1 . 已知各项均不为0的数列
满足
(
是正整数),
,定义函数
,
是自然对数的底数.
(1)求证:数列
是等差数列,并求数列
的通项公式;
(2)记函数
,其中
.
(i)证明:对任意
,
;
(ii)数列
满足
,设
为数列
的前
项和.数列
的极限的严格定义为:若存在一个常数
,使得对任意给定的正实数
(不论它多么小),总存在正整数m满足:当
时,恒有
成立,则称
为数列
的极限.试根据以上定义求出数列
的极限
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39bf7b5dc247fe10b6bfd984413a5e6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8323901a49cac29afd7d62864f088077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd9ea8ffdea8c77370ea3e5f563dc35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51fec2729d8e927de9392ee90d1e0389.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6f0a55fa53bf5f8e6654897975bcf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3324481138f2dc750f9ad889054abe1.png)
(i)证明:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/416a72de4d0030203a867cc3b7b95d83.png)
(ii)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0857559ed421cc7c614708f34f9f3324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de777c4e44546bcfe26ad5b6bb418052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad481cbfb67ac9cdbc0537f3de23b022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856b137a34d2d5b20671b7a3c7a29606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb9de1835c164233db8b623489fbda0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eded65284816fdf6bf335b0c2a78e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eded65284816fdf6bf335b0c2a78e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
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解题方法
2 . 已知幂的基本不等式:当
,
时,
.请利用此基本不等式解决下列相关问题:
(1)当
,
时,求
的取值范围;
(2)当
,
时,求证:
;
(3)利用(2)证明对数函数的单调性:当
时,对数函数
在
上是严格增函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1419108104429f6df5d5352a05211e36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db5e0630a1632f6368fb824ebfdead0d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7326ea56be82bd616fec7e6aa3c884c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1419108104429f6df5d5352a05211e36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca16bee4a8ecee60c31f9aaac02539b0.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27eb687fdf1568ab06ce8119845823c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c92098b3da769963a2320cf1d8dad00a.png)
(3)利用(2)证明对数函数的单调性:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82869dad28f771d088772a2c2b08b187.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
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名校
3 . 设函数
定义域为
.若整数
满足
,则称
与
“相关”于
.
(1)设
,
,写出所有与
“相关”于
的整数;
(2)设
满足:任取不同的整数
,
与
均“相关”于
.求证:存在整数
,使得
都与
“相关”于
;
(3)是否存在实数
,使得函数
,
满足:存在
,能使所有与
“相关”于
的非零整数组成一个非空有限集?若这样的
存在,指出
和
的大小关系(无需证明),并求出
的取值范围;若这样的
不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cae7b35b6dbdeafb82810fb8239121c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b056a90a2751f04ba5fff3dc5c1d0674.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d53f0be9e922c54b74dc21ef147d81c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f713f92ce74aa961b391fe544e609a68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e196c4f6545854d1fee5fea9609d01d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cec48f249cb8141bad725728996fbf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0becd5c2342ac2cef8d24b6e7e8a0abc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f4b983d54b0b2d085456306ef564bda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e8936c9fe1e81726455908657a29fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
(3)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7489d1555eaffa5d7d26d37df5d4355a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e196c4f6545854d1fee5fea9609d01d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8380733ca1aaccc36e3b0c658bd6011b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee175df20c19745745059464e643079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
4 . (1)设
,
,求证:
;
(2)已知
,
,且
.证明:
或
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54d8bf9316bb1dfb0559333ce56b35a6.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061813f1ec633c5c4c393c4de7938322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f9e131cdd242d56b6dba05ab3363ef3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef8e5b510c343f9d3d626fa1a4b36bad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e36ffaf917dcebc8719f2ca539a774ec.png)
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名校
解题方法
5 . 若函数
满足:对任意的实数
,
,有
恒成立,则称函数
为 “
增函数” .
(1)求证:函数
不是“
增函数”;
(2)若函数
是“
增函数”,求实数
的取值范围;
(3)设
,若曲线
在
处的切线方程为
,求
的值,并证明函数
是“
增函数”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9cec0474c43086ea39cb457048313c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dca031c9a6a1199cfee4c3d91c52099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/916ae6490922319a1d394fbedd8d951a.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/916ae6490922319a1d394fbedd8d951a.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b34671abe25726a52a57850ab248fe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/916ae6490922319a1d394fbedd8d951a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/974f122681f314e8202e02861cabf8cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/916ae6490922319a1d394fbedd8d951a.png)
您最近一年使用:0次
2023-12-21更新
|
736次组卷
|
5卷引用:上海市奉贤区2024届高三一模数学试题
上海市奉贤区2024届高三一模数学试题(已下线)上海市高二下学期期末真题必刷03(常考题)--高二期末考点大串讲(沪教版2020选修)(已下线)上海市奉贤区2024届高三一模数学试题变式题16-21重庆市育才中学校2023-2024学年高二下学期三月拔尖强基联盟联合考试巩固测试数学试题四川省屏山县中学校2023-2024学年高二下学期第一次阶段性考试数学试题
名校
6 . 已知
.
