2024高三·全国·专题练习
1 . 已知
定义在
上且
,
,当a,
,
时,有
.
(1)试判断函数
在
上是增函数还是减函数,并证明该结论.
(2)设
,求证:
.
(3)若
,求x的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd1db6c94b94afc372212a81cc1f4dd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249a976e88133f3b3733f09137cf5c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc4c79d578d4b0d74b84c3f6579e8806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96bc2eeaca8a8ce4bcce2bff011a11bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b84952d33957e5b90d8cd3b3bcc127.png)
(1)试判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e966083a8c143204a48b8406f62dcc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d65ffb2191a2d5182e671b73f30598c7.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a60168f2f9ae5baa0c753bc8154d46d6.png)
您最近一年使用:0次
2 . 已知函数
.
(1)求证函数
为奇函数;
(2)判断
在区间
上的单调性,并用定义进行证明;
(3)求
在区间[2,6]上的最大值与最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c47b2d73a4858fe5a169a0964c7e878e.png)
(1)求证函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
3 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e5ff2705eb737adef9a6dc70559d79.png)
(1)已知
为单调递增函数,请判断
的单调性,并用单调性定义证明;
(2)若
,求证:方程
在区间
上有且仅有一个实数解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b72eb501bf5451af98ab894176fb2a9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e5ff2705eb737adef9a6dc70559d79.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b161347f6a2fcfd9bf0acf1e8a03fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b67287da8b741b449aa283c688fd080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99eaeb2ab68a49074d623ffca072fed8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa482d7bcaa385bfc3548b42a4bfb60.png)
您最近一年使用:0次
名校
4 . 设
,函数
.
(1)若
,求证:函数
为奇函数;
(2)若
,判断并证明函数
的单调性;
(3)若
,函数
在区间
上的取值范围是
,求
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5029bd373d0a619fd342eeb67a03dd2e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ac9eb4f13a6ec140f7050e8d7dde52c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ac9eb4f13a6ec140f7050e8d7dde52c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711e45f600c091e6830c0b70cd012ca3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1897096c9888358bf2b8322f66b8ccc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8573eecbc29f522671b3892ec406c50b.png)
您最近一年使用:0次
2024-01-26更新
|
353次组卷
|
2卷引用:河南省信阳市信阳高级中学2023-2024学年高一上学期12月月考数学试题
解题方法
5 . 已知函数
,(其中
是自然对数的底数)
(1)判断函数
在
上的单调性(不必证明);
(2)求证:函数
在
内存在零点
,且
;
(3)在(2)的条件下,求使不等式
成立的整数
的最大值.
(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2449e5f1b9bb4207c417e54c015159ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27f935fa5d0ae1b208aff21aa468ecf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4015b3933584f7e0b4b27ee20aec5aa4.png)
(3)在(2)的条件下,求使不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7e97df7844dd6633cfa48c0dcc385a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/670fe3513adf8e865c006336f75077ff.png)
您最近一年使用:0次
解题方法
6 . 定义在正实数集上的函数
满足下列条件:
①存在常数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
,使得
;②对任意实数
,当
时,恒有
.
(1)求证:对于任意正实数
、
,
;
(2)证明:
在
上是单调减函数;
(3)若不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①存在常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df3855a4c053b11330f1d98affcea7df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb04d514baf56eec084671b88898770b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67cff059e78d45b51400779ef4f9a888.png)
(1)求证:对于任意正实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6521ef75f0a05fe62cdfd2fbbe0430b6.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(3)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca3811dafef1b3c18d715f50d7d34b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
7 . 已知函数
,
,
.
(1)当
时,判断函数
的奇偶性并证明;
(2)当
且
时,利用函数单调性的定义证明函数
在
上单调递增;
(3)求证:当
且
时,方程
在
内有实数解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0cc9b1b321520eae2bf944a9c85c9ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19339e3904e9541ff26b30ae5f1242b2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657435e1fda84118e7f63c97505c8b75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
(3)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a871ef7bf13de3e15489d65b57a3cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99caed81bfb141d6e7dac8f6fe9db069.png)
您最近一年使用:0次
名校
解题方法
8 . 若非零函数
对任意x,y均有
,且当
时,
.
(1)求
,并证明
;
(2)求证:
为
上的减函数;
(3)当
时,对
时恒有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b6585b5af98d4c7801c1edaf2e6ead0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d752d8db8a05b3ec7312f6ac8b64a07.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e38fffbc7ab9882480f4faa72390e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c73ed206046205dc9e41285f74d81dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec25b9d7ca47b780a744c2ebbf31d925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e59b1dd6e7640a36050cbbbcc6449606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
解题方法
9 . 已知函数
.
(1)用单调性定义证明:
在
上单调递增;
(2)若函数
有3个零点
,满足
,且
.
①求证:
;
②求
的值(
表示不超过
的最大整数).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4247d7790d83be16bc74aa5e5d12dd63.png)
(1)用单调性定义证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f8994d83bf4a688c0ab897a5a40fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a1cc5cfec94bc5686b41b043acdc8ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d995c5d2e1e0305d805032e18997986a.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28cbe8f17c4472d8663f9ccbe3b98f6.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59077d1948911b13d68a572eadbca3cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
10 . 已知函数
.
(1)判断函数
的奇偶性,并证明你的结论;
(2)用函数单调性定义证明:函数
在
上是减函数;
(3)写出函数
的值域(结论不要求证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d389b78f753622d6ed895eff86c8e59b.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)用函数单调性定义证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(3)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次