解题方法
1 . 已知函数
,
.
(1)当
时,求曲线
在点
处的切线方程;
(2)当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f37416e467b553ba75a636533304c9f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/347c62b44fae618a37c145b3b5d1f1db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
您最近一年使用:0次
2 . 已知函数
,且
在
上的最小值为0.
(1)求实数
的取值范围;
(2)设函数
在区间
上的导函数为
,若
对任意实数
恒成立,则称函数
在区间
上具有性质
.
(i)求证:函数
在
上具有性质
;
(ii)记
,其中
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55386df48bce6389f5ea9dd827b2600d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d65bdc820ab87b9a7909d2be591abec.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b81a631c1fcd5fa6986baca8c7f754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/277a2bf55ddf8cf07f22b2128712e2b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08653fc03ff2c4ccaf3ab8b18474ee17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b81a631c1fcd5fa6986baca8c7f754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(i)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9626dc41063c34f4243b5a637668b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(ii)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88209b9c5c9503721afc5696b8943a10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a2f05512a14030b8a9cd9c118ed962f.png)
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今日更新
|
234次组卷
|
3卷引用:江苏省南通市如皋中学2024届高三下学期高考适应性考试(三)(3.5模)数学试题
解题方法
3 . 已知函数
.
(1)
时,求
的零点个数;
(2)若
恒成立,求实数
的最大值;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cf8a50553b1b9040eb5fd8149602f0b.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f3c2be7482719651bcf491949681e05.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43920f5171ed31db2520ef00e4c5fc24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e7c3a84d5c3ab338a6b95d1e4a7ce8a.png)
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名校
解题方法
4 . 已知函数
.
(1)求函数
在
处的切线方程.
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc037f008a8b878b1245e9e296031f0f.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34710f572d5db6f5ba109066204ae97c.png)
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名校
解题方法
5 . 设
是直线
与曲线
的两个交点的横坐标,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dae74c724114bfeff024dd7b79f5edc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46111e4d12c21798aa213c0d7804c2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55b8f1f4a005ada52c225801007495a9.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-06-17更新
|
165次组卷
|
2卷引用:江苏省华罗庚中学2024届高三下学期5月适应性考试数学试卷
6 . 已知函数
.
(1)讨论
的单调性;
(2)当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46c64890f20311b50987a8a41c78c41f.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f5f7a36e251bbc424ccc127ebb2881.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8cf24d9858ad4e30f2f194e8c97d38.png)
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名校
解题方法
7 . 帕德近似是法国数学家帕德发明的用多项式近似特定函数的方法.给定两个正整数m,n,函数
在
处的
阶帕德近似定义为:
,且满足:
,
,
,…,
.注:
,
,
,
,…已知
在
处的
阶帕德近似为
.
(1)求实数a,b的值;
(2)当
时,试比较
与
的大小,并证明;
(3)已知正项数列
满足:
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16563cfb206d0394cac2a0c2595dda6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adcb8c6a69df1a0deaba265e204d5f99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047a8c1ed551fccee1c1848746c5f282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72029562177dfc99a171c9013eb90227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4573475f70860a3d99b92a329d0d07f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca214aa6276b96d67a451c3fdbc59b3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cba6d8d56270fc72edd1af793542c036.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/030c5fc27fb5c07e4d6c913653af07ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb3c747a781e60fc62b9227562c184cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff6838d84b68c6f0d3b93b196d9b08d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40765d09390381658d5b4dc0160366cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e4d09296cabc6d6dcc16c7f17aaa44.png)
(1)求实数a,b的值;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047056c99b39c70fa40d3c8178e5b631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9966dfe9109671c587892bd32f0b6699.png)
(3)已知正项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de9743efd677eb188b1f412799923d97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b10e4e524dd686e35ab3e6482192a201.png)
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2024·江苏连云港·模拟预测
名校
解题方法
8 . 已知函数
(
,且
).
(1)若
,求函数
的最小值;
(2)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b02f7eb75c4920528be28f08541c276.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/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655b06387179d53c1e474fcfcb408b1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/467ebe7ef361ddf4cfab29baeefc66aa.png)
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名校
9 . 已知
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef2a45773db8d347f0cfa4e4fca7fd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fefaae8824438cec10b0f8486a40d24.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-05-16更新
|
693次组卷
|
2卷引用:江苏省扬州市仪征市四校202届高三下学期4月联合学情检测数学试卷
解题方法
10 . 已知函数
.
(1)若
,求
的最小值;
(2)设数列
前
项和
,若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c65664309a5af21b878b7720991fe10.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc3e5be1796493161a4df7e28a6f6b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad5c8fc2f1b7e3dd6635e850d3d1ee1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bd54a4949e7ead132cc159f98ccaca5.png)
您最近一年使用:0次