名校
解题方法
1 . 固定项链的两端,在重力的作用下项链所形成的曲线是悬链线.1691年,莱布尼茨等得出“悬链线”方程
,其中
为参数.当
时,就是双曲余弦函数
,悬链线的原理运用于悬索桥、架空电缆、双曲拱桥、拱坝等工程.类比三角函数的三种性质:①平方关系:
;②两角和公式:
,③导数:
定义双曲正弦函数
.
(1)直接写出
,
具有的类似①、②、③的三种性质(不需要证明);
(2)当
时,双曲正弦函数
的图像总在直线
的上方,求直线斜率
的取值范围;
(3)无穷数列
满足
,
,是否存在实数
,使得
?若存在,求出
的值,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/226ad7337354c5ee27aed367ac7e897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed02acb0c7b4e40c26f6760627a033e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af7ca3fcd9a43d520ed650b80ef2dad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c960a553e62119bd03b43eb3efa4112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bf160d9a666a2f63ccc608836ae6eb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbcc2e6bbcbd9344009a0b032a42fbeb.png)
(1)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c540f798ab69463cf35af2772a3a19cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b1ee2c2965ab4a51d26062fb0e665a5.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba71c207f3a94133eb53ea1b05e4b393.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ecf3a1fecf89a37a677393d0bfe27b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b0d21e828e1f9407851c80d0f6e1b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-03-19更新
|
879次组卷
|
3卷引用:上海市四校(复兴高级中学、松江二中、奉贤中学、金山中学)2024届高三下学期3月联考数学试卷
上海市四校(复兴高级中学、松江二中、奉贤中学、金山中学)2024届高三下学期3月联考数学试卷(已下线)上海市四校(复兴高级中学、松江二中、奉贤中学、金山中学)2024届高三下学期3月联考数学试题变式题17-21上海市建平中学2024届高三下学期三模考试数学试题
18-19高一下·上海浦东新·期末
名校
2 . (1)证明:
;
(2)证明:对任何正整数n,存在多项式函数
,使得
对所有实数x均成立,其中
均为整数,当n为奇数时,
,当n为偶数时,
;
(3)利用(2)的结论判断
是否为有理数?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7d969abdb2f6638663e80e15bffd247.png)
(2)证明:对任何正整数n,存在多项式函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e89220eb96a4757f2988362bc04e80c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc2b21d31f1bb8801b0117b49086a634.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a68a728745bb3bd33917dc715c4fc945.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31bd42f8e3f220a7b1c6f6945e73bc10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feaffe7219b4b165cf67c7751dff8876.png)
(3)利用(2)的结论判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d82121ba82f39bb5e8068bd11ed6d74.png)
您最近一年使用:0次