名校
解题方法
1 . 已知正
的边长为
,内切圆圆心为
,点
满足
.
(1)求证:
为定值;
(2)把三个实数
,
,
的最小值记为
,b,c},若
,求
的取值范围;
(3)若
,
,求当
取最大值时,
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41322821ce31416fdac8dd6e0aa41c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8180faf978008d2bc7704cb69c3c40.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304010e1253e0fc6f7578c210be321f9.png)
(2)把三个实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c4ac0a523138c4597301dbd6ed3abb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bb980e0614df97e69a89948d3b21ccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c20fc69bb272fc609c2a7c95f888373c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc95236ed98064b97d67045706a21906.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4e7bf9200b351a259ddfc6c0266129d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d380dea30f490babb2aef4edc49afc6.png)
您最近一年使用:0次
2021-08-26更新
|
1633次组卷
|
4卷引用:浙江省温州中学2020-2021学年高一下学期期中数学试题
名校
2 . 已知函数
的图象如图所示,无理数
.
![](https://img.xkw.com/dksih/QBM/2022/4/29/2968697529106432/2970679662092288/STEM/60b2aaf4-8500-43f1-8d4a-afb850906aa0.png?resizew=152)
(1)求
的解析式并解不等式
;
(2)证明:函数
在定义域内有唯—零点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b460f80f14d11033695ec14d4d9bac7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d5bbb3b61a210d1b370f0ddfd21e90.png)
![](https://img.xkw.com/dksih/QBM/2022/4/29/2968697529106432/2970679662092288/STEM/60b2aaf4-8500-43f1-8d4a-afb850906aa0.png?resizew=152)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f81ed7f6a4475e0fa682fa81ee747da3.png)
(2)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7794c66472b0095e0424ba6762e12ced.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78d78b94688efed1b5ffc54b4928bdeb.png)
您最近一年使用:0次
2022-05-02更新
|
146次组卷
|
2卷引用:广东省江门市第一中学2021-2022学年高一下学期期中数学试题
名校
解题方法
3 . 定义函数
为“正余弦”函数.结合学过的知识,可以得到该函数的一些性质:容易证明
为该函数的周期,但是否是最小正周期呢?我们继续探究:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216fe768d8ce994867dde9ad5708d7ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4fb17f6c4d2a854d76062ee167c6c.png)
.可得:
也为函数
的周期.但是否为该函数的最小正周期呢?我们可以分区间研究
的单调性:函数
在
是严格减函数,在
上严格增函数,再结合
,可以确定:
的最小正周期为
.进一步我们可以求出该函数的值域了.定义函数
为“余正弦”函数,根据阅读材料的内容,解决下列问题:
(1)求“余正弦”函数的定义域;
(2)判断“余正弦”函数的奇偶性,并说明理由;
(3)探究“余正弦”函数的单调性及最小正周期,说明理由,并求其值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7051f44b01baed6574abaca7f3d7b6e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e2d7c958e99bcd9d7f251c19ee3544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216fe768d8ce994867dde9ad5708d7ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4fb17f6c4d2a854d76062ee167c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa1dd1e3ecbf87b4c4a2b4ab71f5859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7051f44b01baed6574abaca7f3d7b6e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7051f44b01baed6574abaca7f3d7b6e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7051f44b01baed6574abaca7f3d7b6e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d51992c05a557cf6058664f1f8961e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8386e2f935d78f9137e1d9cb050223e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b429642b4cc19a976d2592c3bf685ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7051f44b01baed6574abaca7f3d7b6e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/430d24c464431cb2900239095f23f9bf.png)
(1)求“余正弦”函数的定义域;
(2)判断“余正弦”函数的奇偶性,并说明理由;
(3)探究“余正弦”函数的单调性及最小正周期,说明理由,并求其值域.
您最近一年使用:0次
4 . 对
,定义
.
(1)求
的最小值;
(2)
,有
恒成立,求A的最大值;
(3)求证:不存在
,且m>n,使得
为恒定常数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f166b8917034ebc7522d1a160707f6a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7de87e4f04e15189c927b34b2e5afb.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde2576b383ae3c851529435805b3adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b206982b923b94befb9985e51f6499cb.png)
(3)求证:不存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c61a450b5c1c412aca3294e9eb4e9874.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c29ca729804f56f23d760ab66b79f68.png)
您最近一年使用:0次
2021-07-19更新
|
556次组卷
|
3卷引用:上海市大同中学2023-2024学年高一下学期期中考试数学试卷
名校
解题方法
5 . 定义向量
的“伴随函数”为
; 函数
的“伴随向量”为
.
