1 . 意大利画家达·芬奇在绘制《抱银貂的女子》时曾思索女子脖子上的黑色项链的形状对应的曲线是什么?即著名的“悬链线问题”.
年后约翰·伯努利与莱布尼茨得到悬链线的解析式为
,其中
为悬链线系数,
称为双曲余弦函数,且
,相应地双曲正弦函数为
.若直线
与双曲余弦曲线
和双曲正弦函数曲线
分别相交于点
,曲线
在A点处的切线与曲线
在
点处的切线相交于点
,给出如下结论:
①函数
为奇函数;
②
;
③
的最小值为
;
④
的面积随
的增大而减小.
其中所有正确结论的序号是_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca15cd772284da8cf1899d388df3a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23463dfec7ceb339b634613a0afee9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e7c627427318b62d977ff7a86c2cb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1392aa2eb76daff9047a0c6a3c077ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed0d713cb8d99fe07395c8536ee3b10b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d71f015144ffaf1faec94a259b4a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff92ef23dd31bb91ece0b416b231fd40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bfce28fedd1a1f0941f24ae6725497.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ec29c0bd794e89448bb7a6b71d5b045.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/112a622a3a8ca1ed0bfca9f3f142ec21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
其中所有正确结论的序号是
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