1 . 将函数
的图象向左平移
个单位长度后,再把图象上所有点的横坐标伸长为原来的2倍,得到函数
的图象,若
与
的图象关于
轴对称,则
的一个单调递增区间为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3067458ed081dfa89fa963c00e4a6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aeb076bad84890e24dbdc945ad543cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 已知
,若
,使
成立,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ca3f0a4b2d06539e74594736881aaa.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dcbe8b4bcd32e5a64ebfd873f8cbb2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c43f45b7b6ad276af317b62deb0403aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd19790a2ff5a3f0e4bbb4770cbfeca5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ca3f0a4b2d06539e74594736881aaa.png)
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3 . 已知函数
,则以下结论正确的为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49d7965e727bef22e520eae65c55c0d5.png)
A.![]() ![]() |
B.![]() ![]() |
C.![]() ![]() |
D.将![]() ![]() |
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解题方法
4 . 在
中,
,则下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d14700df9fd609cd56da233d38ba9b08.png)
A.![]() |
B.![]() |
C.![]() |
D.向量![]() ![]() ![]() |
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5 . 如图,在
中,
,
为
的中点,
与
交于
点
设
,
.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97202521b8a0fafa6cd5bef52620a8c6.png)
(2)试用
表示
;
(3)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8945281a44657d65731ee7bebffa0ac5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b9d8a08fc52c31cc1a7f527d18b55c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f386f5b56b07b96f2600da1be15414a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97202521b8a0fafa6cd5bef52620a8c6.png)
(2)试用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2caf2e65bebc1523f8e89b59a90f2ab.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231ca1d2eef7dc64d75d713ea3335c21.png)
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解题方法
6 . 已知
,
,其中
,
.
(1)求
的值;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a2e2c779a79ea66d6d134b3f3e65003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03106022757d2899b6cf2c0455e263eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a6d589e032939e6135174eac55aa7ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3741c462a9186a80fcf1a3d7f6fa989c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22b3adfb25816cf11f7760d868c29cb7.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
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7 . 已知
,
恒成立,则实数
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f63b8d7f1005987bfec6efcb4f5b7039.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8079b1c177693ac34c225431e1aa2fe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
A.1 | B.![]() | C.2 | D.4 |
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8 . 已知
为坐标原点,函数
图象与
轴的一个交点为
,与
轴交于点
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9448bf1d6136b3a108e7ea60506ad39.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4991f5aea1d23a639bffc86a48b80243.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4420ef2452903556b13d76a7b6adb90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9448bf1d6136b3a108e7ea60506ad39.png)
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解题方法
9 . 已知单位向量
,
满足
,则
,
的夹角为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0411792b587ddd3e04440392f011c224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95d660852c5226ff65a21cfb36b8b39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/408efd32d3ae1e07e44716b024708029.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0411792b587ddd3e04440392f011c224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95d660852c5226ff65a21cfb36b8b39.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
10 . 某工厂有甲、乙两个生产车间,其污水瞬时排放量
(单位:
)关于时间
(单位:
)的关系均近似地满足函数
,其图象如图所示.
(1)根据图象求函数解析式;
(2)若甲车间先投产,1小时后乙车间再投产,求该厂两个车间都投产
时刻的污水瞬时排放量;
(3)由于受工厂污水处理能力的影响,环保部门要求该厂的两个车间任意时刻的污水排放量之和不超过
,若甲车间先投产,为满足环保要求,乙车间比甲车间至少需推迟多少小时投产?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ff4266515b801477248b32e10f3ac4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f42a97e3ae09c48e1d587f59af3621bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/795ea8d61f4e4e138231819356f4073b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/22/f9c7e29c-132e-490f-a765-86601184cddc.png?resizew=182)
(1)根据图象求函数解析式;
(2)若甲车间先投产,1小时后乙车间再投产,求该厂两个车间都投产
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16dca1f69db5d45d7e0195b60f546a40.png)
(3)由于受工厂污水处理能力的影响,环保部门要求该厂的两个车间任意时刻的污水排放量之和不超过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d18b1b3fa4bc1f8e48a68b9f77e37e3b.png)
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