解题方法
1 . 已知函数
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1893ec3241bbeb7909e5a1ecfb7c1760.png)
__________ ;
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de5677b1a7224100c07624ac6f43df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1893ec3241bbeb7909e5a1ecfb7c1760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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2023-01-06更新
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337次组卷
|
2卷引用:北京市昌平区2022-2023学年高一上学期期末质量检测数学试题
名校
解题方法
2 . 已知
,且
,函数
,
在
上是单调减函数,且满足下列三个条件中的两个:①函数
为奇函数;②
;③
.
(1)从中选择的两个条件的序号为_______,依所选择的条件求得
______,
_______(不需要过程,直接将结果写在答题卡上即可)
(2)在(1)的情况下,若方程
在
上有且只有一个实根,求实数m的取值范围.
![](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/6b7d388df8a41777cbc3755fbd80efd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7926703c19e89a7438753101df731738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e88c844860c1d1eaeb80660679ca928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a1e4572e907ff8abb63b998d6d5c1e.png)
(1)从中选择的两个条件的序号为_______,依所选择的条件求得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
(2)在(1)的情况下,若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6735e3aa27d0ba04ec310fb4bfd9ceb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
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2023-01-05更新
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242次组卷
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2卷引用:北京十一实验中学2022-2023学年高一上学期期末教与学诊断数学试题
名校
解题方法
3 . 已知函数
,若
存在最小值,则实数a的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/139b2f132baa6c4c9278a8e624f87aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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2023-01-05更新
|
497次组卷
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3卷引用:北京十一实验中学2022-2023学年高一上学期期末教与学诊断数学试题
解题方法
4 . 已知函数
给出下列四个结论:
①当
时,
;
②若
存在最小值,则a的取值范围为
;
③若
存在零点,则a的取值范围为
;
④若
是减函数,则a的取值范围为
.
其中所有正确结论的序号是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ebe96b300085ce5604e6c0a21a6992d.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57773e33670190531389702ec3a3de29.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e58768fc0df02f60aa54d00fe063c52.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8898d2159c9309333db4431e066b376.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c92083b0dc465138ec13031b9f4a62b.png)
其中所有正确结论的序号是
您最近一年使用:0次
解题方法
5 . 已知函数
,若
,则
的解集为___________ ;若
,
,则a的取值范围为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e7062ea42c2f1ef458ebeae587a5410.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b624d88827e92e12bc0a8f1067cbe72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
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名校
解题方法
6 . 函数
的定义域是_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fbcb3e1248710974e56ca9a31b79c9b.png)
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2023-01-05更新
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865次组卷
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7卷引用:北京市西城区2022-2023学年高一上学期数学期末试题
名校
解题方法
7 . 已知
,当
时,
的单调减区间为__________ ;若
存在最小值,则实数
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7faf034a15c3626ce398f644517c47bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.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/0a6936d370d6a238a608ca56f87198de.png)
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1015次组卷
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2卷引用:北京市海淀区2022-2023学年高一上学期期末数学试题
8 . 已知函数
,
①当
时,
在
上的最小值为__________ ;
②若
有2个零点,则实数a的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee3c635d6e2ab9eaa09a6fed3c6f564a.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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2023-01-04更新
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529次组卷
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4卷引用:北京市东城区2022-2023学年高一上学期期末统一检测数学试题
北京市东城区2022-2023学年高一上学期期末统一检测数学试题北京市第一零九中学2023-2024学年高一上学期12月月考数学试卷湖南省株洲市炎陵县2023-2024学年高一上学期1月期末数学试题(已下线)北京市第四中学2024届高三上学期10月月考数学试题变式题11-15
9 . 已知函数
,
,若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70dfd3b70aab0849a459a241d904aa73.png)
(1)求
值;
(2)判断函数
的奇偶性,并用定义给出证明;
(3)用定义证明
在区间
上单调递增.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c3efdb4474748c4862b8098482a6ea9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70dfd3b70aab0849a459a241d904aa73.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)用定义证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
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2023-01-04更新
|
328次组卷
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3卷引用:北京市怀柔区2022-2023学年高一上学期期末考试数学试题
10 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44af88a9086d44d6645c6bf534cfc8eb.png)
(1)若不等式
的解集为
,求
的最小值;
(2)若
且
,求方程
两实根之差的绝对值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44af88a9086d44d6645c6bf534cfc8eb.png)
(1)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c51f4794adcaf0fbc653bfe40b48e08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c57d3ce9e64e5c7739e42e435cd743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70dfd3b70aab0849a459a241d904aa73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
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