真题
1 . 若函数
恰有一个零点,则
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed0abc69199027468e3c0216acc74c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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7日内更新
|
1929次组卷
|
5卷引用:专题08平面解析几何
2 . 已知函数
,若
的图象与
轴有3个不同的交点,则实数
的取值范围是__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fa3bb77c971beb9a62f166fde545458.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e44d9de2cee26966ad19e87a7d6c85b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
3 . 定义在
上的
满足对
,关于
的方程
有7个不同的实数根,则实数a的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b475bccb3bb1fc3c663cf4b6a7ff65ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b91de238ebb9abfc2a3f8171f17886b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36fead197fbe41d3aa2923f85ebe148d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
4 . 设
,若关于x的方程
有三个不同的实数根,则实数t的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/955efc3ec6a981f38d08d9ad0549cacf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72a8935d43b0dc67ee168106bac7e78c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
5 . 已知函数
,函数
有四个不同的零点
,
,
,
且
,
,则实数
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/571240fc9ec9fda942480e60b0a04d46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f4d70a3e2c1335c178fee01917d14ff.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/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36fa12840947e81b725d7d55df561cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3604274ad6707a906eba371a9e884144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6f82d05881ac8b3a18bba8665c4845.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
6 . 已知函数
的零点为
的零点为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3a88cea6e5ba43dd2649f4b4618702b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2c4ce2227db17c099728728d641aca4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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7日内更新
|
669次组卷
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3卷引用:专题09 指数函数与对数函数的综合(一题多变)
解题方法
7 . 法国数学家弗朗索瓦·韦达发现了一元二次方程的根与系数之间的关系,将其推广到高次方程,并在其著作《论方程的识别与订正》中正式发表,后来人们把这个关系称为韦达定理,即如果
是关于x的实系数一元n次方程
在复数集C内的n个根,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/988acbe8533ef50c899650a057717cf5.png)
试运用韦达定理解决下列问题:
(1)已知
,
,
,求
的最小值;
(2)已知
,关于x的方程
有三个实数根,其中至少有一个实效根在区间
内,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44258e924e42ec263b5236499252d4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f44bf708f38a916de0572d8ef1cf45a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/988acbe8533ef50c899650a057717cf5.png)
试运用韦达定理解决下列问题:
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3eb9b6fe8959ae9e71e857b6d6fed49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/460b68eaa42bc8929edf81e21ad0bca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc2818de1c0d7d347718672b0bcec32.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73254f32b6da29ecc32df2e9f87a4c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a070d41a05c5193153ae18e0235a492.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4a90cfdbfa05577b6ec0b22739e7c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754826457671db8939098215943e656a.png)
您最近一年使用:0次
名校
8 . 己知函数
若函数
有5个不同的零点,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e108aeb240893cf807e7f351921f7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1abaa2c17ab08b2e508e00d9cc8c2035.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024高三·全国·专题练习
9 . 方程
的实根个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835e374b5529ea62837bbfdbdccb584a.png)
A.4 | B.3 | C.2 | D.1 |
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解题方法
10 . 拉格朗日中值定理是微分学的基本定理之一,其内容为:如果函数
在闭区间
上的图象连续不断,在开区间
内的导数为
,那么在区间
内存在点
,使得
成立.设
,其中
为自然对数的底数,
.易知,
在实数集
上有唯一零点
,且
.
时,
;
(2)从图形上看,函数
的零点就是函数
的图象与
轴交点的横坐标.直接求解
的零点
是困难的,运用牛顿法,我们可以得到
零点的近似解:先用二分法,可在
中选定一个
作为
的初始近似值,使得
,然后在点
处作曲线
的切线,切线与
轴的交点的横坐标为
,称
是
的一次近似值;在点
处作曲线
的切线,切线与
轴的交点的横坐标为
,称
是
的二次近似值;重复以上过程,得
的近似值序列
.
①当
时,证明:
;
②根据①的结论,运用数学归纳法可以证得:
为递减数列,且
.请以此为前提条件,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63313f7ac7402fcb5a9a840db64c6f08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090a91e4f3c8930674f98a9fa527709b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63313f7ac7402fcb5a9a840db64c6f08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d59685311c7aa9ca98b1fdbabde40171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15432e3c4e6c1d9cde98ec9187d162c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dcd143a57a268a5a8ef486e2a4d5c0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00108fe668a98c905f3f92b720e35a0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8e356055d318b6d336e9e33a1e78aad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70142f9c28dc50c8ab41e71b19d18fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a8488679e2fa13e44ffa5b4d802848d.png)
(2)从图形上看,函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15432e3c4e6c1d9cde98ec9187d162c2.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/15432e3c4e6c1d9cde98ec9187d162c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de261e9b4defbc0be6440397031a87b8.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/168e68d052280fe48e1a3a6de67c6f2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8559f5db9b978cb2bd290dbce7268629.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/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/a24a2c53e3b0b1c08803e95419f909d3.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/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/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87529d4cadc1e84f72d462cb8e3afac0.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1a778faac194e8de4d5178454bd04c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f274881a6ad83e68c9b6652ebf4dc09.png)
②根据①的结论,运用数学归纳法可以证得:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1fd18a909cecbaee7115d6b15631d83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2adb4f1a98a9db3b5d4e4cfc7560fdb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee28be9d207a3d3eed938484f980195.png)
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