1 . 定义函数
.
(1)求曲线
在点
处切线的斜率;
(2)若
对任意的
恒成立,求实数k的取值范围;
(3)讨论函数
的零点个数,并判断
是否有最小值,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db88bb3e5d4952aa9f96e7a25cff10e5.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2425552313d50a253bfb3cb4e9974ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9aafbe37839d77fcdd3e1c60c3b3a2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f19847d820451b7a95afc6822ec2163.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
(3)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
您最近一年使用:0次
2024-03-28更新
|
131次组卷
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2卷引用:2024届山东省泰安肥城市高考仿真模拟(二)数学试题
名校
解题方法
2 . 剪纸,又叫刻纸,是一种镂空艺术,是中国古老的民间艺术之一,已知某剪纸的裁剪工艺如下:取一张半径为2的圆形纸片,记为
,在
内作内接正方形,接着在该正方形内作内切圆,记为
,并裁剪去该正方形内多余的部分(如图所示阴影部分),记为一次裁剪操作,
重复上述裁剪操作
次,最终得到该剪纸.则第4次裁剪操作结束后所得
的面积为______ ;第n次操作后,所有裁剪操作中裁剪去除的面积之和为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0385df6c7f8ee7ab503b6ed35933695b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee7bb49247387a9028602315729f8d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e4ce93705afe34d7c48d509885a155a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/15/4cf70112-e86b-44d0-ab3d-b744197477ac.png?resizew=116)
您最近一年使用:0次
3 . 如果数列
满足:
且
,则称数列
为
阶“归化数列”.
(1)若某4阶“归化数列”
是等比数列,写出该数列的各项;
(2)若某11阶“归化数列”
是等差数列,求该数列的通项公式;
(3)若
为n阶“归化数列”,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa0fca4198a6d5c5b76e5e1716dc4e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b007de7a10971043aef1233438dd41c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)若某4阶“归化数列”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若某11阶“归化数列”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e68bb741ac2c0d27e2c7077f8c0fee0.png)
您最近一年使用:0次
2016-12-03更新
|
2302次组卷
|
3卷引用:山东省实验中学2024届高三下学期第一次模拟考试数学试题
4 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0c1cf727ac5793bfbe8b58515a8dd29.png)
.
(1)讨论
的零点个数.
(2)正项数列
满足
,
(
),求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0c1cf727ac5793bfbe8b58515a8dd29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec3e3bcd67cf1a355986c6e3132470c7.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)正项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/352d9b76dcf639368fa68cae70149802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a00279b758d34f093589618dc76ffbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7f3f50d9fab6c44d619524652f6721.png)
您最近一年使用:0次
2020-07-21更新
|
489次组卷
|
2卷引用:山东省泰安肥城市2020届高三适应性训练(一)数学试题
名校
5 . 已知函数
的图象经过点
和
,记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23a941fd5008f9ef49e8adad40063b4e.png)
(1)求数列
的通项公式;
(2)设若
,
,
,求
的最小值;
(3)求使不等式
对一切
均成立的最大实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d2a119403159f251ca90d8b6f23ecbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39ea1f5bdd213c7c3a571b4c38850bf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79485e42b7546ccfa3cd6d08491460f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23a941fd5008f9ef49e8adad40063b4e.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7d3d55a85012933f91c5d8d27d8801d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d47456f316f2a761cf3f081decf3d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec6a5cb93ba04f2e1b9209f8c4642e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)求使不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a04b7defcd768444d1cce4990548b3b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
您最近一年使用:0次
2018-07-14更新
|
828次组卷
|
3卷引用:山东省泰安市宁阳县第一中学2020-2021学年高三上学期模块考试数学试题
6 . 已知
为数列
的前n项和,
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7f2da7ec053ee949ca736b71c7b26e2.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b708c8dcb2d66eb2ce0b3718a9cd924a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb52995d72a9da6aa60a087852e7f6cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9faeed3aa0314ddbde724f10ffc1181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7f2da7ec053ee949ca736b71c7b26e2.png)
您最近一年使用:0次
解题方法
7 . 已知
.
(1)判断
在
上的单调性;
(2)已知正项数列
满足
.
(i)证明:
;
(ii)若
的前
项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3e87d4c6641d71a33a10329a51ec8c0.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(2)已知正项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94f57164b597f420a363936f1cf57d12.png)
(i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc5bd3034d1b2e9288d66453a4ae228.png)
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc9cc3e41fc2994c6c7efa487447bf4.png)
您最近一年使用:0次
8 . 设
是等差数列,
是各项都为正整数的等比数列,且
,
,
,
.
(1)求
和
的通项公式;
(2)若数列
满足
(
),且
,试求
的通项公式及其前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebaf2a2590bb84d646957f913d78f6dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c4b39c1e6a25ac7ff1d9fe2d2afa7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/855e62067cf1080a0d0db8c89b6b3e90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0935a7807fd0dab7607010324b7c926.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
9 . 已知数列
满足
,
,且
.
(I)设
,求证
是等比数列;
(II)①求数列
的通项公式;
②求证:对于任意
都有
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c67982d68cd67e77824a7ae26ab96b8.png)
(I)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e308cd7b453df3c7235de6fc1ff4dee8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
(II)①求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
②求证:对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d726666f99a5a41dd673a2330e377b17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbbf644f0916961a7fc09e5a7fb46e60.png)
您最近一年使用:0次
2016-12-04更新
|
714次组卷
|
2卷引用:2016届山东省东营市胜利一中高三最后一卷理科数学试卷