名校
解题方法
1 . 设定义在
上的函数
与
的导函数分别为
和
.若
,
,且
为奇函数,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](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/e2d9ef1ee14460261cb9161a14a9cf15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0791590492af54730b09dae1715a71f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d7661d3fc28f785b438ad8c8f9d240a.png)
A.函数![]() ![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
7日内更新
|
834次组卷
|
3卷引用:高三数学考前押题卷3
名校
解题方法
2 . 已知函数
及其导函数
的定义域均为
,记
.若
与
均为偶函数,且
,则下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090a91e4f3c8930674f98a9fa527709b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55d6fa911e3396b34fb470c10b063fde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1aa50ff3aa2aa872bc41acaab8787b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb1755255a99ef00869962bb8e745ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb7326ef4ba9ace3e76f3c17370a2d8e.png)
A.![]() | B.![]() ![]() |
C.![]() | D.![]() ![]() |
您最近一年使用:0次
名校
解题方法
3 . 英国数学家泰勒发现的泰勒公式有如下特殊形式:当
在
处n(
)阶导数都存在时,
.注:
表示
的2阶导数,即为
的导数,
(
)表示
的n阶导数,该公式也称麦克劳林公式.
(1)写出
泰勒展开式(只需写出前4项);
(2)根据泰勒公式估算
的值,精确到小数点后两位;
(3)证明:当
时,
.
![](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/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fb7618da716747c7cf514bbd1c58ad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33cfe27fd2276a7c542f062c17b4d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/008ab9b6200370bd8d534a6317cb88e2.png)
(2)根据泰勒公式估算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d62638ee25e93270870aa42a1972593b.png)
(3)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9140ad56e13c6e89242f9cea2abf151e.png)
您最近一年使用:0次
名校
解题方法
4 . 已知函数
,
及其导函数
,
的定义域均为
,若
的图象关于直线
对称,
,
,且
,则( )
![](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/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18377150b1ced455e66c9054f7305379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/097b4f1d906fa77a62768d8aa7490088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bb821d367d7b4fbb520368728aec3af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45014b89f4ad836abba5cc21342131bd.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
5 . 已知函数
,若函数
有4个零点,则
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b1604e4e586fcd6445b73f964b1011.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6785823721fb2e288b417ba2d617ef04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
6 . 已知定义在
上的可导函数
和
满足:
,且
为奇函数,则导函数
的图象的一个对称中心为__________ .(写出一个即可);若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/953429ee5defb3a2c68d4ec38405b474.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](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/921ec0c8166584567ff16e7549a30761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6d578f9c98ce402d4cf6e4a23281c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22add663bd26e87d972a10dc5fd9ada1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bc2b7be871fef904c94ef6360ee32bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45a173784888adf2946382fa093ba53a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/953429ee5defb3a2c68d4ec38405b474.png)
您最近一年使用:0次
2024·全国·模拟预测
解题方法
7 . 已知函数
的定义域为
,
是奇函数,
,
,
分别是函数
,
的导函数,
在
上单调递减,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e81e15b871dd32b2438ef8025bcc42d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a4343f10c051cab3f0522ccbaae21a9.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/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be381da62d4a042476aa11dbd5824e8d.png)
A.![]() | B.![]() |
C.![]() ![]() | D.![]() |
您最近一年使用:0次
2024·全国·模拟预测
8 . 已知函数
,且
有两个相异零点
.
(1)求实数a的取值范围.
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c3829d9ff4c94d6fd6181017e7cff42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
(1)求实数a的取值范围.
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f535817437939db1daf3fb7a9d79e510.png)
您最近一年使用:0次
解题方法
9 . 已知函数
及其导函数
的定义域均为
,若
的图象关于直线
对称,
,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c0ed188d083966baaae94e6b86064f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a290d6204cec463ca2083cc899787fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5d7f58f3feaf8d34acf8b4ad7c7c8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b82059eeec3ed6c05451395f25ba74d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07dc7732661a9266477cb20c91e3afcc.png)
A.![]() | B.![]() ![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
10 . 定义在
上的函数
与
的导函数分别为
和
,若
,
,且
,则下列说法中一定正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](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/d757de34c4a2144321859d0e117ddb41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f095a45c021d25fd2f96e6d8600281b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/682dfa0c0762ca05320e9b1519cac231.png)
A.![]() | B.![]() |
C.函数![]() | D.![]() |
您最近一年使用:0次
2024-04-26更新
|
2225次组卷
|
3卷引用:湖北省武汉市2024届高三下学期四月调考数学试卷