名校
1 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9849b8f5976d59dca2e6926c3c048d00.png)
(1)求曲线
在点
处的切线方程;
(2)求证:函数
的图象位于直线
的下方;
(3)若函数
在区间
上无零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9849b8f5976d59dca2e6926c3c048d00.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04adfa887e965fe283aa9661f2ac8def.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-04-24更新
|
432次组卷
|
5卷引用:专题3 导数与函数的零点(方程的根)【讲】
(已下线)专题3 导数与函数的零点(方程的根)【讲】(已下线)专题05导数及其应用全章复习攻略--高二期末考点大串讲(沪教版2020选修)上海市松江二中2023-2024学年高二下学期期中数学试卷云南省玉溪第一中学2023-2024学年高二下学期第二次月考数学试题湖南省衡阳市第一中学2024年高二下学期期中考试数学试卷
名校
2 . 设
,函数
,若函数
恰有4个零点,则实数
的取值范围为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e37c35e33ffa1a55a0693ae2319da91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627cd24f63d5c5987cb718e6eddfe6c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1a576992d969ed5d63a8f77af2c7edc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-04-24更新
|
952次组卷
|
4卷引用:第25题 函数方程是“近亲”,以形助数传“佳话”(优质好题一题多解)
(已下线)第25题 函数方程是“近亲”,以形助数传“佳话”(优质好题一题多解)(已下线)专题6 函数的零点问题(过关集训)(压轴题大全)天津市八校2023-2024学年高三下学期联合模拟考试数学试题(二)天津市第四十七中学2023-2024学年高二下学期第二次阶段性检测(6月)数学试题
3 . 若有穷自然数数列
:
满足如下两个性质,则称
为
数列:
①
,其中,
表示
,这
个数中最大的数;
②
,其中,
表示
,这
个数中最小的数.
(1)判断
:2,4,6,7,10是否为
数列,说明理由;
(2)若
:
是
数列,且
,
,
成等比数列,求
;
(3)证明:对任意
数列
:
,存在实数
,使得
.(
表示不超过
的最大整数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8b9092e6c4f9186b55324c3a43ecd5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd5fe1c847904911c89504cef0973214.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1445aef0f66cacf3c0b358775623fab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b14e03f30c56d9943e4a82d0e029b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94beabf4bfbaa67081f1755fa5553a8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e598a5ba40123abea0f6e4559535a61b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b14e03f30c56d9943e4a82d0e029b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1daaf260a47403a2bdddd1268ebc44cd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a878ab2590307a7a6f7afe576b7112c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d1cb4ffc937e336200fd70fc089041a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da4cd81500bdb43118150dbdb1541e6.png)
(3)证明:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8b9092e6c4f9186b55324c3a43ecd5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e005b9c19a9b287aeefaa3af850beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f161c2a3717f1b6c62d0d7dae0b606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2024·全国·模拟预测
解题方法
4 . 已知双曲线
的左、右焦点分别为
,
,点
是
上一点.若
为
的内心,且
.
(1)求
的方程;
(2)点A是
在第一象限的渐近线上的一点,且
轴,点
是
右支上的一动点,
在点
处的切线
与直线
相交于点
,与直线
相交于点
.证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1723a5c1980f59baa9a949624d049332.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5076829e649b3f3866d4a7e07a5713e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697c20fca284394bf5d5b9e5f6d952e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f9d178764408489b0b336ea0ee42a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ddd3b35e93494d5bddf56f3b3007f5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)点A是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5dc06fe67c281c3ad3d19d6d8c98a67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2752e086b85f9fbb95010bf771072af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a873e20e420dc0904e8cc90eb230fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f93c3a552853bd28fdffe4de661d256.png)
您最近一年使用:0次
名校
5 . 设函数
,
.曲线
在点
处的切线方程为
.
(1)求a的值;
(2)求证:方程
仅有一个实根;
(3)对任意
,有
,求正数k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c927a4fcfc5c875001648ac315ae17c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c31c4f39399ec245a67db2933ed639f2.png)
(1)求a的值;
(2)求证:方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a73db674d29eae8f8921eff5944983.png)
(3)对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44672d44c44a6bf67ec4243399b0e5.png)
您最近一年使用:0次
2024-04-22更新
|
1314次组卷
|
5卷引用:专题15 导数与三角函数联袂【练】
解题方法
6 . 已知椭圆
的右焦点为
,长轴长为
.过F作斜率为
的直线交E于A,B两点,过点F作斜率为
的直线交E于C,D两点,设
,
的中点分别为M,N.
