名校
解题方法
1 . 已知抛物线
为抛物线
上两点,
处的切线交于点
,过点
作抛物线
的割线交抛物线于
两点,
为
的中点.
(1)若点
在抛物线
的准线上,
(i)求直线
的方程(用含
的式子表示);
(ii)求
面积的取值范围.
(2)若直线
交抛物线
于另一点
,试判断并证明直线
与
的位置关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58de54f99bfa33c290ceffe1e8c33e7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(i)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(ii)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dca049735b45fb9b2533c68605eddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e0a8cfb3747c454e0698e12857ffae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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名校
解题方法
2 . 微积分的创立是数学发展中的里程碑,它的发展和广泛应用开创了向近代数学过渡的新时期,为研究变量和函数提供了重要的方法和手段.对于函数
在区间
上的图像连续不断,从几何上看,定积分
便是由直线
和曲线
所围成的区域(称为曲边梯形
)的面积,根据微积分基本定理可得
,因为曲边梯形
的面积小于梯形
的面积,即
,代入数据,进一步可以推导出不等式:
.
;
(2)已知函数
,其中
.
①证明:对任意两个不相等的正数
,曲线
在
和
处的切线均不重合;
②当
时,若不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78e5de9b684beb1bafc89efd5af8b8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/644ba16341e356b57ea153e840555290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb9e8df0db7e14434837c5ad77f27e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f42b2a9736c8943106472a7398d2892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe83f1ae7e5f05d8bed6bf6f42db0e7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e02b3995488ad13babd4eeb6f99c40e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe83f1ae7e5f05d8bed6bf6f42db0e7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe83f1ae7e5f05d8bed6bf6f42db0e7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b601337ff73bafe04fc3e40d0061fddd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aef73511ddedc2ab4b5bf17500554971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/422f124d4c171787c292326b1d1c655c.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d6c7daa90a08a84c1fe48d29ffe86e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe52e15d70c4355d101d333f8e6dc258.png)
①证明:对任意两个不相等的正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a24a2c53e3b0b1c08803e95419f909d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecaca8409b3f51d22667a14559c58ea4.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86304c3e26200299a0480641525a283.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d64909edca036b1463f214d977604.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-03-13更新
|
1660次组卷
|
6卷引用: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
(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湖南省长沙市周南中学2024 届高三下学期第二次模拟考试数学试题甘肃省兰州市2024届高三下学期三模数学试题河北省正定中学2024届高三三轮复习模拟试题数学(二)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安徽省淮南第二中学2023-2024学年高二下学期期中教学检测数学试题
解题方法
3 . 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)
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2024-03-13更新
|
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5卷引用: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
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
名校
4 . 如图,在平面直角坐标系
中,半径为1的圆
沿着
轴正向无滑动地滚动,点
为圆
上一个定点,其初始位置为原点
为
绕点
转过的角度(单位:弧度,
).
表示点
的横坐标
和纵坐标
;
(2)设点
的轨迹在点
处的切线存在,且倾斜角为
,求证:
为定值;
(3)若平面内一条光滑曲线
上每个点的坐标均可表示为
,则该光滑曲线长度为
,其中函数
满足
.当点
自点
滚动到点
时,其轨迹
为一条光滑曲线,求
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c9643bf4dd7e04efa4644412491725.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c81b29ac8a01886b25dcef55c5f6877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2ce55c4ff508755d16c375625437027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69218ef831edc8173b4029ea99eda87.png)
(3)若平面内一条光滑曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc031988b2a4dcd840069dbd3a1c810e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dfe48a76ae71f8925b731e8c330bdb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5d69e7fb25c60ee47440a1ece037544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8a8bcf6ef69b6bdfc84e8472a259bf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/016b58ad9076316abaf809dea297256a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/016b58ad9076316abaf809dea297256a.png)
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2024-03-13更新
|
1232次组卷
|
3卷引用:河南省南阳市西峡县第一高级中学2023-2024学年高二下学期第一次月考数学试卷
解题方法
5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bdee65db35313743a537d96ed2f0831.png)
(1)若
、
在
处切线的斜率相等,求
的值;
(2)若方程
有两个实数根
,试证明:
;
(3)若方程
有两个实数根
,试证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bdee65db35313743a537d96ed2f0831.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f6bfdb24ecf5da863405c2b40936ff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba4e318eba446aef74e47ff27fda7bc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/997d775991025c149f6a656931cf5db7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b87b477193037370c7cd460aa8af84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ba6f1cb9a8489f25f9f9342ae9607d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26225aadb1a29223725c698a3d8f55ea.png)
(3)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09ee18c937a4646a2cad1be7e2b6649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ba6f1cb9a8489f25f9f9342ae9607d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a642c61b048e72d63146f40e9acd01e.png)
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2024高三上·全国·专题练习
6 . 已知函数
、
,
的图象在
处的切线与
轴平行.
