解题方法
1 . 英国物理学家、数学家牛顿在《流数法》一书中,给出了高次代数方程的一种数值解法——牛顿法.如下左图,具体做法如下:先在
轴找初始点
,然后作
在点
处切线,切线与
轴交于点
,再作
在点
处切线,切线与
轴交于点
,再作
在点
处切线,依此类推,直到求得满足精度的零点近似解
为止.
,初始点
,若按上述算法,求出
的一个近似值
(精确到0.1);
(2)如上右图,设函数
,初始点为
,若按上述算法,求所得前
个三角形
的面积之和;
(3)用数学归纳法证明与正整数有关的命题的步骤如下:①证明当
(初始值)时命题成立;②以“当
时命题成立”为条件,推出“当
时命题也成立”.完成这两个步骤就可以证明命题对从
开始的所有正整数
都成立.设函数
,按上述牛顿法进行操作,且
;
证明:①对任意的
,均有
;
②
为递增数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f71483635bc5bc6680051b9aaed85765.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe3a98816dba75cbb11620e7ed372c35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34632cf7058027def02525a8a0192b0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5604a6f0518feb8d6b3614a63c4d61de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/243989300efbd8c55ee767025490cac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ac32cbe433e4360f46a12ebe57841ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34732ae551c25032c24dacba0f7d1506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8efec283823fe25b28c325fc4fe99424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfa32997808121b79607346a4e46c26f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd9f851f16517ca9eaa79776cc3d559b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(2)如上右图,设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b39c5d66018f0736a0457961c91e1c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daab9aff134c4821a3784beaddba2320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1c44d297934c7502c4112eec807c095.png)
(3)用数学归纳法证明与正整数有关的命题的步骤如下:①证明当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ca4f2b82d9d7a8323c8d697338a6a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ca3f79fe5affe6d8d932bff4800cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba21f3d0cfc86d40e2e06446623ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c0499728def1fd57e66a6d9bce1f07b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e835fab669911f8d200e05b59b1c6ff.png)
证明:①对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c33759950935daad9aef020ed03a95c.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1fd18a909cecbaee7115d6b15631d83.png)
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2 . 若函数
恰有两个极值点,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b6d9203b52641dadd289e2ad6104854.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
3 . 一动圆与圆
外切,同时与圆
内切,动圆的圆心的轨迹
与
轴交于
两点,位于
轴右侧的动点
满足
,并且直线
分别与
交于
两点.
的方程及动点
的轨迹方程;
(2)直线
是否过定点?若是,求出该定点的坐标;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d008f0825083c74d3da4d87db1eab440.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/869b84b96637d80f7dbb2bde218a4e72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67f4f7b86f19521dec6a334e8575370a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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解题方法
4 . 在半径为1的圆
中,以圆心
为中心作一个正六边形
,再分别以其各边为底边,圆
上的点为顶点作等腰三角形
,如图,沿虚线剪开后,分别以
为折痕折起
,使
重合,得到六棱锥,则当六棱锥体积最大时,正六边形的边长为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239eab132ad665ff850eb3534ee19b75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80edb3049a8391c224dba21094954766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239eab132ad665ff850eb3534ee19b75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c5465c3be81e4156ff7cc7fb1f3559.png)
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解题方法
5 . 已知
分别为椭圆
的左顶点和左焦点,直线
与椭圆交于
两点,若直线
交线段
于
,则椭圆的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8348c89c6f13053325f4e1c62e29a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0b9af8dcc33088cedc3fbefaab69970.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
6 . 已知函数
.
(1)当
时,求函数
的极值;
(2)求函数
的单调区间;
(3)当
时,若
在
时恒成立,求整数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38a884c696e802c2962004fdf519482b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e9222ffc26c0e6bfbf252ab5d8a520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1749eb0942146be0ef6c0b39a33d8b06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4921923069c4f38a0af1ff8637e35b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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7 . 已知函数
.
(1)求函数
的单调区间;
(2)若
恒成立,求实数
的取值集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cff7978e698b20c3b12f2e9d3a00c47b.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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6卷引用:湖北省部分省级示范高中2023-2024学年高二下学期4月期中测试数学试题
湖北省部分省级示范高中2023-2024学年高二下学期4月期中测试数学试题2024届海南省省直辖县级行政单位琼海市高考模拟预测数学试题安徽省马鞍山市第二中学2023-2024学年高二下学期5月月考数学试题江苏省海安市实验中学等四校联考2023-2024学年高二下学期5月检测数学试题(已下线)第12题 分类讨论法讨论函数的单调性(高二期末每日一题)(已下线)专题09 导数与零点、不等式综合常考题型归类--高二期末考点大串讲(人教B版2019选择性必修第三册)
8 . 已知
,则
的大小关系正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8b9b0319b04ffaed294f767ba89ae69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 对于函数
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/728f2cc68f8ca8ef2faa681785798259.png)
A.函数![]() ![]() |
B.![]() |
C.若方程![]() ![]() |
D.对任意正实数![]() ![]() ![]() ![]() |
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10 . 已知椭圆
:
(
)的半长轴的长度与焦距相等,且过焦点且与
轴垂直的直线被椭圆截得的弦长为3.
(1)求椭圆
的方程;
(2)已知直线
:
与椭圆
交于
,
两点,过点
的直线交椭圆
于
,
两点(
在靠近
的一侧)
(ⅰ)求
的取值范围;
(ⅱ)在直线
上是否存在一定点
,使
恒成立?若存在,求出
点坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34517f479fb08f6096d2fb0362f3ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0accaaa66de4dfd9ed8257fa942c2cff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7f6a03826a5ad351c1f7ca553a6945.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/591ccce336af06e51e7f4887c287b80f.png)
(ⅱ)在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34517f479fb08f6096d2fb0362f3ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3d14da8892d33751940b69a790bc5c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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