(1)求椭圆E的方程;
(2)若
,设点F到直线
的距离为d,求d的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(1)求椭圆E的方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4cc51d393a94365f7008de5eae8879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
解题方法
7 . 已知点P在圆
上,过点P作x轴的垂线段
,D为垂足,Q为线段
的中点,当点P在圆上运动时,点Q的轨迹为Γ.
(1)求Γ的方程;
(2)设
,
,过点
作直线与Γ交于不同的两点M,N(异于A,B),直线
,
的交点为G.
(ⅰ)证明:点G在一条平行于x轴的直线上;
(ⅱ)设直线
,
交点为H,试问:
与
的面积之积是否为定值?若是,求出该定值;若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
(1)求Γ的方程;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383f12cb70ca55eba4ff012771dbfa9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3544997cc034ed882c0d0a3bdbf5f957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0e1ba8ef888dfe9a639dddd38d6d603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
(ⅰ)证明:点G在一条平行于x轴的直线上;
(ⅱ)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3b785ebbf5889849e872f461669f71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f584dfa75ec20e4cba4216998b454dd.png)
您最近一年使用:0次
8 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e12018892a39fd5fda4a2bec62d438d2.png)
(1)讨论函数
的单调性;
(2)若函数
与函数
有相同的最小值,求a的值;
(3)证明:对于任意正整数n,
(
为自然对数的底数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2946a355e8ddd83c61ae79dfbf765669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e12018892a39fd5fda4a2bec62d438d2.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37f63e51c3353f7bad9cdbcae4a5172.png)
(3)证明:对于任意正整数n,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b098311cd342e6ef5b85db8b6056ab59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913b7537e011acfeec11952731351388.png)
您最近一年使用:0次
9 . 已知曲线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
,
是坐标原点, 过点
的直线
与曲线
交于
,
两点.
(1)当
与
轴垂直时,求
的面积;
(2)过圆
上任意一点
作直线
,
,分别与曲线
切于
,
两 点,求证:
;
的直线
与双曲线
交于
,
两点(
,
不与
轴重合).记直线
的斜率为
,直线
斜率为
, 当
时,求证:
与
都是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d80b861ba40387cb2bcd04945f5a371a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5226a2e1ee83a869b1133a234e9f3108.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)当
![](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/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
(2)过圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be68dfb4d8b5f3adfc250b7d23e64165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.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/ada25f76504c3fd1226da43c94cb4277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/944e8452701ba3a0bf9d8561f7a4cad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1892b7c3cd7bea116f532f66fba44662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b647e083b52664749a2c07a13b6089c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/284185654ca00ac9df0155d4c519a063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d303eb7923a91dcecc2d9bc1133d5c5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b38d23c520f89002afb0338bcb7b62c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22871505498b73670d0ee432ba402631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2297d08e5496a1af3f9ed1a1bbaea06.png)
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10 . ①在微积分中,求极限有一种重要的数学工具——洛必达法则,法则中有一结论:若函数
,
的导函数分别为
,
,且
,则
;
②设
,k是大于1的正整数,若函数
满足:对任意
,均有
成立,且
,则称函数
为区间
上的k阶无穷递降函数.
结合以上两个信息,回答下列问题:
(1)证明
不是区间
上的2阶无穷递降函数;
(2)计算:
;
(3)记
,
;求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22add663bd26e87d972a10dc5fd9ada1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ceac3910b9f134bab0b92e8d9a9eb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74acc4d2f565d7088e8d737718e89602.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e0c1abf0378a7f5d79672f622b275e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e54d86850a733707433da2e423a5c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/580f20b900b6d8c9e90c84a0588ae74d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c3e441923ed3c1a32720d6aeac2f599.png)
结合以上两个信息,回答下列问题:
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64d1f6f459292de1002f863203ce91a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fab11f38ab8593932082ec4d9c8c91f.png)
(2)计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8063898825e02107b7e04f6eba28cb8c.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602d05de8ada4a6f4d53bab28430f684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d40b0c4fd043d372c463db08659e779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caea9a696f22c76f8f4563ac45d124b1.png)
您最近一年使用:0次
2024-04-18更新
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456次组卷
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6卷引用:专题14 洛必达法则的应用【练】
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