名校
1 . 极值的广义定义如下:如果一个函数在一点的一个邻域(包含该点的开区间)内处处都有确定的值,而以该点处的值为最大(小),这函数在该点处的值就是一个极大(小)值.
对于函数
,设自变量x从
变化到
,当
,
是一个确定的值,则称函数
在点
处右可导;当
,
是一个确定的值,则称函数
在点
处左可导.当函数
在点
处既右可导也左可导且导数值相等,则称函数
在点
处可导.
(1)请举出一个例子,说明该函数在某点处不可导,但是该点是该函数的极值点;
(2)已知函数
.
(ⅰ)求函数
在
处的切线方程;
(ⅱ)若
为
的极小值点,求a的取值范围.
对于函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47db6b322f19cefcd70d0f8433917f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1459527045d2d138d1ee4b441aade53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55e6c43466d743ea37287656b85821c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570e972f51cd1d11acfd80a01c0512fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55e6c43466d743ea37287656b85821c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(1)请举出一个例子,说明该函数在某点处不可导,但是该点是该函数的极值点;
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae34b02b147bb49131a01316e07efaf.png)
(ⅰ)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d1735755a0f13e329df682712dd1d6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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2 . 第二十五届中国国际高新技术成果交易会(简称“高交会”)在深圳闭幕.会展展出了国产全球首架电动垂直起降载人飞碟.观察它的外观造型,我们会被其优美的曲线折服.现代产品外观特别讲究线条感,为此我们需要刻画曲线的弯曲程度.考察如图所示的光滑曲线
上的曲线段
,其弧长为
,当动点从
沿曲线段
运动到
点时,
点的切线
也随着转动到
点的切线
,记这两条切线之间的夹角为
(它等于
的倾斜角与
的倾斜角之差).显然,当弧长固定时,夹角越大,曲线的弯曲程度就越大;当夹角固定时,弧长越小则弯曲程度越大,因此可以定义
为曲线段
的平均曲率;显然当
越接近
,即
越小,
就越能精确刻画曲线
在点
处的弯曲程度,因此定义
(若极限存在)为曲线
在点
处的曲率.(其中
,
分别表示
在点
处的一阶、二阶导数)
的焦点到准线的距离为3,则在该抛物线上点
处的曲率是多少?
(2)若函数
,不等式
对于
恒成立,求
的取值范围;
(3)若动点
的切线沿曲线
运动至点
处的切线,点
的切线与
轴的交点为
.若
,
,
是数列
的前
项和,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d0dd437ad522066cc7d4b7d208e2866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/505d83f4d34a8cd385577a6ce93a4b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aea61ddc41f927684c6dfaacdd7f8e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0636a11a086df66133bd50e43481a546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/427eceadd7bb569ff140ea73d650db1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0636a11a086df66133bd50e43481a546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aea61ddc41f927684c6dfaacdd7f8e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/952bd235a906f77d227dfcfe1cbea780.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/505d83f4d34a8cd385577a6ce93a4b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.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/0e313d2b28b6d3d6273346e8f9bb78c9.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/9b4d2174f411d9db6ab7b2aea47818cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc2b6c6aec8cfad1ce0277d6db9759c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8516f71467b419293fa27df70bdaed74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ad52c0008b852946f7e316474e396d.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd589f01fd5de86d37e197e022f9dc36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/692a685d89c02da9bab03b7adbd66adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aedc1c8a16e306bcd6e5154f9ed6dfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
(3)若动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d637a9d76ce3058a0e9b561c832d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cac935140541b5e1ba7d7dfffdd8325.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3cbcc09d6f5004f2509aad50eef40f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4223bd6ee8f82d59d244371fbcddc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1e858cf44005397a29962fda98a020d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3819480e1e624208f729ad8653e4f24f.png)
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3 . 在直角坐标平面内,将函数
及
在第一象限内的图象分别记作
,
,点
在
上.过
作平行于
轴的直线,与
交于点
,再过点
作平行于
轴的直线,与
交于点
.
,请直接写出
的值;
(2)若
,求证:
是等比数列;
(3)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/052d51f01f5755f2f5571b199b776122.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b67c2cf5341e5f184482e26b4a428dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40eff3177abccb34ce65059ebb044d69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15520cf5be7c2685975aac51bc99ac4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15520cf5be7c2685975aac51bc99ac4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c15016fc7de1cd5971b7d38c70071e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14835bf3f00139ccec0694d0924db795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b93de100d473ce4b0ae2119361bf075.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/263b7015b9db8408066bac48d5dfec02.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14835bf3f00139ccec0694d0924db795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3939ac4d5544ab922514c790e9de9b3.png)
您最近一年使用:0次
名校
解题方法
4 . 已知双曲线
的渐近线为
,左顶点为
.
(1)求双曲线
的方程;
(2)直线
交
轴于点
,过
点的直线交双曲线
于
,
,直线
,
分别交
于
,
,若
,
,
,
均在圆
上,
①求
的值,并求点
的横坐标;
②求圆
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b75308335340230171130238f4dc6c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f4c1016bf87b416cff0f3fa79d3ef9c.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a4ea8632b4e4227131ba693deb10233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dda561466043a1648a62dbaa1a7a8d19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
②求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
解题方法
5 . 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
6 . 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
7 . 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
8 . 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)
您最近一年使用:0次
解题方法
9 . 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
10 . 泰勒公式是一个非常重要的数学定理,它可以将一个函数在某一点处展开成无限项的多项式.当
在
处的
阶导数都存在时,它的公式表达式如下:
.注:
表示函数
在原点处的一阶导数,
表示在原点处的二阶导数,以此类推,
表示在原点处的
阶导数.
(1)根据公式估算
的值,精确到小数点后两位;
(2)当
时,比较
与
的大小,并证明;
(3)设
,证明:
.
![](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/6368fec0c2c25db7c29b014d60270e97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90f07fcb0ae10d6d68a29552955f9587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b3ec7ada52f4850719a970aeb59ca16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/557057dab9ea3a5e42857dc305b66192.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f29b6f33826b7a6d9e5090fc0d135ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)根据公式估算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b0052214fdfd681b7703fedcfbfd65d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/483d7559ab4408d8f7fa63e14313a818.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efd9f874878e11c3fa25143023e8f95a.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f360bbd96198de7f111a98aa9244fc45.png)
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2卷引用:甘肃省张掖市某校2023-2024学年高三下学期模拟考试数学试题