解题方法
1 . 已知定义在
上不为常数的函数
满足
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2628e2dd7a988cc80530e739c22b2280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1273c46b7fcc753edffec8da083f60b.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
2 . 在棱长为2的正方体
中,
为
的中点,以
为原点,OB,OD,OO1所在直线分别为
轴、
轴、
轴,建立如何所示空间直角坐标系.若该正方体内一动点
,满足
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22a20b689283cc8b311eddae4c8c4242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49ea83a384f056dadaacfa349cc84130.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bfcaf2a345411411cf94422703e9269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e588cb555e36f28c5db66d213ef064d4.png)
A.点![]() ![]() | B.![]() ![]() |
C.![]() | D.三棱锥![]() ![]() |
您最近一年使用:0次
解题方法
3 . 设A,B为椭圆C:
的短轴端点,P为椭圆上异于A,B的任意一点,D在直线
上.
(1)求直线
,
的斜率的乘积;
(2)证明:
;
(3)过右焦点F作x轴的垂线
,E为
上异于F的任意一点,直线
交C于M,N两点,记直线
,
,
的斜率分别为
,
,
,是否存在
,
,
的某个排列,使得这三个数成等差数列?若存在,加以证明;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6922c5dbeead5d1225b2933e92719f2f.png)
(3)过右焦点F作x轴的垂线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4c865445dda4a59b6d5cb18fd74404.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/dbf434334b09cc0fdd4e86e84e6ceb00.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/dbf434334b09cc0fdd4e86e84e6ceb00.png)
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解题方法
4 . 如果三个互不相同的函数
,
,
在区间
上恒有
或
,则称
为
与
在区间
上的“分割函数”.
(1)证明:函数
为函数
与
在
上的分割函数;
(2)若函数
为函数
与
在
上的“分割函数”,求实数
的取值范围;
(3)若
,且存在实数
,使得函数
为函数
与
在区间
上的“分割函数”,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d61157daf46974d1a08cd4b465a92abe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af28992f69a3dab36678839b8a5e5720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38e00b49aa78de649f34d8bb9d5179ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8190660962c1d992d7d61a69c21a2737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6583d861ba47d9123d75dc90b8df0c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7334919736e5ed881f691e4ca738b4ce.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8352b2e643a7ce605334f1b0e572bfb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a05ba1bc6c7bc24879b2a17ef2351c59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23afc43a8c5b8cfe6bf2a1caed920c01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2372f424431ce7b547a66b7d61d75421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a06e1578853d2072cef33395de8784d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3046b064d62833c805c84d5a8866c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8829770dd5a85c2ecaf82edea669869d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aea89f800e9af713ec91e00fb287008.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ed21127710fb6adcf694bd14aff321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
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5 . 已知椭圆
的离心率为
,且过点
.过椭圆
上的点
作圆
的两条切线,其中一条切线与椭圆
相交于点
,与圆
相切于点
,两条切线与
轴分别交于
两点.
的方程;
(2)
是否为定值,若是,请求出
的值;若不是,请说明理由:
(3)若椭圆上点
,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90627d25fa0d0e5345c834b96331e77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/959e5ab675f526dfb54b05f8f82151b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b33328faae2d2d4921900e97424de5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2228629b80d4efbfd2a226a863274520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2228629b80d4efbfd2a226a863274520.png)
(3)若椭圆上点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2c81a4d934b8e4565969a8e7921111c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
您最近一年使用:0次
解题方法
6 . 若一个多面体的各面都与一个球的球面相切,则称这个球是这个多面体的内切球.在四棱锥
中,侧面
是边长为1的等边三角形,底面
为矩形,且平面
平面
.若四棱锥
存在一个内切球,设球的体积为
,该四棱锥的体积为
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f737b04ce09bc7e1ed86dc9b3c85203b.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
7 . 已知
是定义在
上的函数,如果存在常数
,使得对区间
的任意划分:
,都有
成立,则称
是
上的“绝对差有界函数”.
(1)分别判断
,
是否是
上的“绝对差有界函数”,若是“绝对差有界函数”,直接写出
的最小值(不需证明);若不是“绝对差有界函数”,直接写出函数的值域(不需证明);
(2)对定义在
上的
,若存在常数
,使得对任意的
,都有
,求证:
是
上的“绝对差有界函数”;
(3)设
是
上的“绝对差有界函数”,满足
,
,且对任意的
,都有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/804319e6cb58f07ee82ee364e334f36b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cddd157e5a81d11a17daeae7882b85f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
(1)分别判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee02fa2349fe9b9dd17c11665352c06e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a552e0f8ccb78f2eec126ba95d8c399.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)对定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f20b947d584a1dc48676c2ae6e2af52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ecdccf4a334ea959a456533c40d53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ac1c23f2a39df0652588ce63221df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bea8bf593f594c51fc7cc547482bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fd80e859f2a7935d7d621e202422621.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
8 . 已知函数
,其中
表示
,
中的最大值,若函数
有3个零点,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b532b68bfc793ca4826283d97458ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385e1459ada24f66206d0de24a85ad0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
9 . 已知
,下列四个结论:①
,②
,③
,④
.其中错误的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1bb486cbf98ae341a35a17e79fae7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7b0e6eb011614deef2d50ceab01c8d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7e0b26fa1a2c42bf24833e241ea25a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec504e75b5fe6435a94047a2f0b9443.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9dd82388f903f53c58ff6d655dd7d14.png)
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
10 . 已知动点
到点
的距离比到直线
的距离小1,设动点
的轨迹为曲线
.
(1)求曲线
的轨迹方程;
(2)已知点
,过点
作直线
与曲线
交于
两点,连接
分别交
于
两点.
①当直线
的斜率存在时,设直线
的斜率为
,直线
的斜率为
,试判断
是否为定值?若是,求出该定值;若不是,请说明理由;
②求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c441c7e1d4bc397894cc8a6a169e0d58.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7471451108cf5d0fbb66e8819759a6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
①当直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d930e03944fdb88ffb1b06c52f57ca4b.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0023c9e8e0fec24d3aa77d09b2e4e62.png)
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