19-20高一·浙江杭州·期末
1 . 已知抛物线
的焦点为F,A为抛物线C上异于原点的任意一点,过点A的直线l交抛物线C于另一点B,交x轴的正半轴于D,且有
,当点A的横坐标为
时,△
为正三角形.
![](https://img.xkw.com/dksih/QBM/2020/11/3/2585105299791872/2585152151937024/STEM/f6f0ee845735471a8d90af7162ecb0fa.png?resizew=219)
(1)求抛物线C的方程;
(2)若直线
,且
和抛物线C有且只有一个公共点E,求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d985a6326bae94867aa0fa132e896667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa3254460ecbacecb3e57c5dce227f4.png)
![](https://img.xkw.com/dksih/QBM/2020/11/3/2585105299791872/2585152151937024/STEM/f6f0ee845735471a8d90af7162ecb0fa.png?resizew=219)
(1)求抛物线C的方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e88c9366bb209931c6b28353dbab9a52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
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2 . 已知抛物线
的内接
满足直线
都是抛物线
的切线.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/c965b7bb-c17e-4aa0-9d77-20a69b635d28.png?resizew=169)
(Ⅰ)证明:
是抛物线
的切线;
(Ⅱ)已知G为
的重心,求
上的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374fe9986ebbc986fc422e514ab93a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/c965b7bb-c17e-4aa0-9d77-20a69b635d28.png?resizew=169)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
(Ⅱ)已知G为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa5fe243b7f7874c56c0410ce644b88e.png)
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解题方法
3 . 已知函数
.
(Ⅰ)若
恒成立,求实数a的最大值;
(Ⅱ)若
恒成立,求正整数a的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb0b55c269a8c20c465e4cb44ae95a6.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb6c9c69606bbf4f3e94275e0491703.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
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4 . 已知椭圆
的左焦点
,点
为椭圆C上一点,如图,经过圆
上一动点P作椭圆C的两条切线分别切于点A,B,切线分别与圆O相交于异于点P的点M,N.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/5c16e354-4238-46d9-9c27-07d167cfb51c.png?resizew=252)
(1)求椭圆C的方程;
(2)记
.
(i)证明:
;
(ii)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17618d8d22ebb3fd6835a7eb139b4f95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/972e310785333d1f608db89586ae837b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f62686f6f9118291c444a8d5a4d0f8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/5c16e354-4238-46d9-9c27-07d167cfb51c.png?resizew=252)
(1)求椭圆C的方程;
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/195a75bd930d89560bd2974c23c255e1.png)
(i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/467927b7e2860d6fedee32bdd0958adf.png)
(ii)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60138017c5e26202533126213e4c80d5.png)
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解题方法
5 . 已知函数
,其中
是自然对数的底数.
(1)若
有三个极值点
,
(i)求实数
的范围;
(ii)求证:
;
(2)若
有三个零点
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c58cab464a4364c3eb63b21187cc5ecc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aae6f2334212a5c6f8e29f1345835d67.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdbcebe6adbb6abcc3706bb8b3652797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
(i)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9b0c4ce20f493a7edf5ca34c571560b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed0874db583bdba067056872f236e372.png)
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6 . 已知椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff739204ba760216f82a5802e92cb244.png)
左顶点为
,离心率为
,且过点
.
![](https://img.xkw.com/dksih/QBM/2020/10/10/2568028685623296/2569376604782592/STEM/7c153ce2518b468490fe7139e8a7a7ae.png?resizew=168)
(1)求
的方程;
(2)过抛物线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
上一点P的切线
交
于
两点,线段
,
的中点分别为
.求证:对任意
,都存在这样的点P,使得
所在直线平行于
轴.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff739204ba760216f82a5802e92cb244.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e454c7161999e2a67138869f59d319b.png)
![](https://img.xkw.com/dksih/QBM/2020/10/10/2568028685623296/2569376604782592/STEM/7c153ce2518b468490fe7139e8a7a7ae.png?resizew=168)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
(2)过抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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解题方法
7 . 已知函数
,
.其中
,
为常数.
(1)若函数
在定义域内有且只有一个极值点,求实数
的取值范围;
(2)已知
,
是函数
的两个不同的零点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f684e1a86c9eadf392420ec3d31e8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a12d1f442576182a4f5e6e57b0f30eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8cae6d37a195a005adec79e3f312fa8.png)
您最近一年使用:0次
8 . 已知函数
,
.
(1)若
,求函数
在
上的单调区间;
(2)若
,不等式
对任意
恒成立,求满足条件的最大整数b.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fad29e5b0c7596f0d67de50b5387d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ff8dca35b759d3051b62badd7d76bc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a35f583b51648519c8037ff9e1130761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68397aabfec82d81635a0ac1bdd5eaa3.png)
您最近一年使用:0次
2020-10-10更新
|
1230次组卷
|
6卷引用:浙江省五校2020-2021学年高三上学期第一次联考数学试题
浙江省五校2020-2021学年高三上学期第一次联考数学试题(已下线)【新东方】杭州新东方高中数学试卷319(已下线)考点44 导数与函数的单调性-备战2021年新高考数学一轮复习考点一遍过(已下线)第五章 一元函数的导数及其应用-2020-2021学年高二数学同步课堂帮帮帮(人教A版2019选择性必修第二册)湖北省武汉市2020-2021学年高二下学期第一次调研数学试题(已下线)专题2-7 导数压轴大题归类-1
名校
9 . 已知
,函数
.
(1)若函数
恰有2个零点,求实数a的取值范围;
(2)若
,求实数x的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e44fe6b40e6531e53ec96557d8cf96c.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eedfd48e5718ea98ba4e7ac434672444.png)
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2020-10-09更新
|
1178次组卷
|
2卷引用:浙江省杭州市第二中学2020-2021学年高一(尖子班)上学期开学考数学试题
名校
10 . 设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31aebeaf09e071ddf4698a8babe013b6.png)
(1)若
,求函数
的图象在
处的切线方程;
(2)若不等式
在区间
上恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31aebeaf09e071ddf4698a8babe013b6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62830517d5b2885fb0cc883b1b1db63d.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba097900f4a0fecc7cf0a3279aad92e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9290b715477462dab9cb56e2e477aa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2020-10-07更新
|
699次组卷
|
2卷引用:广东省2021届高三上学期调研数学试题