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1 . 已知函数
.
(1)若
,求曲线
在点
处的切线方程;
(2)若
,试讨论
的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08c175efdda7cf6dd5d113ce98bfa8d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3897bf276a0b6c2121917d39b369df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c7d6a607085cd85bea646a11243cc3c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96a967d4c78e4d658d1fd4afb33c3ea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
您最近一年使用:0次
2024-05-20更新
|
1408次组卷
|
5卷引用:辽宁省抚顺市六校协作体2024届高三下学期5月模拟考试数学试卷
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2 . 已知函数
,函数
,且
,定义运算
设函数
,则下列命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afbecf96f4a56400b24bc3dc6c5b547e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/116b80ed2eedbb36fa1898b7fcd681c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a4eaa80b44625890339d6a0065c241.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c29c4327642af92a63376313e3498d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bf97f28c31f9dbd8823694f666610e.png)
A.![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() |
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2024-05-08更新
|
1176次组卷
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7卷引用:辽宁省抚顺市六校协作体2024届高三下学期5月模拟考试数学试卷
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3 . 平面几何中有一定理如下:三角形任意一个顶点到其垂心(三角形三条高所在直线的交点)的距离等于外心(外接圆圆心)到该顶点对边距离的2倍.已知
的垂心为D,外心为E,D和E关于原点O对称,
.
(1)若
,点B在第二象限,直线
轴,求点B的坐标;
(2)若A,D,E三点共线,椭圆T:
与
内切,证明:D,E为椭圆T的两个焦点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24e12c97516329a6776fe48c450d93b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c8ef6f3640bd70e40f3b591c8bcc14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b45db8dd8768994af51206565379fd.png)
(2)若A,D,E三点共线,椭圆T:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2024-05-08更新
|
1123次组卷
|
5卷引用:辽宁省抚顺市六校协作体2024届高三下学期5月模拟考试数学试卷
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4 . 设函数
.
(1)讨论
的单调性.
(2)证明:
.
(3)当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/181d3aa3dec00a9c63fa2987c77bd0ea.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84c1e0c67c135532494ef7cf732fb7ef.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98d4a677b734a48f8116d67afceead44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f95ca867dde8e6812ba191138994b13.png)
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解题方法
5 . 如图所示,在圆锥内放入两个球
,它们都与圆锥的侧面相切(即与圆锥的每条母线相切),且这两个球都与平面α相切,切点分别为
,数学家丹德林利用这个模型证明了平面α与圆锥侧面的交线为椭圆,记为Γ,
为椭圆Γ的两个焦点.设直线
分别与该圆锥的母线交于A,B两点,过点A的母线分别与球
相切于 C,D 两点,已知
以直线
为x轴,在平面α内,以线段
的中垂线为y轴,建立平面直角坐标系.
(2)点 T在直线
上,过点T作椭圆Γ的两条切线,切点分别为M,N,A,B分别是椭圆Γ的左、右顶点,连接
,设直线
与
交于点P.证明:点 P 在直线
上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d096cd7bd8a5a2219fd7dd166bbb8460.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643ef7d761de0e794fc39937dc72ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d096cd7bd8a5a2219fd7dd166bbb8460.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf8b37e0e2651f72ee6f80489cdf6d15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643ef7d761de0e794fc39937dc72ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643ef7d761de0e794fc39937dc72ac6a.png)
(2)点 T在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e4d7503a7d57ba242ad4e05c7006a0.png)
![](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/f23d29646155e27b172ecdf263e2d702.png)
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2024-04-18更新
|
587次组卷
|
3卷引用:2024届辽宁省抚顺市六校协作体高三下学期第三次模拟数学试卷
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解题方法
6 . 已知函数
满足
,设
,若
,当
则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8c836e52209d22457a492048712573f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a514cda5ad85580ad8a1e99c1633c99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0890beb1ea4a85eff10004f87223bd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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7 . 已知函数
在区间
上单调递增,且其图像关于点
对称,则下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ab15470ca1bd4de73a4ac19973277b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3697c286ea301d21ff0dc4305d935883.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f647daa2fca119a336cd837ddabb88fe.png)
A.![]() |
B.![]() ![]() |
C.函数![]() ![]() |
D.方程![]() ![]() ![]() |
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解题方法
8 . 已知
是定义域为
的奇函数,函数
,且当
时恒成立,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c19b5e7ec97fb0dc579c3f0c47f2727.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/967d2a64967055bf7847d26f5eb7bb08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f66193ff4404822ce1410b60d251569.png)
A.![]() | B.不等式![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
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解题方法
9 . 已知函数
满足对任意
,都有
,且当
时,
,函数
是定义域为
的偶函数,满足
,且当
时,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fd7af568e3d9f444beb0ff41426477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74325e5da185c3f6c5f20d91027a4589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd26cf4ba8fe98bc4dbc37103b805dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71bb7883ea87e6275472dbe14ee62357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1275f567f4313471df4daad443743f43.png)
A.![]() | B.![]() |
C.![]() ![]() | D.![]() |
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10 . 已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/727088002886910f1b8bff4492c8f453.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0fa0035770a41d223aadf0a1c5e186b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/727088002886910f1b8bff4492c8f453.png)
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