名校
解题方法
1 . 已知函数
,且存在
,使得
,设
,
,
,
.
(Ⅰ)证明
单调递增;
(Ⅱ)求证:
;
(Ⅲ)记
,其前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c3cfd92b7157867ed0bbf56b6ea2c9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50fa3ac831917a350333d50a86d07958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f66a2b3d90f0d935d6c8ebaf675349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62b6ab454199d2738ea1b5cefb133d50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc85a01f2a5b003d545aabd58658f430.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f347a1bd45e8fe728bef4952ff2e6f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b48b8a1b0a32980f175a122e21ea715c.png)
(Ⅰ)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(Ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8c6648cdc6f9ffd069014c2d642400e.png)
(Ⅲ)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ca472f02af024cd9550d751767f6044.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/5737f1f9cad2471f3ca53241b25a1eb9.png)
您最近一年使用:0次
19-20高三下·浙江·阶段练习
名校
2 . 设函数
.
(1)当
时,求函数
的单调区间;
(2)当
时,
①证明:函数
有两个零点
,
;
②求证:
,注:
为自然对数的底数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6563e8a7b836485cff8449065af225ce.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bacabf50cf9866e06d04853cc11d5079.png)
①证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d4c1d435fa5efac0459ddefa34aae5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2beb22b735da7cb8054dd722450632f5.png)
您最近一年使用:0次
3 . 设
,数列
满足
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8addca7b9084d6a29d1af473274a550e.png)
.
(1)当
时,求证:数列
为等差数列并求
;
(2)证明:对于一切正整数
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be362dec96173f246ff747264007817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47769ca08edfa79fc200b9f37d197335.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8addca7b9084d6a29d1af473274a550e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/855ce769f6795d1463744a0d74901fb7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2f2d7c81cb44416bcdf59419637682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b191044f5c024f377d999910b78b422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)证明:对于一切正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85476c3cbc9d4f78b1aa5946694b85bd.png)
您最近一年使用:0次
名校
4 . 已知函数
的最大值为
.
(1)若关于
的方程
的两个实数根为
,求证:
;
(2)当
时,证明函数
在函数
的最小零点
处取得极小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5365d754d9c46bfa4e43f7b363ad1f43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/760f804646698060703c5458ff5637c7.png)
(1)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3461ab1b17c62a3beae29f34f0d05b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0158862238e250d2a2598b7d4ecd148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eeb0a7c38d0fc522bfd7cca20598b32.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6455e38ff53ede2508e4d9cb23f0b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/774545eed21eefebe5407dfc630861b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
您最近一年使用:0次
2018-05-21更新
|
1512次组卷
|
4卷引用:浙江省杭州地区四校2018-2019学年高三上学期联考数学试题
浙江省杭州地区四校2018-2019学年高三上学期联考数学试题【全国市级联考】山西省太原市2018届高三第三次模拟考试理科数学试题河北衡水中学2018届高三数学理科三轮复习系列七-出神入化6(已下线)专题13 导数法妙解极值、最值问题-备战2022年高考数学一轮复习一网打尽之重点难点突破
解题方法
5 . 已知各项为正的数列
满足:
,
(
).
(1)求
;
(2)证明:
(
);
(3)记数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135610aed76b3236cdaf3931481556f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e0ff8ff5b51d663c040810957242ba9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed529240a883f68f0921e818addeb9c8.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eeb650c5d035f8f67a65788f7c1ae67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e0ff8ff5b51d663c040810957242ba9.png)
(3)记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a15c37e6c1c27103628017944193e75e.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/c9f950fedce1e5ead461e7f52b734908.png)
您最近一年使用:0次
名校
6 . 已知数列
满足上:
,
.
(1)若
,证明:数列
是等差数列;
(2)若
,判断数列
的单调性并说明理由;
(3)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b66280badd3b6c4cc7629f024d1e67b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87743e3348c037162aa605bb6bb2220c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86304c3e26200299a0480641525a283.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf33b2a94eae16760d746f9b4b8dbc.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86304c3e26200299a0480641525a283.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d27884f5e62dda8dd97ecb5d62f86a0.png)
您最近一年使用:0次
7 . 设
是定义在R上的函数,对任意
恒有
.当
时,
,且
.
(1)求证:
;
(2)证明:
时恒有
;
(3)求证:
在
上是减函数;
(4)若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef60b6eaf3094507d72b6c07dfcfaae1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b253bed990e08769d68d3d0c32eb69c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f7fde71807463dbdfd8fce1655a5a9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd6536528d13d326f3c8f0b41e8266bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c286e75e9d00df48c0d713332e4979b3.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572678505807872/1572678511673344/STEM/2027559bdbaa47a38d4fdbe0c0b7ea0e.png)
(2)证明:
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572678505807872/1572678511673344/STEM/bd40dcfe5c2a487ea7701c29d5d0e9f9.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572678505807872/1572678511673344/STEM/3e4234dca0f94063a857743ffd862865.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(4)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9b943596d167efd4a05be98bfbe33a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
8 . 在单调递增数列
中,
,
,且
成等差数列,
成等比数列,
.
