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解题方法
1 . 设函数
,
.
(1)若
,且函数
与
的图象有正格点(横、纵坐标均为正整数)交点,求
的值;
(2)已知
,对于满足(1)中条件的
,求数列
的前
项和
;
(3)若正实数
使得
的图象关于直线
对称,所有满足条件的
构成的数列记为
,且
单调递增.求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead65ac45d3221139a8385c78823af04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d82332f79318e612122e696354826c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03f0fadbe551b0e0eb7bf9440be740b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c805b00411b65c3a1c419d745ad04172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701554763bdbbf2689a8dae07608da38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f422edb72f7e1d5529a5570feb77df.png)
(3)若正实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead65ac45d3221139a8385c78823af04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c63e1c64c42b7f3b7fdc396d4756cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6364bbc8dbdc0b20d26dfd01b03ec413.png)
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2 . 下列说法正确的有( )
A.二次函数![]() ![]() |
B.平面内![]() ![]() ![]() ![]() ![]() |
C.集合![]() ![]() ![]() |
D.全称量词命题“每一个四边形的四个顶点在同一个圆上”是假命题 |
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解题方法
3 . 对于实数构成的集合
.若对任意
都有
(其中“
”表示普通的乘法运算),则称集合
对“
”是封闭的.
(1)已知集合
,判断
是否属于集合
;
(2)在(1)的条件下,若
,证明
的充要条件是
;
(3)若集合
对“
”都是封闭的,试判断
是否对“
”封闭,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8af42f2ec410ad1b28be69d3415ed10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a9f1ff137e76626b7b608cef7c36349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
(1)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50dae68b646f975a8a0c6bed67d028ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e57ed82958abb00776e75987aa62d723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)在(1)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9ecef225b27b5857d2d76fbe5b34982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf22d7d1a965bda25168a233fb6290c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff58fdfe14af9fb8aa0e0cf0d60853a.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81a3375139541ed61929fa658f16bb7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2468403b3eba9e40bfa36f464e927738.png)
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解题方法
4 . 已知
,
,
.
(1)若命题
为真命题,求实数
的取值范围;
(2)若
是
的充分不必要条件,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a51bda25ca665ab3ba8b630162bb50c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f95a98e5d53508d166af88d4510bff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/720a74de9582471920fc0157c1509c1f.png)
(1)若命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2022-10-12更新
|
171次组卷
|
6卷引用:江苏省扬州市高邮市2020-2021学年高一上学期期中学情调研数学试题
名校
5 . 下列判断或结论正确的是( ).
A.![]() ![]() | B.![]() |
C.锐角是第一象限角 | D.若![]() ![]() |
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6 . 设
,
,(
),则下列选项与
,
,
等价的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c70bc24b9a05465aee92bf8e77813109.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0dab5756cd6dde998058ecfe5b213f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d79eb54650d3d400455b637c0b1ccc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2a8128f333a6a6b558a3089c7f3ed88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7be99edf312446cc01f4aac66ff8cc8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd30edfbb8d6d4a421947349f62a6494.png)
A.方程![]() ![]() |
B.不等式![]() ![]() |
C.存在互不相等的两个实数![]() ![]() ![]() ![]() |
D.存在三个互不相等的实数![]() ![]() ![]() ![]() ![]() ![]() |
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2021-10-17更新
|
153次组卷
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2卷引用:上海市奉贤中学2020-2021学年高一上学期10月月考数学试题
名校
7 . 通过相等关系和不等关系的类比,我们可以得到很多不等式的性质,比如等式具有传递性:设
、
、
,如果
,
,那么
,我们可以类比得到不等式的传递性:设
、
、
,如果
、
,那么
.请你根据下列等式性质,类比得到相应的不等式性质.(无需证明)
(1)设
、
,如果
,那么
、
;
(2)设
、
、
、
,
、
,如果
,那么
.
![](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/0097ca400d4619a94c4282c1ef6ec68e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f22fec5a381ae8aca93d876e54c79de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b05d3b8f5c9df891ef6fbcaf12f43207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/759b29a7b2b3735306f1a650355a7858.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/0097ca400d4619a94c4282c1ef6ec68e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46196aec06c25d5c8f9b1d3a8f50a889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/069390dd908ff203327958117a226593.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58424beef0de6926a633bc188b5bc23a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f22fec5a381ae8aca93d876e54c79de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bea2f871d6a05af4839cf84111384dc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c35ebeda85591e71aa1b523ce5aa2a3.png)
(2)设
![](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/993e45b3291e3be0f6ea493743cb48b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812be9806122241c476ba1db516c4823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df50f7ca6a558c16090f6fce5db81d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e73211359fe89a6d48deeb68bec9ffcb.png)
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8 . 展示某同学解答的两题:
【题1】已知
,求
的值.
解答:由
,可得
,
所以
,即
,解得
或
,
所以
或
,由于
或
均满足
,故
的值是1或4.
【题2】若函数
在区间(-1,1)内恰有一个零点,求实数
的取值范围.
解答:由
,解得
,
所以,实数
的取值范围是
.
该同学的上述解答都正确吗?若不正确,请说明理由(或举反例说明);
选择其中一个你认为解答错误的题,写出你的正确解答过程.
【题1】已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d58b1f9787c9b8596d5b9bc6f0a9c41f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4e7bf9200b351a259ddfc6c0266129d.png)
解答:由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d58b1f9787c9b8596d5b9bc6f0a9c41f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bf59f5520b0612aa25731a83b7f48ae.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a805718ede5fb77f776f67af67bd6ca8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c0bfb1ac4c9091f08ac7172b007053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42498f6e0fc9a61c9857b70a87f02c5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01d9bcbc75ffbf824b9ec266030df358.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b32361241c4906a09dc79db55351bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e87a46fbb3f24cc37638c8c25cc6baae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b32361241c4906a09dc79db55351bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e87a46fbb3f24cc37638c8c25cc6baae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c328c9c4ec69c4275e27576fb61655.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4e7bf9200b351a259ddfc6c0266129d.png)
【题2】若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b1dd5a3a791e266159dcdbd1fbbe657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
解答:由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7703c4bb5f4c0d604cfdcb0993ba809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cdd3ad4b904bee1ebadc9a402a8a453.png)
所以,实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/030261c59c4aa6c7ffea06043b4122a4.png)
该同学的上述解答都正确吗?若不正确,请说明理由(或举反例说明);
选择其中一个你认为解答错误的题,写出你的正确解答过程.
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9 . 下列命题中正确的是( )
A.函数![]() ![]() |
B.若定义在![]() ![]() ![]() ![]() ![]() |
C.![]() ![]() ![]() |
D.函数![]() |
您最近一年使用:0次
2021-08-17更新
|
387次组卷
|
2卷引用:辽宁省大连市第一中学2020-2021学年高一上学期期中数学试题