(1)求
,
的关系式并求
的单调减区间;
(2)证明:对任意实数
,关于
的方程:
在
,
恒有实数解;
(3)结合(2)的结论,其实我们有拉格朗日中值定理:若函数
是在闭区间
,
上连续不断的函数,且在区间
内导数都存在,则在
内至少存在一点
,使得
.如我们所学过的指、对数函数,正、余弦函数等都符合拉格朗日中值定理条件.试用拉格朗日中值定理证明:
当
时,
(可不用证明函数的连续性和可导性).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/805cc5abd1128e45df7cad0a9e2045db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ddf844e3848b8bf52c0ec506fe749c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e464a3586f84fcdf7d221619f8018144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ffe604dac7e511c06aa339460743ba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)证明:对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636a8d9e362e768e825a98afdea2bd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94df95ba3ef31cd7a065d112c619e88e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7957f902f96c3adb9d374d92ff87d287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/486cdd923c2b4c92928b10ab6266e792.png)
(3)结合(2)的结论,其实我们有拉格朗日中值定理:若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f944dbcd1a2a1cc595573f63b244e9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4cfd131ea8772fea719318c865c907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2982ec308d84c83d538a58dae3ff1569.png)
当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e14206c7d228a7c2259a7b27da8813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa5f5a7cf79c07caa572cfee93371a91.png)
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2024·全国·模拟预测
7 . 如果有且仅有两条不同的直线与函数
的图象均相切,那么称这两个函数
为“
函数组”.
(1)判断函数
与
是否为“
函数组”,其中
为自然对数的底数,并说明理由;
(2)已知函数
与
为“
函数组”,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8fd1e808e015f4cb43d2e3a0529ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8fd1e808e015f4cb43d2e3a0529ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bea75e6fa8f587c7afff0ffb563b921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db192285632d1991b4ee7a003a52205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a3eda8f315eb3b1e949c7a0989b9bd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30612ee82e71ff4c6f831f1b43c25bf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024高三·全国·专题练习
8 . 设函数
上任意两点的斜率属于集合
,则称函数
是斜率集合
上的函数.
(1)写出一个
上的函数;
(2)写出一个
上的函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
(1)写出一个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b781a41f7c14b6733b8cb6c380171af1.png)
(2)写出一个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dda33e04a6c6220b1cfac0adacc8013e.png)
您最近一年使用:0次
名校
解题方法
9 . 若函数
在定义域内存在两个不同的数
,
,同时满足
,且
在点
,
处的切线斜率相同,则称
为“切合函数”.
(1)证明:
为“切合函数”;
(2)若
为“切合函数”(其中
为自然对数的底数),并设满足条件的两个数为
,
.
(ⅰ)求证:
;
(ⅱ)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](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/abf7c745cd02f4620a175cf00ec85e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a24a2c53e3b0b1c08803e95419f909d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecaca8409b3f51d22667a14559c58ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe0de54dfc96a2291e8d5e56676eabc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fb46178ba0560d96bd3a05891505b95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c20b8bd265b07dd90690ad4e349c6dc.png)
(ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84cde09c609543feedc2e0c11992b2bd.png)
您最近一年使用:0次
2024-01-03更新
|
1036次组卷
|
4卷引用:重庆市沙坪坝区南开中学校2024届高三上学期第五次质量检测数学试题
重庆市沙坪坝区南开中学校2024届高三上学期第五次质量检测数学试题(已下线)微考点2-5 新高考新试卷结构19题压轴题新定义导数试题分类汇编重庆市南开中学校2024届高三上学期第五次质量检测数学试题江西省赣州市南康中学2024届高三上学期新高考“七省联考”考前数学猜题卷(一)
10 . 对于函数
,分别在
处作函数
的切线,记切线与
轴的交点分别为
,记
为数列
的第n项,则称数列
为函数
的“切线-
轴数列”,同理记切线与
轴的交点分别为
,记
为数列
的第n项,则称数列
为函数
的“切线-
轴数列”
(1)设函数
,记
“切线-
轴数列”为
,记
为
的前n项和,求
.
(2)设函数
,记
“切线-
轴数列”为
,猜想
的通项公式并证明你的结论.
(3)设复数
均为不为0的实数,记
为
的共轭复数,设
,记
“切线-
轴数列”为
,求证:对于任意的不为0的实数
,总有
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ed953d6e0bd80a5da66552c7bfbcbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd3d48fa9493a86f262569df235a82ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.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/8292395dc894796602a60486e575a808.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a79b9eaa5e7ab7a1e5c512b571914dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36460040ddea4761eee10d537b14a1f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36460040ddea4761eee10d537b14a1f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ef5756fec38d1b4dc62358b45c3352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e845964df4b271bd7b4cf99ede79be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(3)设复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80bcf306a6aa8554d1d7fc8317f4e946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fcfebd9f5a57036e6df6b6e14865da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec5f303f666e164582da05968d9d8cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe6f044a9b06a7a769e613c977cbfb87.png)
您最近一年使用:0次
2024-01-01更新
|
443次组卷
|
7卷引用:模块一专题1【练】《导数的概念、运算及其几何意义》单元检测篇B提升卷(人教A2019版)
(已下线)模块一专题1【练】《导数的概念、运算及其几何意义》单元检测篇B提升卷(人教A2019版)(已下线)模块二 专题1 与曲线的切线相关问题(已下线)模块二 专题3 与曲线的切线相关问题(人教B版)(已下线)模块二 专题4 与曲线的切线相关问题(高二北师大版)上海市普陀区桃浦中学2022-2023学年高二下学期期中数学试题(已下线)模块一 专题1 《导数的概念、运算及其几何意义》B提升卷(苏教版)(已下线)模块二 专题1 与曲线的切线相关问题(苏教版高二)