
为区间
上的增函数,则称
为区间
上的T函数.
定义二:若对
,
,都有
恒成立,则称
为区间
上的T函数.请根据上述材料,解决下列问题:
(1)已知函数
.
①判断
是否为
上的T函数,并说明理由;
②若
且
,求
的最小值
(2)设
,当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
定义一:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d0c99ddd028f0bc3b1d64924ff0f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
定义二:若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8b0433a4d3b4bc56893eac40a8927cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d4b161021e543d0d8a966e0dd82832a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4b5430922a80463e6b2333d3b61062.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
(1)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59f43812bb224e922688cb688b76d805.png)
①判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4138f6987cd2ee9e56b2ac80e84f9e24.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ccee041ba1852b2f3ee2b3a2dfeb0b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ce0d847c20978e3b2d58b97ebf43b55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/832714cf1b2b257b6edf8ebd57da83ea.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24715f8aed7a100fb047ca95a8ae64de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b67784e0c5b774a658b3c12fe05800df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e54a82cfc5dd2895edddf53a9f8c3ad.png)
您最近一年使用:0次
5 . 高斯是德国著名的数学家,近代数学的奠基者之一,享有“数学王子”的称号,用其名字命名的“高斯函数”定义为:对于任意实数x,记
表示不超过x的最大整数,则
称为“高斯函数”.例如:
,
.
(1)设
,
,求证:
是
的一个周期,且
恒成立;
(2)已知数列
的通项公式为
,设
.
①求证:
;
②求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7179c645736d68c90023f83d7f11ed01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a84bb2c73d7560f8543ee90fd3cfd87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce33c9b4713d3027ffcc1321800bfdc.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc886ed87255efa6007b3e5d1df429a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69cde4038ab5a4ede107d02d41861fba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/058f67ed1a4372f6a807c14d4c8fa3a4.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbb605f0ddd311d1a092c5be5ae29260.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f275ffdb11a31a07fc8569ddda7a6a.png)
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6 . 已知函数
.
(1)求曲线
在点
处的切线方程;
(2)设
,证明:
在
上单调递增;
(3)判断
与
的大小关系,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90abf4340754de993128fefcf93c3d9b.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3832d863e6cefdfe45cff4319e1fbdb.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/146d3d11d5f0a324f3ad2dcaa6021c0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd50020c0e3198d4a6b2d26a413b1b8.png)
(3)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d68f75f7903e505329ce87861809ba31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc8ae8993088868740f8a641cd896ecf.png)
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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)
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解题方法
8 . 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
|
1079次组卷
|
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
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山东省菏泽第一中学人民路校区2024届高三下学期3月月考数学试题(已下线)模块3 第8套 全真模拟篇安徽省黄山市2024届高中毕业班第二次质量检测数学试题(已下线)专题12 帕德逼近与不等式证明【练】天津市武清区杨村第一中学2024届高考数学热身训练卷河北省秦皇岛市部分示范高中2024届高三下学期三模数学试卷
解题方法
9 . 如图,已知直线
,
是
,
之间的一定点并且点
到
,
的距离分别为
,
,
是直线
上一动点,作
,且使
与直线
交于点
.设
.
面积
关于角
的函数解析式
;
(2)画出上述函数的图象;并根据图象求
的最小值;
(3)证明函数
的图象关于
对称.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cdb9d8425d73a68731f30e0c0e22260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80b53eab97158937f92039c1e133b0f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f285174fbf90a9742de57c1e53224cff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/822ba132ca9dd0d4a050659aef3c9b26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c499d3ef329f85e59fd72dec6f453bbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fd7229922fbb3ce09dada883f74fbb1.png)
(2)画出上述函数的图象;并根据图象求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fd7229922fbb3ce09dada883f74fbb1.png)
(3)证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fd7229922fbb3ce09dada883f74fbb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4120436d6ff0c58109473edc068257c3.png)
您最近一年使用:0次
名校
解题方法
10 . 函数
对任意的实数a,b,都有
,且当
时,
.
(1)求
的值;
(2)求证:
是R上的增函数;
(3)解关于实数x的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba5b5f09650569f1846f451c09585728.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2180e18416d40abb243bd23984e7aba.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e38fffbc7ab9882480f4faa72390e23.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)解关于实数x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b6706a0de427b238c481d4bb5fcc692.png)
您最近一年使用:0次