1 . 当x是什么实数时,下列各式有意义?
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3ec8454402ff44a030658b4a46f786c.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac3c9f8dc597df12c501c8d6a8a81118.png)
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2 . 函数
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4cec4155e87d372a443f337bf62f2af.png)
A.当![]() ![]() ![]() |
B.当![]() ![]() ![]() |
C.对任意![]() ![]() ![]() |
D.存在![]() ![]() ![]() |
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7卷引用:河北省唐县第一中学2022-2023学年高二上学期9月月考数学试题
河北省唐县第一中学2022-2023学年高二上学期9月月考数学试题福建省三明第一中学2023届高三上学期第二次月考数学试题江西省宜春市丰城中学2023-2024学年高一下学期第三次段考(5月月考)数学试题山东师范大学附属中学2022届高三下学期高考考前检测(打靶题)数学试题(已下线)专题09导数与函数的单调性-2022年新高三数学暑假自学课精讲精练(已下线)第40练 导数在研究函数中的应用辽宁省沈阳市东北育才学校科学高中部2023-2024学年高二下学期期中考试数学试题
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3 . 两平行直线
和
之间的距离为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee080177fb5a1d6e4b969ee1c8290c5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05317dc974a2029540cea23df5c1b775.png)
A.![]() | B.2 | C.![]() | D.3 |
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4 . 已知
,
,
.
(1)求
的最大值;
(2)求
的最小值.
![](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/743f8ca922b6fed0798fa794aadf922c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f0281e6bbdbe08beeccb55adf84536.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b0113fd4c7d157757571f9a009e02af.png)
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解题方法
5 . 如图,在三棱柱
中,
,
为
的中点,E为
的中点,
和
相交于点P,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc2ddabf078c1b683b067eb1aee1969.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e141fbf1a87b34f062bf4518498deebe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07efb4fa33e8e75784eed4a584e10f1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc2ddabf078c1b683b067eb1aee1969.png)
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6 . 如图,在四棱锥
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2234205f80829a5bbc6ae3a675fe4f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28155ab6f06636cae7e5a4eb07e580d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/836ac3d625647007c99532bac34a6f92.png)
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a8911f5302c0a65c1d28c0ed1c939e.png)
为
的中点.
平面
;
(2)求平面
与平面
的夹角的余弦值的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2234205f80829a5bbc6ae3a675fe4f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28155ab6f06636cae7e5a4eb07e580d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/836ac3d625647007c99532bac34a6f92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d618f2f945043c0fc4b2bb492206d4cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a8911f5302c0a65c1d28c0ed1c939e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c372d059202ec388960b125d4a87dc84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4d781525777c7b5284dffc70b2a28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
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解题方法
7 . 已知直线
与x轴,y轴的正半轴分别交于
两点,O为坐标原点.
(1)求
的最小值;
(2)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2751a2edaff7f91790559a492a4fae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f662756a3c4cbbc8868adbfed6b1f44f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba36a367738b4452e3b6190940284fe7.png)
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解题方法
8 . 在
中,顶点A在直线
上,顶点B的坐标为
边的中线
所在的直线方程为
边的垂直平分线的斜率为
.
(1)求直线
的方程;
(2)若直线l过点B,且点A、点C到直线l的距离相等,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed59365933336b28746c66e2dc34cb50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7ccb93f0e7eedbf5e90c0ee38f08fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533a7b702ada1dd80123e4041271d521.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)若直线l过点B,且点A、点C到直线l的距离相等,求直线l的方程.
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9 . 在空间直角坐标系中,已知向量
,点
,点
.若直线l经过点
,且以
为方向方量,P是直线l上的任意一点,O为坐标原点.
(1)求证:
;
(2)当
,且
时,求点P的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba436b158708e7325885fea7106e92b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c832b5312310a88bef6596496df8daa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bfcaf2a345411411cf94422703e9269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d71d1e5f816103a951d6ebf10af047b.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1f0582d9908f92f14cb02a6ccaf0eae.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1965236b071589fcdd33364bb0a92d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db835cce1e68a580450593b3905e5d8.png)
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10 . 已知点
,过点
的直线l与线段
相交,则直线l的倾斜角的取值范围为_______ ,直线l的斜率的取值范围为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d172482cd87dc31267dd05550a1b2fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc210625e54a64a625eaa3dbf841c9f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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