(1)求函数
的单调区间和极值;
(2)请严格证明曲线
有唯一交点;
(3)对于常数
,若直线
和曲线
共有三个不同交点
,其中
,求证:
成等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647014ad8af603468f4100043c4bde15.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/720777756eaef6fd797e16c7656bd916.png)
(2)请严格证明曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/720777756eaef6fd797e16c7656bd916.png)
(3)对于常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3387f1c69de6c2407212536b35150e5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46111e4d12c21798aa213c0d7804c2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/720777756eaef6fd797e16c7656bd916.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3059524807d8e93433b8d994df6ede70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7169ce3255d2a02a20aa5932d2bd48.png)
您最近一年使用:0次
2023-12-19更新
|
640次组卷
|
4卷引用:上海市嘉定区2024届高三一模数学试题
上海市嘉定区2024届高三一模数学试题(已下线)专题09 导数(三大类型题)15区新题速递(已下线)上海市高二下学期期末真题必刷04(压轴题)--高二期末考点大串讲(沪教版2020选修)广东省广州市第二中学2023-2024学年高二下学期期中考试数学试题
23-24高二上·上海·课后作业
7 . 请指出下列各题用数学归纳法证明过程中的错误.
(1)设
为正整数,求证:
.
证明:假设当
(
为正整数)时等式成立,即有
.
那么当
时,就有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b265260b1c40af006ba6f66a11ed576.png)
.因此,对于任何正整数
等式都成立.
(2)设
为正整数,求证:
.
证明:①当
时,左边
,右边
,等式成立.
②假设当
(
,
为正整数)时,等式成立,即有
,
那么当
时,由等比数列求和公式,就有
,等式也成立.
根据(1)和(2),由数学归纳法可以断定
对任何正整数
都成立.
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b502d9c57239d9f42fdf849878018061.png)
证明:假设当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef7ca2b3e8061384501f668e59696a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d8963d68c930f5b28cc8b92c43d469b.png)
那么当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba21f3d0cfc86d40e2e06446623ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b265260b1c40af006ba6f66a11ed576.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced66f7e147b6276e1ce9e2b67510141.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8883d7d43d3f61a771d16537c52ac451.png)
证明:①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90bae886c8ab958aa4c693bf8e0627d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90bae886c8ab958aa4c693bf8e0627d.png)
②假设当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef7ca2b3e8061384501f668e59696a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2397df3279607612ea3cbef101ee0bf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a439aebc27b99718f09e1dff2649482f.png)
那么当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba21f3d0cfc86d40e2e06446623ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b838d781d5ce98ddcc08af86c1f27ae.png)
根据(1)和(2),由数学归纳法可以断定
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8883d7d43d3f61a771d16537c52ac451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
8 . 对于函数
,分别在
处作函数
的切线,记切线与
轴的交点分别为
,记
为数列
的第n项,则称数列
为函数
的“切线-
轴数列”,同理记切线与
轴的交点分别为
,记
为数列
的第n项,则称数列
为函数
的“切线-
轴数列”
(1)设函数
,记
“切线-
轴数列”为
,记
为
的前n项和,求
.
(2)设函数
,记
“切线-
轴数列”为
,猜想
的通项公式并证明你的结论.
(3)设复数
均为不为0的实数,记
为
的共轭复数,设
,记
“切线-
轴数列”为
,求证:对于任意的不为0的实数
,总有
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ed953d6e0bd80a5da66552c7bfbcbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd3d48fa9493a86f262569df235a82ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8292395dc894796602a60486e575a808.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a79b9eaa5e7ab7a1e5c512b571914dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36460040ddea4761eee10d537b14a1f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36460040ddea4761eee10d537b14a1f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ef5756fec38d1b4dc62358b45c3352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e845964df4b271bd7b4cf99ede79be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(3)设复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80bcf306a6aa8554d1d7fc8317f4e946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fcfebd9f5a57036e6df6b6e14865da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec5f303f666e164582da05968d9d8cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe6f044a9b06a7a769e613c977cbfb87.png)
您最近一年使用:0次
2024-01-01更新
|
443次组卷
|
7卷引用:上海市普陀区桃浦中学2022-2023学年高二下学期期中数学试题
上海市普陀区桃浦中学2022-2023学年高二下学期期中数学试题(已下线)模块一专题1【练】《导数的概念、运算及其几何意义》单元检测篇B提升卷(人教A2019版)(已下线)模块二 专题1 与曲线的切线相关问题(已下线)模块二 专题3 与曲线的切线相关问题(人教B版)(已下线)模块一 专题1 《导数的概念、运算及其几何意义》B提升卷(苏教版)(已下线)模块二 专题1 与曲线的切线相关问题(苏教版高二)(已下线)模块二 专题4 与曲线的切线相关问题(高二北师大版)
名校
解题方法
9 . (1)已知实数
,
满足
,求证:
.
(2)若实数
,
为正数,且满足
,用反证法证明:
和
中至少有一个成立.
![](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/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/838b9f49811c77cbf7d12d3af4a63373.png)
(2)若实数
![](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/4a7dbc702617c765a573961953cc0901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eba1d7973f41f2050afd1759a0e480e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dfd31530f4f4d297248c3e39f42d8fb.png)
您最近一年使用:0次
10 . 若函数
满足
,称
为
的不动点.
(1)求函数
的不动点;
(2)设
.求证:
恰有一个不动点;
(3)证明:函数
有唯一不动点的充分非必要条件是函数
有唯一不动点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f66a2b3d90f0d935d6c8ebaf675349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/359baaa1ce86fe2403796f44d62429fb.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb0d493ff8d41fbcb33ad51365f46a23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8166c6ec3cfe1f17dabc7b307cb2e1a.png)
(3)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/276b142a9d9f0a87425a668dd6501f15.png)
您最近一年使用:0次