名校
1 . 已知中心为坐标原点,焦点在坐标轴上的双曲线
的一条渐近线与曲线
相切,则双曲线
的离心率可以是_________ .(写出一个结果即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3470c3dee26d9b7499e0ed612f601d78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2023高三·全国·专题练习
解题方法
2 . 已知定义域为
的函数
存在导函数
,且满足
,则曲线
在点
处的切线方程可以是___________ (写出一个即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.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/fb75e503f1eef6034a3c7675dc7d7ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93994f2ba11401d1dca3c07d7faf1d7d.png)
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解题方法
3 . 已知函数
同时满足下列两个条件;①在
上单调递增;②曲线
在
上存在斜率为1的切线,则实数a可以为______ .(写出符合要求的一个值即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25cdb9c41a4aa4a0152beda25a762ba8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
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4 . 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一牛顿法.首先,设定一个起始点
,如图,在
处作
图象的切线,切线与
轴的交点横坐标记作
:用
替代
重复上面的过程可得
;一直继续下去,可得到一系列的数
,
,
,…,
,…在一定精确度下,用四舍五入法取值,当
,
近似值相等时,该值即作为函数
的一个零点
.若要求
的近似值
(精确到0.1),我们可以先构造函数
,再用“牛顿法”求得零点的近似值
,即为
的近似值,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.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/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6c6cc1e8086c67bed8f50f2bbb19c79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efbc757957fe3ec6c6e6671d9da2d3a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd9f851f16517ca9eaa79776cc3d559b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bde9d25ffb5af342be0b4968b7b1b34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd9f851f16517ca9eaa79776cc3d559b.png)
A.对任意![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.当![]() ![]() |
D.无论![]() ![]() ![]() |
您最近一年使用:0次
2021-08-07更新
|
1431次组卷
|
9卷引用:江苏省宿迁市2020-2021学年高二下学期期末数学试题
5 . 人们很早以前就开始探索高次方程的数值求解问题.牛顿在《流数法》一书中给出了牛顿迭代法:用“作切线”的方法求方程的近似解.具体步骤如下:设
是函数
的一个零点,任意选取
作为
的初始近似值,曲线
在点
处的切线为
,设
与
轴交点的横坐标为
,并称
为
的1次近似值;曲线
在点
处的切线为
,设
与
轴交点的横坐标为
,称
为
的2次近似值.一般地,曲线
在点
处的切线为
,记
与
轴交点的横坐标为
,并称
为
的
次近似值.在一定精确度下,用四舍五入法取值,当
与
的近似值相等时,该近似值即作为函数
的一个零点
的近似值.下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8559f5db9b978cb2bd290dbce7268629.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a24a2c53e3b0b1c08803e95419f909d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9fa2ec4de452006f2e0dc06cd4e7192.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a5b0f908cdae073db61be5b42fbcf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a5b0f908cdae073db61be5b42fbcf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3002f56900c2924bfd79fc3865b0a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3002f56900c2924bfd79fc3865b0a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3002f56900c2924bfd79fc3865b0a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
A.![]() |
B.利用牛顿迭代法求函数![]() ![]() ![]() ![]() |
C.利用二分法求函数![]() ![]() ![]() ![]() |
D.利用牛顿迭代法求函数![]() ![]() ![]() ![]() |
您最近一年使用:0次
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6 . 如果方程
能确定y是x的函数,那么称这种方式表示的函数是隐函数.隐函数的求导方法如下:在方程
中,把y看成x的函数
,则方程可看成关于x的恒等式
,在等式两边同时对x求导,然后解出
即可.例如,求由方程
所确定的隐函数的导数
,将方程
的两边同时对x求导,则
(
是中间变量,需要用复合函数的求导法则),得
.那么曲线
在点
处的切线方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2329774440278b274651ca465704a856.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2329774440278b274651ca465704a856.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d318c5ba5c7154bbcc95f8ec8e3d4a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63fe744d4980ba5e09c4074e0643e635.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8e70497c791fd23d1f37a544f2f73f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b4d2174f411d9db6ab7b2aea47818cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f76f3dbccb8db423d81c796cf1e8f4d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6f58a44e22ec20612a8aacba7295e4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96932f0ba294e407eabb7b1e324e66c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/100e975b1e92a21f9533b42f8cd7d258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-04-18更新
|
1175次组卷
|
4卷引用:河北省邢台市2024届高三下学期教学质量检测(一)数学试题
7 . 已知函数
,其中
.
(1)当
时,求曲线
在点
处的切线方程;
(2)若
在
上存在极值,求实数
的取值范围:
(3)写出
的零点个数.(直接写出结论即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f6fd0297d13ef19b5203a5ce1fb698a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e72f6b2ef3329828cb8fc873eeba7c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/150e8e4ca6aa729a72a6a17c36b8ebfe.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/879234adbae93aa72b7e101b3738d4e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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8 . 已知函数
,
.
(1)当
时,求曲线
在点
处的切线的方程;
(2)若曲线
与
轴有且只有一个交点,求
的取值范围;
(3)设函数
,请写出曲线
与
最多有几个交点.(直接写出结论即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ecf88c5647f13d1c7886da8a7b1bcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da989240786ef7c3e2d903f30caf59e3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/706a19c530fee983ba3d24079bddb737.png)
(2)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06ca643eb4f1093f1e4d430eabddf789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
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9 . 下列五个命题,其中正确命题的个数为( )
①已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/315c84dc5c31e1ec58b0957a24caf400.png)
②过原点作直线
的切线,则切线方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c603ebebcc2551c4c58a4b1758ed1ad1.png)
③已知随机变量
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4effc9159da3fff945e127842f9836bd.png)
④已知
为正整数,用数学归纳法证明等式
时,若假设
时,命题为真,则还需利用归纳假设再证明
时等式成立,即可证明等式对一切正整数
都成立
⑤在回归分析中,常用
来刻画回归效果,在线性回归模型中,
表示解释变量对于预报变量变化的贡献率,
越接近1,表示回归的效果越好
①已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/978c9adecf65391ace71f8157368cb8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/315c84dc5c31e1ec58b0957a24caf400.png)
②过原点作直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f2eff609c6043c2a89a6dd163fe2244.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c603ebebcc2551c4c58a4b1758ed1ad1.png)
③已知随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8b891ec9d9abbb7ffaa6d1ad01978a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9500cfe7f5ca2b282c258734534e4d36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4effc9159da3fff945e127842f9836bd.png)
④已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a7f91d2a8c6a2089372c66069664e98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac31dc10e8978562277e84eb9daa923f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba21f3d0cfc86d40e2e06446623ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
⑤在回归分析中,常用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c85067c53e936ef32da818efe04bdbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c85067c53e936ef32da818efe04bdbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c85067c53e936ef32da818efe04bdbb.png)
A.2 | B.3 | C.4 | D.5 |
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10 . 曲线
的一条切线的斜率为1,则该切线的方程可以是__________ (写出一个满足要求的答案).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf36e9bbe4dc23bb02d452d38afb9d4.png)
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