1 . 曲线的曲率定义如下:若
是
的导函数,令
,则曲线
在点
处的曲率
.已知函数
,
,且
在点
处的曲率
.
(1)求
的值,并证明:当
时,
;
(2)若
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0268c3aeac7836cf0d453efc67f3ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe7522a3f232bd0b7a7850ae674db43f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ae838c10d4fc8c474d7873dc8cfd07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b72cd624f7e5bfe6549f3e62f0432a17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d4aa0ab41b5773fd67600fe2de77d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c6b6a11760d0724b0b60e55970e229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b301df975f8b3b3ba0cab5c4f8f12028.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05fce924911d5ed93147dfce9e41c2b0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a9e96e2ed7d9cd25c06f9a51a7210a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de6e9b440a15088e5f450cd4438ae72f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c3fdcd52eebd86207b01a571c845f6.png)
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2021-05-02更新
|
791次组卷
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5卷引用:山西省晋城市第一中学校2024届高三上学期11月期中数学试题
山西省晋城市第一中学校2024届高三上学期11月期中数学试题湖南省永州市2021届高三下学期三模数学试题(已下线)专题3.13 不等式的证明问题-2021年高考数学解答题挑战满分专项训练(新高考地区专用)(已下线)第五篇 向量与几何 专题21 曲率与曲率圆 微点1 曲率与曲率圆(一)(已下线)拔高点突破05 函数与导数背景下的新定义压轴解答题(九大题型)
2 . 证明下列不等式:
(1)用综合法证明:若
,
,求证:
;
(2)用分析法证明:
.
(1)用综合法证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80287215203122127583e8299f9dfe66.png)
(2)用分析法证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14c19d94ff48082c1cd213c82c99abf0.png)
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名校
3 . 如图1,在
中,
,
,点D是线段AC的中点,点E是线段AB上的一点,且
,将
沿DE翻折到
的位置,使得
,连接PB,PC,如图2所示,点F是线段PB上的一点.
,求证:
平面
;
(2)若直线CF与平面
所成角的正弦值为
,求线段BF的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08313da7b66283d2e0b3987f3e6761f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cedd51383f8f047f565191b128cec637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c38dfd14dde969702dff97ef2270f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cff7399ecc698e2fb415147c96d0d03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d31767eb718a0327eca546fe6a189cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14f95bd1d1d76dc662129716ef859ed7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94270844f197d524bf1da4f1385befd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37793a3a810e823e10c340986f55ddd.png)
(2)若直线CF与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ca53e20efea6aba3b60261ee5f0f4e.png)
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2024-04-19更新
|
924次组卷
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3卷引用:山西省晋城市2024届高三第二次模拟考试数学试题
名校
解题方法
4 . 如图所示,在等腰直角
中,
,点
、
分别为
,
的中点,将
沿
翻折到
位置.
;
(2)若
,求平面DEF与平面DEC夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc0ff6ac76f024f57a606db5cda137e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3cd6a7b1a8edf3a190c4bf09fca6bcf.png)
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2024-06-14更新
|
142次组卷
|
2卷引用:山西省晋城市第一中学校2023-2024学年高二下学期第四次调研考试(5月)数学试题
名校
5 . 已知椭圆
的离心率
为
的上顶点,
为椭圆
上任意一点,且满足
的最大值为4.
(1)求椭圆
的方程;
(2)已知
.过点
的直线
(斜率存在且不为1)与椭圆
交于
两点.证明:
平分
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc231ad55c226c9bc51247c7323c440a.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe73f01a31b3fbd401fda4270486d66.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa0b650c5cfcdc793ca76faab05526bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/a09245fd7604997221b9a1a6e8fb752f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2f9c3b578fc0598d5ec6c79404c6cc2.png)
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解题方法
6 . 在
中,角A,B,C所对的边分别为a,b,c,且
.
(1)证明:
为等腰三角形.
(2)若D是边BC的中点,
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2818bff73d7e297bfbcda3d22d1a153.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若D是边BC的中点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb9af00d442a5c693c970f30efcc916f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2024-06-11更新
|
1278次组卷
|
3卷引用:山西省晋城市第一中学校2024届高三下学期高考模拟预测数学试题
解题方法
7 . 已知函数
(
).
(1)若
,求
的图象在
处的切线方程;
(2)若
对于任意的
恒成立,求a的取值范围;
(3)若数列
满足
且
(
),记数列
的前n项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9ffd54ce2a16250f77e7819306c6d67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d32d1a5a0732c7e4af737555e44ff9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c355f11471a38f5583a434a1ddeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3b621694ea855745959e451ab8d84f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b4cd599990014f71ab8253199a917a.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588e4f939835eeb5feefdb5d37c921e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca1d86c9f078347773f700fee49d1d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c9892d5b37a00bde9648eebfc438d1.png)
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2024-05-01更新
|
1073次组卷
|
3卷引用:山西省晋城市2024届高三第二次模拟考试数学试题
名校
8 . 已知函数
.
(1)若
恰有两个零点,求a的取值范围;
(2)若
的两个零点分别为
(
),求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e498dc0ac7b435ae0b600df63b9e2950.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.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/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4d60d1ff5429bd35707fd80d714dc93.png)
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2024-04-01更新
|
655次组卷
|
5卷引用:山西省晋城市第一中学校2024届高三下学期高考模拟预测数学试题
名校
解题方法
9 . 已知
为公差不为0的等差数列
的前
项和,且
.
(1)求
的值;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5226b1157bf9469864a0c238d58e65d6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae2e6956e0073cef684fef6a16bead0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc8dd99dba987abc303cfbdbf9dbab1d.png)
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2024-03-08更新
|
2295次组卷
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7卷引用:山西省晋城市第一中学校2023-2024学年高二下学期第二次调研考试数学试题
解题方法
10 . 已知椭圆的焦点是椭圆
的顶点,椭圆
的焦点也是
的顶点.
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/654317ca05d25fee978869723ba8d0c8.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937c5db73d81da5525d4d35885dac04f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8112f9185c7d48b015d9cd0525616b31.png)
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