解题方法
1 . 已知数列
是首项为9,公比为
的等比数列.
(1)求
的值;
(2)设数列
的前
项和为
,求
的最大值,并指出
取最大值时
的取值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d97eceb4b46753a5858278599b85cfe.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d35bda8e529c177a37a751469d871499.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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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解题方法
2 . 已知函数
.
(1)求函数
的极值;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5052b849281c5f3cd5dc25612b0f7e2.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29fb8a47e812e9a75be27fe7d114b9fd.png)
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解题方法
3 . 已知
,证明:
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc3e5be1796493161a4df7e28a6f6b7.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cfe11ba2ac9fc23b8f6d5346e8e68cd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebe03f24aab32e769e27727536cc1e8f.png)
您最近一年使用:0次
2023-03-10更新
|
867次组卷
|
2卷引用:河北省唐山市2023届高三一模数学试题
名校
4 . 悬链线(Catenary)指的是一种曲线,指两端固定的一条(粗细与质量分布)均匀,柔软(不能伸长)的链条,在重力的作用下所具有的曲线形状,适当选择坐标系后,悬链线的方程是一个双曲余弦函数,其解析式为
,与之对应的函数
称为双曲正弦函数,令
.
(1)若关于
的方程
在
上有解,求实数
的取值范围;
(2)把区间
等分成
份,记等分点的横坐标依次为
,
、
、
、
、
,设
,记
,是否存在正整数
,使不等式
有解?若存在,求出所有
的值,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea6d30f5080e0b5abd19388cf692505.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ece9be74b86b840885f5b869f476f938.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/009935dae2483304749bfa46ceb6eecc.png)
(1)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f182d62ec0878854941c254b34d8786e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f01a8fb2de5c86483d71a65fd3e1da6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)把区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa482d7bcaa385bfc3548b42a4bfb60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa2362b35cf9d7c30d41e047de466278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b53f7ddf019c9234ab67e70e150f0be0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68ee2cff7313e9edaa5b8b8a7527862c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d688971073c91c735e751d31277d08e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0112ab5328cf8f3d1891e6709241fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2023-03-10更新
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3卷引用:2023年普通高等学校招生统一考试数学模拟预测试题(一)
解题方法
5 . 若函数f(x)=loga(x+a) (a>0且a≠1) 的图象过点A(-1,0).
(1)求a的值;
(2)求函数
的定义域.
(1)求a的值;
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/165fac063bfd88d301a59cf768e46364.png)
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2023-02-22更新
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545次组卷
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2卷引用:河南省驻马店树人高级中学2023届高三下学期高考模拟三(艺术)数学试卷
解题方法
6 . 正项数列
的前n项和
满足
,且
.
(1)求数列
的通项公式;
(2)设数列
满足
,
为数列
的前n项和,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5400637a79e6e7af3ae5214be34a615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8141d87fb02b08c88b0c9f27f839a7d9.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1305e33bb79e7acc6d022015ecca4058.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c7a1a4063c897dcfd1809723512a62d.png)
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7 . 已知集合
或
,
.
(1)当
时,求
;
(2)若“
”是“
”成立的必要不充分条件,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/336c9edbd1e5b95c1286260fde7552cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0444fdc3a544e16b6817e43ee1d6ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304eb66c2014fdd4fec30f9783b0a5ed.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.png)
(2)若“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
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2023-02-14更新
|
578次组卷
|
6卷引用:河南省驻马店树人高级中学2023届高三下学期高考模拟三(艺术)数学试卷
解题方法
8 . 已知函数
.
(1)若
,求a的值;
(2)已知某班共有n人,记这n人生日至少有两人相同的概率为
,
,将一年看作365天.
(ⅰ)求
的表达式;
(ⅱ)估计
的近似值(精确到0.01).
参考数值:
,
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a9f96bc558481a14b0911041295e28a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
(2)已知某班共有n人,记这n人生日至少有两人相同的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532084481ae3a67c8208b7783bf22e8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb86b569914509657744de5f6834164.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532084481ae3a67c8208b7783bf22e8e.png)
(ⅱ)估计
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae22e1ab354fdcd7529e60fb9bc16b2c.png)
参考数值:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/debb5dd603b8ab0e1072f1e3ef6a5b1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1169b573cc38f13e4c97d28e08de1c53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a76d32c76b9c4893dfe0d97469929dc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c0ab940dddecfebe43a3ebb7d79f779.png)
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9 . 已知函数
为奇函数.
(1)求常数
的值;
(2)当
时,判断
的单调性;
(3)若函数
,且
在区间
上没有零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad50e570831ffcabb38074c6adabe13.png)
(1)求常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/553ce7e15659d64bdae3d4a847da4dd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9f88173ef0c29bedd0155b7893d2474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-02-04更新
|
1150次组卷
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3卷引用:海南省琼海市四校大联考2023届高三12月数学科试题
名校
解题方法
10 . 已知
,且
.证明:
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fed98a219097783e0ca2f41483cac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc81613d0ab98c59daa708ed9e1606fe.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6da97a3e07d2b9fbfcabe019836598b6.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a757d35f2aafe65ff66a481909bf0ea.png)
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2023-01-29更新
|
376次组卷
|
5卷引用:全国名校大联考2022-2023学年高三第六次联考文科数学试题
全国名校大联考2022-2023学年高三第六次联考文科数学试题内蒙古阿拉善盟第一中学2022-2023学年高三上学期期末考试数学(理科)试题内蒙古阿拉善盟第一中学2022-2023学年高三上学期期末考试数学(文科)试题(已下线)专题12-2 不等式选讲归类-1(已下线)第1课时 课后 分数指数幂(完成)