1 . 设函数
,
.
(1)若函数
在点
处的切线方程为
,求实数
,
的值;
(2)在(1)的条件下,当
时,求证:
;
(3)证明:对于任意正整数
,不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/129961679b50baca31d081dd6af51d34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cfdccf88b4dd13ddcf13373b71c5034.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f1a686b80b8f109a929f58c2de7201d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)在(1)的条件下,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc4136bd17997e11a7f8abcb19f9018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab42740d8f095b5f7825d14c4c312096.png)
(3)证明:对于任意正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4687ea0588433399fcba64ca5e4857.png)
您最近一年使用:0次
2020-12-15更新
|
668次组卷
|
5卷引用:甘肃省兰州市西北师范大学附属中学2021-2022学年高三上学期期中数学试题
名校
解题方法
2 . 已知,图中直棱柱
的底面是菱形,其中
.又点
分别在棱
上运动,且满足:
,
.
![](https://img.xkw.com/dksih/QBM/2020/5/2/2453970522234880/2453997798014976/STEM/4358c504-ca50-4dc5-b48b-a8ee2b0667d6.png)
(1)求证:
四点共面,并证明
∥平面
.
(2)是否存在点
使得二面角
的余弦值为
?如果存在,求出
的长;如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa102f519d541f2e4d10a8975a41c36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d6dc34b0b71d46a91eb8dd8db01f5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360a93b9662f0ab8a69b131497520b53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/626db48efbecf4e318252ba13baff47d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1357d24d53b523a55b3eea7b21fa16f1.png)
![](https://img.xkw.com/dksih/QBM/2020/5/2/2453970522234880/2453997798014976/STEM/4358c504-ca50-4dc5-b48b-a8ee2b0667d6.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d6dc34b0b71d46a91eb8dd8db01f5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c51c4a1148587943fe9ba210f6141ee.png)
(2)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e807172fa9eca2416f92f341adc06165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
您最近一年使用:0次
2020-05-02更新
|
1267次组卷
|
5卷引用:甘肃省兰州市第一中学2020届高三冲刺模拟考试(三)数学(理)试题
甘肃省兰州市第一中学2020届高三冲刺模拟考试(三)数学(理)试题2020届河南省高三第十次调研考试数学(理)试题江西省分宜中学、玉山一中等九校2019-2020学年高三联合考试数学理科试卷河北省衡水中学2019-2020学年高三下学期第十次调研数学(理)试题(已下线)1.4 空间向量的应用-2021-2022学年高二数学尖子生同步培优题典(人教A版2019选择性必修第一册)
2014·北京石景山·一模
名校
解题方法
3 . 给定椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
,称圆心在原点
,半径为
的圆是椭圆
的“准圆”.若椭圆
的一个焦点为
,其短轴上的一个端点到
的距离为
.
的方程和其“准圆”方程;
(2)点
是椭圆
的“准圆”上的动点,过点
作椭圆的切线
交“准圆”于点
.
①当点
为“准圆”与
轴正半轴的交点时,求直线
的方程并证明
;
②求证:线段
的长为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da001dad7941e6c9858637d7b62cec59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c86bc114a286413e3933352392080a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
①当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce08b357f11ef44c3e8207ac574422a.png)
②求证:线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2016-12-02更新
|
1800次组卷
|
8卷引用:2014届甘肃省兰州一中高考模拟四理科数学试卷
(已下线)2014届甘肃省兰州一中高考模拟四理科数学试卷(已下线)2014届甘肃省兰州一中高考模拟四文科数学试卷(已下线)2014届北京市石景山区高三一模理科数学试卷2015-2016学年河北省石家庄一中高二下期中文科数学试卷河北省衡水中学2017届高三高考猜题卷(一)数学(理)试题山西省大同市第一中学2019-2020学年高三下学期模拟(六)数学(理)试题北京一零一中学2023届高三下学期开学考数学试题(已下线)微专题07 直线与圆锥曲线的相切问题
4 . 选修4-5:不等式选讲
(1)已知实数
满足
,证明:
;
(2)已知
,求证:
-
≥
+
-2.
