名校
解题方法
1 . (1)已知
,求证
;
(2)已知
,函数
的最小值为M,实数
,且
,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5842f47b99932df68efbb64eb847e956.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411100df59e7a9dc8d4ad77d497b6fa9.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c49ac7e0f2b4d74032a37865ca10b09f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb713e5fc677848147f3045c1058cc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b5d514b065f6e6368cc0a02d23a55ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8474e2337da8a29965f88dc1bc8e6ca.png)
您最近一年使用:0次
名校
解题方法
2 . 记
的内角
所对的边分别为
,已知
.
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e717c243991f038d7bc21a0fdad985b.png)
(2)若
的面积
,求
的最大值,并证明:当
取最大值时,
为直角三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce7af7c5df749c6fa9bbe87faa72c66d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f2599ca8b6b683e57a82699c8b1ebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55abde5108e7846f496584016ce82286.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e717c243991f038d7bc21a0fdad985b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3a88d9c428cc72bdf012746e2781a64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2022-12-06更新
|
755次组卷
|
3卷引用:安徽省皖优联盟2022-2023学年高三上学期12月第二次阶段性联考数学试题
名校
3 . (1)已知
,
,
,求证:
.
(2)用分析法证明:对于任意
时,有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061813f1ec633c5c4c393c4de7938322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5558c083d34cbb0a58d3ce1dc6f5778e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128294be1f10b83df30ad60d4c696224.png)
(2)用分析法证明:对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6964979a90a2036e9dd541c40cb50be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e8010392b125fb5f015992bad5d6fa.png)
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解题方法
4 . 已知
,
是椭圆T.
上的两点,且A点位于第一象限.过A作x轴的垂线,垂足为点C,点D满足
,延长
交T于点
.
(1)设直线
,
的斜率分别为
,
.
(i)求证:
;
(ii)证明:
是直角三角形;
(2)求
的面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05193d9096bd9da9230acc14228aa4e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/817edbb8e01ced216a63c838c7b1a288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0617414b2ad7c96f1a3df4a6dd935395.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b60af8e12b6205f65f8cb0ecd870601d.png)
(1)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
(i)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30bf02b822ea9ded2e9fdc868d74ab96.png)
(ii)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
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5 . 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)
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解题方法
6 . 证明下列不等式:
(1)当
时,求证:
;
(2)设
,
,若
,求证:
.
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6455e38ff53ede2508e4d9cb23f0b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b0745ecaef6c9d1b65666e30892f597.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feac4de538eecda2cb5cf860cd665261.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3183647223da8dceeeee49bb69c64166.png)
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2018-02-27更新
|
1017次组卷
|
2卷引用:湖北省孝感市八校2017-2018学年高二上学期期末考试数学(文)试题
名校
7 . 已知
,我们知道
成立.
(1)求证:
;
(2)同理我们也可以证明出
.由上述几个不等式,请你猜测一个与
和
有关的不等式,并用数学归纳法证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81cbab062d7c2b918dca90e9e92682f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4df660da8b095ea86e010d54080be614.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47b2e22d798a51902cbfd62a24641009.png)
(2)同理我们也可以证明出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c9b07fd25b6e44656f6b186c7bb6915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a83ebbc345b194f2a9063d8e10e40672.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5da2c6ead4d33e9a602dc85bd55c598.png)
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2017-06-27更新
|
296次组卷
|
3卷引用:福建省三明市第一中学2016-2017学年高二下学期第二次月考数学(理)试题
福建省三明市第一中学2016-2017学年高二下学期第二次月考数学(理)试题(已下线)专题12.2 直接证明与间接证明、数学归纳法(精练)-2021年高考数学(理)一轮复习讲练测陕西省西安市第一中学2020-2021学年高二下学期期中理科数学试题
名校
8 . 设,我们常用
来表示不超过
最大整数.如:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d959974d562cb9ef138676ae943bc19c.png)
(2)在锐角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38335830b93ac4d99c28a8e209eecb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f5573b30734d65648f61c0a94c98de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6c9bcb51024df4a7d1a04e46ca12549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6f4e9bb8b453665bfe9b8fa24711cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26a1633c3dde29b96636a2300ab074f5.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f48da06492a0b0c8a31a5dc1531e8f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47bb945c963b0d56df9d784d3e3288c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a9d89ec3d1181091ea159b40952b65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
9 .
的内角
的对边分别为
,
,
,满足
.
(1)求证:
;
(2)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a988a30fb553c74d1f3f0f8062eeb45.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fefb66baf2c738593be618b5895c4975.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/413323ab92f73c1eabb235731bb5c399.png)
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名校
10 . 如图,是一座“双塔钢结构自锚式悬索桥”,悬索的形状是平面几何中的悬链线,悬链线方程为
(c为参数,
),当
时,该方程就是双曲余弦函数
类似的有双曲正弦函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b383983da73f97c0ec7922556b84c49.png)
和
的值;
(2)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70dfa06870da52663bbb4c7e18217dd9.png)
(3)
不等式
恒成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ad2f5a11d7437f506adab0996961269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594663e98b797cdc4efbd098cc15854f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d712038d937090679d0e8cee56b47a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b383983da73f97c0ec7922556b84c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7b3d6bb49565cf01620a0259431d7ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1272e4f338038b3b9468cb9ecc06fe26.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70dfa06870da52663bbb4c7e18217dd9.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8d489d153159fcf945322bf0c6761a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3120403a25e9fc836f06a7781d23c6ec.png)
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