(Ⅰ)(ⅰ)求证:数列
为等差数列;
(ⅱ)求数列
的通项公式.
(Ⅱ)设数列
的前
项和为
,证明:
,
.
![](https://img.xkw.com/dksih/QBM/2015/3/30/1572050177368064/1572050183577600/STEM/2e08acc48f0b40a7abfbf10ed8d4d220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d8e8f821111de8075e5c3dfb22a5d6.png)
![](https://img.xkw.com/dksih/QBM/2015/3/30/1572050177368064/1572050183577600/STEM/d38e3a4322944de5936679c72b227012.png)
![](https://img.xkw.com/dksih/QBM/2015/3/30/1572050177368064/1572050183577600/STEM/f35a59c609cc4c278ae6c6645c0a57b8.png)
![](https://img.xkw.com/dksih/QBM/2015/3/30/1572050177368064/1572050183577600/STEM/72eabbe954064aa1b973914c8c6fa9e9.png)
(Ⅰ)(ⅰ)求证:数列
![](https://img.xkw.com/dksih/QBM/2015/3/30/1572050177368064/1572050183577600/STEM/922fea699deb4280823895b67427f330.png)
(ⅱ)求数列
![](https://img.xkw.com/dksih/QBM/2015/3/30/1572050177368064/1572050183577600/STEM/88ebdecc57164f0eab66aa81e99d806c.png)
(Ⅱ)设数列
![](https://img.xkw.com/dksih/QBM/2015/3/30/1572050177368064/1572050183577600/STEM/7243d64298aa4093901dc98a222e9e09.png)
![](https://img.xkw.com/dksih/QBM/2015/3/30/1572050177368064/1572050183577600/STEM/0e02509405e648109c87a89024b7d7e1.png)
![](https://img.xkw.com/dksih/QBM/2015/3/30/1572050177368064/1572050183577600/STEM/41667ac835a14e6fa4cea0838d4d86f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e19c066f405598229b8123ae152df314.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d726666f99a5a41dd673a2330e377b17.png)
您最近一年使用:0次
9 . 如图,已知曲线
:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497aceb0440d794dfedf2cdd42e131ce.png)
及曲线
:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc9e65f2fa9af923d5db7cff37782d7.png)
,
上的点
的横坐标为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
.从
上的点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
作直线平行于
轴,交曲线
于点
,再从点
作直线平行于
轴,交曲线
于点
,点
(
,2,3……)的横坐标构成数列
.
![](https://img.xkw.com/dksih/QBM/2016/3/8/1572525822836736/1572525829177344/STEM/b12a6ba397f64d30b29f8afd385551f4.png?resizew=246)
(1)试求
与
之间的关系,并证明:
;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497aceb0440d794dfedf2cdd42e131ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab03556c333ab0b55fe86c937b2a5763.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc9e65f2fa9af923d5db7cff37782d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab03556c333ab0b55fe86c937b2a5763.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9993f6dc979bfbe11ca160daf225d6a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f79dc80683f49c71b505e4bb711dbbb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15520cf5be7c2685975aac51bc99ac4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15520cf5be7c2685975aac51bc99ac4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c15016fc7de1cd5971b7d38c70071e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://img.xkw.com/dksih/QBM/2016/3/8/1572525822836736/1572525829177344/STEM/b12a6ba397f64d30b29f8afd385551f4.png?resizew=246)
(1)试求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e22720a7250e79903635cb6eb368b6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14835bf3f00139ccec0694d0924db795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/265ec3d91f1abd3cb756888d21ee7ae3.png)
您最近一年使用:0次
名校
10 . 已知函数
.
(1)若
在
有两个零点,求实数
的取值范围;
(2)设函数
,证明:
存在唯一的极大值点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64af8919d4a55d42dc0e34ca22048033.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb0f72986f9cb066960f19b0f4162920.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9054f1a2cdb38e84fc301db2f7d59e4.png)
您最近一年使用:0次
2022-05-30更新
|
906次组卷
|
4卷引用:浙江省金色联盟(百校联考)2020-2021学年高三上学期9月联考数学试题
浙江省金色联盟(百校联考)2020-2021学年高三上学期9月联考数学试题(已下线)类型八 隐零点问题-【题型突破】备战2022年高考数学二轮基础题型+重难题型突破(新高考专用)山东师范大学附属中学2021-2022学年高二下学期期中考试数学试题福建省龙岩第一中学2022-2023学年高二下学期第一次月考数学试题