名校
解题方法
1 . 已知函数
满足如下条件:①对任意
;②
;③对任意
,总有
;
(1)证明:满足题干条件的函数
在
上单调递增;
(2)(i)证明:对任意的
,其中
;
(ii)证明:对任意的
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bed35af28313885be08105433a4a7f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249a976e88133f3b3733f09137cf5c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a9344f4fca7b9779ca7720e5277ea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27ee37508cc0e961aea8189f66c088bd.png)
(1)证明:满足题干条件的函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)(i)证明:对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd310679d278f4d3797195f3c5957e7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
(ii)证明:对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b994965c0644432692fbd7d7743f9a09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/219598f1289ddb370d632ea141731d52.png)
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2023-02-11更新
|
201次组卷
|
2卷引用:广东省茂名市五校联盟2022-2023学年高一上学期期末联考数学试题
名校
2 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e2fcfe346cb13eee1a6a792007d32c2.png)
(1)判断并证明函数
在区间
上的单调性;
(2)已知
,试比较三个数a,b,c的大小,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e2fcfe346cb13eee1a6a792007d32c2.png)
(1)判断并证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe3039fe791903968af776dddcfb0c7.png)
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名校
解题方法
3 . 设函数
是奇函数.
(1)求
的值;
(2)判断函数
的单调性,并用函数单调性的定义进行证明;
(3)已知
,
,
,试比较三个实数a,b,c的大小并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31413adaabce92c19800be8e538dc106.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db0159ca437ffcf3b1fa43cf541055a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebdc49df6c61728153682bed3e677ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03d22c8328612e136ce96272d389aec6.png)
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2023-01-09更新
|
299次组卷
|
2卷引用:广东省广州市海珠中学2022-2023学年高一上学期期末数学试题
名校
4 . 已知函数
.
(1)求f(1),f(2)的值;
(2)设a>b>1,试比较f(a),f(b)的大小,并说明理由;
(3)若关于x的不等式
恒成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cfee2c4efc91317d8e0ade4c839d863.png)
(1)求f(1),f(2)的值;
(2)设a>b>1,试比较f(a),f(b)的大小,并说明理由;
(3)若关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72196c2a2b0cf84ed15cb172cdabb454.png)
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2021-11-19更新
|
484次组卷
|
4卷引用:广东省广州市华南师范大学附属中学2021-2022学年高一上学期期中数学试题
广东省广州市华南师范大学附属中学2021-2022学年高一上学期期中数学试题福建省福州市三校2022-2023学年高一上学期期中联考数学试题(已下线)专题3.5 函数性质及其应用大题专项训练【六大题型】-举一反三系列(已下线)3.2.1 单调性与最大(小)值——最值(第2课时)(分层作业)-【上好课】
5 . 已知函数
.
(1)证明:函数
在区间
上单调递减;
(2)已知
,试比较三个数a,b,c的大小,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d7211d89e2d825df0024a298175d2f.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/180c5a2ace3358323b3d9a4c39fbf955.png)
您最近一年使用:0次
名校
解题方法
6 . 已知函数
(
,且
).
(1)若
,试比较
与
的大小,并说明理由;
(2)若
,且
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79573f3c214324712f0399831914cd96.png)
三点在函数
的图像上,记
的面积为
,求
的表达式,并求
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a04546d92fd165fc1ad2cc82c2dbb25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d41acc47493556617fe7b9e55093d10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e5e0727058d0254cbcc50c2a1400a7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e3d9d86ac5a0f90301f8952bdc4c90.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4e53a8120baa5f9087d873d89d8da53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5a46aa7bc51f99f321547eeca25c011.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79573f3c214324712f0399831914cd96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7872f0996380cfedf9f4a50f9232b97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe4c851b58de4e6c6ee3597029f411a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3466b71d1d9117438ed50388a57d9397.png)
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2021-01-28更新
|
503次组卷
|
3卷引用:广东省广州市越秀区2020-2021学年高一上学期期末数学试题
解题方法
7 . 已知
.
