1 . 对于函数
的导函数
,若在其定义域内存在实数
和
,使得
成立,则称
是“跃然”函数,并称
是函数
的“跃然值”.
(1)证明:当
时,函数
是“跃然”函数;
(2)证明:
为“跃然”函数,并求出该函数“跃然值”的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851c68ef2e0703706f3b528daa902eb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79faaa73be5986e48442dcd5e80bc0a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
(1)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2a51944c720568f35d443589dfc1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/189e0f9d87a2d5fc08838ef19dee6d6b.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b1a851f8e1dcaa446c0afa18656dfa8.png)
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名校
2 . 帕德近似是法国数学家亨利·帕德发明的用有理多项式近似特定函数的方法.给定两个正整数
,
,函数
在
处的
阶帕德近似定义为:
,且满足:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a46eaf1cdc0ea6f6b18e8fba22ee7ae2.png)
.(注:
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51793a343298909a499b0b150660ccb.png)
为
的导数)已知
在
处的
阶帕德近似为
.
(1)求实数
的值;
(2)证明:当
时,
;
(3)设
为实数,讨论方程
的解的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16563cfb206d0394cac2a0c2595dda6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a46eaf1cdc0ea6f6b18e8fba22ee7ae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e4baac3118da93995e49b29a5d377e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca214aa6276b96d67a451c3fdbc59b3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51793a343298909a499b0b150660ccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385c9d5f9d6c2c720dd99273021cafd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eea7fa65b493fc1bdf84e16d39ae07d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35dd621776dee688a0175a1abe39c258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40765d09390381658d5b4dc0160366cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8de781718020ed3f99538b8e25d6186.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447d6f62c09c1d05346fd16a24159f6e.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cccba081685984454ee4fa955dc4f7ea.png)
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3 . 如图,已知二面角
的棱
上有
两点,
,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754bbd99327195520a4ca3ce3b9a0577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02b1536ba47578b97fec0a0c6d179429.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a6be488d3d68485aaea00e4db96e1ac.png)
A.当![]() ![]() ![]() ![]() |
B.当二面角![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() |
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解题方法
4 . 如图,D为圆O:
上一动点,过点D分别作x轴y轴的垂线,垂足分别为A,B,连接BA并延长至点W,使得
,点W的轨迹记为曲线C.
(2)若过点
的两条直线
,
分别交曲线C于M,N两点,且
,求证:直线MN过定点,并求出定点坐标;
(3)若曲线C交y轴正半轴于点S,直线
与曲线C交于不同的两点G,H,直线SH,SG分别交x轴于P,Q两点.请探究:y轴上是否存在点R,使得
?若存在,求出点R坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd32c18b556a282803d81e9a229de012.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15066261aaefa8e7384aeca62213497b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce08b357f11ef44c3e8207ac574422a.png)
(3)若曲线C交y轴正半轴于点S,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a0b95d5ba514e87d8d36a0854b1c5d.png)
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2023-02-10更新
|
732次组卷
|
3卷引用:湖北省“荆、荆、襄、宜四地七校”考试联盟2023-2024学年高二下学期期中联考数学试卷变式题16-19
(已下线)湖北省“荆、荆、襄、宜四地七校”考试联盟2023-2024学年高二下学期期中联考数学试卷变式题16-19山东省潍坊市2022-2023学年高二上学期期末考试数学试题山东省潍坊市诸城第一中学2022-2023学年高二下学期2月月考数学试题
名校
解题方法
5 . 曲线的曲率定义如下:若
是
的导函数,
是
的导函数,则曲线
在点
处的曲率
已知函数
,
,曲线
在点
处的曲率为
.
(1)求实数
的值;
(2)对任意的
,
恒成立,求实数
的取值范围;
(3)设方程
在区间
(
)内的根从小到大依次为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7994bbcf39f4dda34e877b21af71f103.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6635a24bf10dd5f951924cd8111802bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7994bbcf39f4dda34e877b21af71f103.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07fa72fc4959804b944bfaa93dbe2b21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a07ce50009a2bb6f6358431c507e14e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb87668d7dc84f470182b32a1790a359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75f521cf86c1dd503870fa5121fcd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97e7417618db2a984a0b1637b03e4174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821309f088a175c00dc0f4828334503d.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31c1c1c885e28ef61bf47d1a61a847bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2c62477c656febc9646b305a64484ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)设方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b29fe377ffb047b7814370ac2785257f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff9f6f21d68ee6a07070e40cf93b208.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d5ec9ad92f37e64eccce922ab1b14e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c032d50e3dde09f453adc34a1c5353ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c642de19a879df2e18cc5c5c44bd5b07.png)
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