名校
解题方法
1 . 已知
且
,若函数
,的最大值不超过1,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eab873855ed8ca580c0ac1f461ccc3b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
2 . 函数
的定义域为
,
为奇函数,且
为偶函数,当
时,
.
①A,B是锐角
的内角,
;
②
;
③
;
④
.
其中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105068fe440b555880e9c566e6fd3f5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d7661d3fc28f785b438ad8c8f9d240a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4e9ed540a4aff2db2f887b81e0b982.png)
①A,B是锐角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a673984ab88416f50a8496242427cdbe.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f227bbeda10306a74beb7cb2e5df2d.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45691cfa763ee20fcfc741fcdb74d8f4.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/220b656c067ac8a548f1f7926c80dd38.png)
其中正确的有( )
A.②③④ | B.①② | C.①②④ | D.①②③ |
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3 . 已知函数
的部分图象如图所示下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fabc46b4c77ed40e1fdf1df623961fee.png)
A.![]() |
B.函数![]() ![]() |
C.函数![]() ![]() |
D.若对于任意![]() ![]() ![]() ![]() |
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4 . 已知函数
(
),则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17ba773dbb67f587923a5978467ab1ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
A.对于任意的![]() ![]() |
B.对于任意的![]() ![]() |
C.当![]() ![]() ![]() |
D.当![]() ![]() ![]() |
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2024-06-12更新
|
229次组卷
|
2卷引用:辽宁省实验中学2023-2024学年高一下学期期中阶段测试数学试卷
名校
5 . 已知
,对任意
都有
,
(1)求
的值:
(2)已知
,若对任意
都有
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6489c6a12fb4b9fdbbcb88ee017c504.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8c6a23e86dbe6c2faf2ee52a20b2d3d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c55d1d0d110b2425b56847b8aacd2fc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01cb2f06e5a5472f5a571ede7029931a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c8a8e268189559aa3c87a43824cf95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b331bbdd68d110681fc4547748b93bb.png)
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6 . 已知函数
,则下列说法错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97b008969eee5d2990c094a88c829e18.png)
A.![]() ![]() | B.![]() ![]() ![]() |
C.当![]() ![]() | D.![]() |
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7 . 已知函数
,则下列结论错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/735acbcca0190a01290c17ad4c165e7e.png)
A.函数![]() | B.函数![]() ![]() |
C.函数![]() ![]() | D.函数![]() ![]() |
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8 . 英国数学家布鲁克·泰勒以发现泰勒公式和泰勒级数而闻名于世.根据泰勒公式我们可知:如果函数
在包含
的某个开区间
上具有
阶导数,那么对于
,有
,若取
,则
,此时称该式为函数
在
处的n阶泰勒公式(其中
,
).计算器正是利用这一公式将
,
,
,
,
等函数转化为多项式函数,通过计算多项式函数值近似求出原函数的值,如
,
,则运用上面的想法求
的近似值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aceb113626093e0e431f30fa45c2c444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f9b92a1988f20c45e8ba3887eeb6b7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e8de51ffc22c61cb3e7225e74ecab83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/909736dad505d81be43aef91e6309bf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235d7f371dd29808dc098c68749709f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80a6580231b1438c017a656f0a0fcc35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223bdf463070d730b90468efc42eadec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a48345d239aaf8e9ca1ff2846c08a99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66db91bb3be9e2b6ad567774e3699758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad040ae0fab73f5dd7b1af48cd3b5f93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4c7d5aee3615cdb65b3dd4e24da7bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f457e696b1504bfb73140699a8e18dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc9e1f1c8fdfa0395c4ba1a08d1f1a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a456ea92bfb3ce171144e8ae5cb2663.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cda9fdee4c700da3a71305ffc505b813.png)
A.0.83 | B.0.46 | C.1.54 | D.2.54 |
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名校
解题方法
9 . 已知O为坐标原点,对于函数
,称向量
为函数
的相伴特征向量,同时称函数
为向量
的相伴函数.
(1)求
的“相伴特征向量”;
(2)已知
,
,
为
的相伴特征向量,
,请问在
的图象上是否存在一点P,使得
,若存在,求出P点坐标;若不存在,说明理由;
(3)记向量
的相伴函数为
,若当
时不等式
恒成立,求实数k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66655b7a6825b124ce596197bf2aa14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b84dac41f87e939f6cc39f38dc59b78d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e723e57753f0a4fe1ef8ca1aee0e2117.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f5bcd9f6f37c678d0c115f81033a063.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0c21dde2ad1e31c337bfb78c810ccb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aab5da44c04986fec56fe0429e7bd38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8995dd0d46aa3505185b312b37d2654.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cde2057eeaf26f3e9dd1748e1e4adc5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6d0f698f257914921dae5b31f9051e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661249bf6499017f9e5e03db3fcd93d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b929fe0f9c13dd6dfabca91a1a4aaa.png)
(3)记向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fffe91c3b3290e5eb048b0028b0a5686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37c37fb4bd069bc873942c8fa00f8b2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1a26abd0fde0e83ffcf32b5f46b073b.png)
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名校
10 . 已知函数
.
(1)若
,函数
为偶函数,求
的最小值;
(2)若
在
上恰有4个零点,求
的取值范围;
(3)若不等式
对任意的
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92ce84a967e8452d2178bfb64e66e9b7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745c26a80e067bd3ba43d8a038afe50d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc36dc63713541d6317579dcf63f494f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dfe024e3e7190544c823fd312ece0f1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77e039a9d305af23cc7ec7c091e1c630.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1eee23d00e338805d4306186b9dd0a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cba49e9b24a7dd4050e302c86d014b74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681dcdf161ec273e48357c528c1a850d.png)
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