名校
解题方法
1 . (1)讨论函数
在区间
内的单调性;
(2)存在
,
,满足
,且
.
(ⅰ)证明:
;
(ⅱ)若
,证明:
.(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa2f102710ab36f730e3295846f2a11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbfe8e7fb253685e0e50bae0c5482314.png)
(2)存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae8646b528af1835efe850241749ea77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167435d42312f20ed1d83d49c022f8a5.png)
(ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a8a1a2dfd5488a95a8693907bdcb9b4.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e16d06a51dcc46f94863e35ec72ba6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dc042c4c577a2fa2060ee13bb89345a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/830b99ffb2e33df5b4049e3ea9e7f8de.png)
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名校
2 . 设
,
.
(1)若x,y均为锐角且
,求z的取值范围;
(2)若
且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d018fc39fe3a5feee51a08ee8c58483e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ebed1b93046c28dd4ce381df0ca441f.png)
(1)若x,y均为锐角且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3085600fba3d8ce8403ddc8b44996f88.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7204495706847fd4c8abc55e89c9a35f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/598caae9102ce0b49bdd2ea12189562d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eca80d80b6e1577762585b69145736b.png)
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3 . 如图,射线
与圆
,当射线
从
开始在平面上按逆时针方向绕着原点
匀速旋转(
,
分别为
和
上的点,转动角度
不超过
)时,它被圆
截得的线段
长度为
,其导函数
的解析式为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59e8a44c0cc68a81eff5a4087c2977a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34517f479fb08f6096d2fb0362f3ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34517f479fb08f6096d2fb0362f3ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a9781cd710e738d50a0f5c00f72e20d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4914f1618e5ac34457b9024e369e04c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4db499c2fbdd1b794ccb619c1fafa3c6.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2卷引用:四川省成都市石室中学2024届高三下学期三诊模拟考试理科数学试卷
名校
4 . 函数
与其导函数为
,满足
,其中
;若
,
,其中
,则下列不等式一定成立的有( )个
①
②![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e49359c5c9d119d81b08e8ca91c404.png)
③
④![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3500100f631dd8326d743a4a2b666a8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22add663bd26e87d972a10dc5fd9ada1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1532cefdaf4b6df045285000b288b6d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ac256ea57fc89c474d34015f8c0154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/372dab8fa0ad684436da35abd1a49af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60132f7361a76fd4e780a6c98de9f1e1.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6800a8cc57f3655f62ca47f7846b8a6.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e49359c5c9d119d81b08e8ca91c404.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46c7bd551420f2adbc8fb35f31a5130c.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3500100f631dd8326d743a4a2b666a8b.png)
A.1 | B.2 | C.3 | D.4 |
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3卷引用:四川省成都市第七中学2023届高三下学期三诊模拟考试理科数学试题
四川省成都市第七中学2023届高三下学期三诊模拟考试理科数学试题四川省广安友谊中学2022-2023学年高二第一次“零诊”模拟考试理科数学试题(已下线)第三章 利用导数比较大小 专题二 同构抽象函数比较大小 微点1 构造抽象函数比较大小(一)——初等型
5 . 设△ABC的内角A,B,C所对的边分别为a,b,c,在以下①、②、③中选择一个作为条件,并加以解答,如果①、②、③都做,则按①给分.
①向量
与向量
平行.
②![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b19988d792b5252222f0a7acf7ef5fd.png)
③![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18242efb0b3c3c1f30dfe6cd6918d42f.png)
(1)确定角A和角B之间的关系;
(2)若D为线段BC上一点,且满足BD=AD=4,若2a=3b,求b.
①向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62eba072d428ffcfda58b5746a576f3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90931e663f5db43a81fbec2d15c18e2c.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b19988d792b5252222f0a7acf7ef5fd.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18242efb0b3c3c1f30dfe6cd6918d42f.png)
(1)确定角A和角B之间的关系;
(2)若D为线段BC上一点,且满足BD=AD=4,若2a=3b,求b.
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2022-06-01更新
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