(1)已知实数
![](https://img.xkw.com/dksih/QBM/2016/3/2/1572510233698304/1572510240079872/STEM/c42133797e144bd798b01c2bcdec893e.png)
![](https://img.xkw.com/dksih/QBM/2016/3/2/1572510233698304/1572510240079872/STEM/1a31445d95db400eb1b539cf279a670d.png)
![](https://img.xkw.com/dksih/QBM/2016/3/2/1572510233698304/1572510240079872/STEM/f22e36bb2d2441ae98abb36308569e68.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eda48853e8bdb7e266370b4e0d5a258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fccd1ef6cb6e28ae7ddc66b7e7bed1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2c70fcaa661df4fbcad820b439accda.png)
您最近一年使用:0次
2016-12-04更新
|
726次组卷
|
2卷引用:2016届甘肃省天水市一中高三上学期期末理科数学试卷
解题方法
5 . 已知函数
.
(1)求函数
的极值点及极值;
(2)若
,且
,求证:
为自然对数的底
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b614cf5dd093d2dcad7e25bcaeb7cb4.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636a8d9e362e768e825a98afdea2bd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2037b0bad7c7a312bac1ac0653d9a491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c35d9402d1cf63a34bc61b6602322032.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
您最近一年使用:0次
解题方法
6 . 如图,
为坐标原点,
为抛物线
的焦点,过
的直线交抛物线于
两点,直线
交抛物线的准线于点
,设抛物线在
点处的切线为
.
与
轴的交点为
,求证:
;
(2)过点
作
的垂线与直线
交于点
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b072ff6d1b83232bebd7d4709ffba4ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2e095298cfb23d9f47811556fc9f9a.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa3eae6aa7672b9eef122fb7a1dab14e.png)
您最近一年使用:0次
2024-03-13更新
|
1613次组卷
|
5卷引用:甘肃省兰州市2024届高三下学期三模数学试题
甘肃省兰州市2024届高三下学期三模数学试题湖北省七市州2024届高三下学期3月联合统一调研测试数学试题山东省潍坊市昌乐北大公学学校2024届高三下学期3月监测数学试题四川省成都市教育科学研究院附属中学2023-2024学年高三下学期4月综合测试数学(理科)试题(已下线)湖北省七市州2024届高三下学期3月联合统一调研测试数学试题变式题16-19
名校
7 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eb10f8ecb4ec7d3136bc662867968f2.png)
(1)若
求曲线
在点
处的切线方程.
(2)若
证明:
在
上单调递增.
(3)当
时,
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eb10f8ecb4ec7d3136bc662867968f2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b20439836def79ea69d967d95e81320a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87676cc3ca413d9ba64fab2cd45c909c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ec994bb92d9945a4369f1215d859ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-05-08更新
|
372次组卷
|
4卷引用:甘肃省白银市2023-2024学年高二下学期5月期中考试数学试题
名校
解题方法
8 . 已知抛物线
上有一点
,
为抛物线
的焦点,
,且
.
(1)求抛物线
的方程;
(2)过点
向圆
(点
在圆外)引两条切线,交抛物线
于另外两点
,求证:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c06d1663b8c2cfbe0308470a3b1c5d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/091bb3c75e9827076e9fbd84685c260e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0c2632c02415c656fb4bda6f89a8b08.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ba90e580d1cad80017e2b197262c8de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2023-12-05更新
|
834次组卷
|
2卷引用:甘肃省兰州市西北师范大学附属中学2024届高三第三次诊断考试数学试题
名校
解题方法
9 . 已知函数
.
(1)若曲线
在
处的切线
与直线
垂直,求实数
的值;
(2)当
时,不等式
对任意
恒成立,求实数
的取值范围;
(3)当
时,求证:存在实数
,使
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b79477a3ea39afb0b0a355da63450c6.png)
(1)若曲线
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9315b85140f138a28c6c9636a48bc441.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cfc7f05de73d4c0c2b5bc2e0560e65d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f391eb1348d7e749caecf0b47ae056.png)
您最近一年使用:0次
名校
解题方法
10 . 已知函数
.
(1)若
恰有两个极值点,求实数
的取值范围;
(2)若
的两个极值点分别为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/125c0225ea4ef140fd3236739a9aa024.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ced2ceab6d52a14af4d477a9ff09823.png)
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