(1)求证:
在
上是增函数;
(2)①
,猜想
与
的大小关系;
②证明①的猜想的结论;
③求函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/726a45a71b078db26b648a5f183bc420.png)
的最值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec84404bbf6cf4a9d992e1760dcfdd4.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b029e85e686623cdef977b2cb1f207a.png)
(2)①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4743ec9c1fee6d4685fb9f959458300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc8b26fb79c1f4d36130c41b18c0f9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f89a8b5cf6996a6455375e405bfb9d.png)
②证明①的猜想的结论;
③求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/726a45a71b078db26b648a5f183bc420.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ee5fbd2082fd90c98e099600f55fa41.png)
您最近一年使用:0次
8 . 已知函数
,
.
(Ⅰ)证明:
在区间
上是增函数;
(Ⅱ)比较
与
的大小(
是自然对数的底数).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61db14a7207a5bed8c0c35a6fe5d9b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ac1b64cb76717bd87cd068fbaf1cf6c.png)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbf702196792c7228b39428e97d54ca4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f114be7ee0ba7cbd2ef8555fe757ca2.png)
(Ⅱ)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9362584c35c9124dc6ccc4ec10d2dfc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1f594cf0f5dcb87a263facd7fd875e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f2da9c76b43741b08bf0d1150ae24e.png)
您最近一年使用:0次
解题方法
9 . 已知函数
,
,设
(其中
表示
中的较小者).
(1)在坐标系中画出函数
的图像;
(2)设函数
的最大值为
,试判断
与1的大小关系,并说明理由.
(参考数据:
,
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64263fe2ca48e694c87496d61e63fb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/073583cf95e1c2bff5c98ec63134885a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca8d6c450789cd73c05134e2c8c5b3cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d533077bb33dd9e38134d2eb25c9a158.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
(1)在坐标系中画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5790d5181783c15fd46d95bf18b796f0.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5790d5181783c15fd46d95bf18b796f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2703c46e8359a0a895d042cc6d8699f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2703c46e8359a0a895d042cc6d8699f8.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27013bb5c9cf1790453311b8e4bc193.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5950b5f1506d9f3ce0b2b12cf5c38f82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9ba1acd988c3ba5b5024e1396ada86.png)
您最近一年使用:0次
10 . 已知函数
为实数),设![](https://img.xkw.com/dksih/QBM/2016/10/27/1573097615572992/1573097621118976/STEM/59179625e5284e94a9ee74590563b338.png)
(1)若
= 0且对任意实数
均有
成立,求
表达式;
(2)在(1)的条件下,当
是单调函数,求实数
的取值范围;
(3)设
满足
,试比较
的值与0的大小.
![](https://img.xkw.com/dksih/QBM/2016/10/27/1573097615572992/1573097621118976/STEM/18bfbbcac01144648891f81c698f0083.png)
![](https://img.xkw.com/dksih/QBM/2016/10/27/1573097615572992/1573097621118976/STEM/59179625e5284e94a9ee74590563b338.png)
(1)若
![](https://img.xkw.com/dksih/QBM/2016/10/27/1573097615572992/1573097621118976/STEM/d244f94f3d4d423e93364e50bfa3ec67.png)
![](https://img.xkw.com/dksih/QBM/2016/10/27/1573097615572992/1573097621118976/STEM/39b666f4b75b4affaf8d869c91ffdc00.png)
![](https://img.xkw.com/dksih/QBM/2016/10/27/1573097615572992/1573097621118976/STEM/7553e22a1bdc45aebb48676676fc47a3.png)
![](https://img.xkw.com/dksih/QBM/2016/10/27/1573097615572992/1573097621118976/STEM/2471cbe9e34548858f401d3d11f5293f.png)
(2)在(1)的条件下,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eb022363446d27d84cd339755deaa58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)设
![](https://img.xkw.com/dksih/QBM/2016/10/27/1573097615572992/1573097621118976/STEM/88d8dcaddb724100aa9bcad671c66a32.png)
![](https://img.xkw.com/dksih/QBM/2016/10/27/1573097615572992/1573097621118976/STEM/3e1f2cbf3f0a4bcd823d3413724f456d.png)
![](https://img.xkw.com/dksih/QBM/2016/10/27/1573097615572992/1573097621118976/STEM/7c2cc0d70fe54a39b6c39adbd27347e4.png)
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