(1)写出
的“伴随函数”
,并直接写出
的最大值;
(2)写出函数
的“伴随向量”为
,并求
;
(3)已知
,
的“伴随函数”为
,
的“伴随函数”为
,设
,且
的伴随函数为
,其最大值为
,
①若
,
,求
的值;
②求证:向量
的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074d049ba730bc0a038a076d5eb10035.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc54bc56c16baa3643686b85a6130e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc54bc56c16baa3643686b85a6130e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074d049ba730bc0a038a076d5eb10035.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49959c3eb6c1611b46757cea82bb78a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/763d7fbdbbb3f412833be6d8a094c31e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c968347eabbb636d20b607a3bcfe0ac3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcbc26dcb07c453ee8a136c7969fabfa.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40fd6ad05ed256d3b2e3e9fb2d97eef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b6799b234237333b0efa331d98f0374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c968347eabbb636d20b607a3bcfe0ac3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/195cf335b2199bd87d1f442b19f39450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec64476aaca08de0808afda3618109c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b76b2a89e7bd4bbcc8d053385ae8edd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0518fab92475787a7be0581733eea67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
②求证:向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed38da21f937df5020532cc9dd35292.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aa2084f1f30c12ea28ee72d59371a9a.png)
您最近一年使用:0次
2021-07-15更新
|
474次组卷
|
6卷引用:北京师范大学附属实验中学2020-2021学年高一下学期期中考试数学试题
名校
6 . 已知函数
的定义域为区间D,若对于给定的非零实数m,存在
,使得
,则称函数
在区间D上具有性质
.
(1)判断函数
在区间
上是否具有性质
,并说明理由;
(2)若函数
在区间
上具有性质
,求n的取值范围;
(3)已知函数
的图像是连续不断的曲线,且
,求证:函数
在区间
上具有性质
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca2452e9315b65152f13e0b85edab77a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/834925e383a1e904951eea76b55bcb4f.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1c079afd1b058adc67a50f48f3d466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d9459134e886dc7fb76a0221dbadb1.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7f9b35017daa8b524c5717a355834a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab9894fcb4fc5e7834839cb05f12d14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9e245dc2e7774139376973a60f97f6.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e9c518d889fe12a5d73ad829bb36e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf5f2b93641d1f16b86d3c1fd398ab7f.png)
您最近一年使用:0次
2021-12-25更新
|
1950次组卷
|
6卷引用:上海市洋泾中学2022-2023学年高一下学期期中数学试题
上海市洋泾中学2022-2023学年高一下学期期中数学试题北京市西城区北京师范大学附属实验中学2022-2023学年高一下学期期中考试数学试题上海市嘉定区2022届高三一模数学试题(已下线)热点13 函数的图象与性质-2022年高考数学【热点·重点·难点】专练(全国通用)(已下线)专题06 三角函数(模拟练)-2湖南省株洲市第二中学2024年第四届“同济大学”杯数理化联赛高一数学试题
名校
7 . 若定义域为
的函数
满足:对于任意
,都有
,则称函数
具有性质
.
(1)设函数
,
的表达式分别为
,
,判断函数
与
是否具有性质
,说明理由;
(2)设函数
的表达式为
,是否存在
以及
,使得函数
具有性质
?若存在,求出
,
的值;若不存在,说明理由;
(3)设函数
具有性质
,且在
上的值域恰为
;以
为周期的函数
的表达式为
,且在开区间
上有且仅有一个零点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd3d641761af730cc20b05a79fad66f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a39800f3595a04a3c9730c531049b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd3d641761af730cc20b05a79fad66f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc6e69ad1a27916fb5c3d5901ded134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04afd6b14d712929799c7d092872c354.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342b4871cd7d7766c9054a1dc0b477a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc6e69ad1a27916fb5c3d5901ded134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a55838863eacaec3c4f56df61169488d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8b79682b1872ca13d4d119adc01613.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced695934528674095a9fcf3db511ebe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a555759e23d21c30f1ed29e7d2453fea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/931db1234c7327aa072f8e96360c96e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6fab7a2597e4d169c942d5c65c98b00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e9fdc1f8ed0ae44b54a9a2a3aca2db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc6e69ad1a27916fb5c3d5901ded134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d396d5349f4b2b9b74f01347c242250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166009a848eadfd8ac7cc83933aa219b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fddb0be24dcd1323c63b8680f5071cdb.png)
您最近一年使用:0次
2021-07-12更新
|
1764次组卷
|
11卷引用:上海市复兴高级中学2021-2022学年高一下学期期中数学试题
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名校
解题方法
8 . 在
中,角
,
,
的对边分别为
,
,
.
,
均为锐角,且满足
.
(1)证明:
是直角三角形;
(2)若
面积为
,求
的周长的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a848e6af9181dd6557ac1cd604f7e3c.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
2021-10-08更新
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1331次组卷
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4卷引用:西藏拉萨那曲高级中学2021-2022学年高二上学期期中考试数学试题
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9 . 在平面直角坐标系中,O为坐标原点,A,B,C三点满足
.
(1)求证:
;
(2)已知
,
,
,
,若
的最小值为
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6983b8b908199ce3ba3e06bd4d8e6c39.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97b0ec538da1d765fa41f8d2cec70e8f.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdd04ec1b4569f53912cd42767fb32e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2937748aea6427cd517ce39771b19ea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce485410257c9c1fae9d87ce3e44cc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5644835a8f27b3fb66cafe1d92d1ac9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1987ecbd076d89da5ef1e2561d79d857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1987ecbd076d89da5ef1e2561d79d857.png)
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解题方法
10 . 已知函数
,其中
.求证:
(1)
,且
;
(2)
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4d6363133c710c00b99fafa01dce16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1948bdb9bfc6493bc0e596d9a0dab5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/accad8245514b083d7434160085188fd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b9f295a43c5d78cf9518456fef0abda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32474ff2d16bb427dc7426e481b20709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2479b7fa52eafe0e011435864bfe9c37.png)
您最近一年使用:0次