名校
解题方法
1 . 在数学中,双曲函数是与三角函数类似的函数,最基本的双曲函数是双曲正弦函数与双曲余弦函数,其中双曲正弦:
,双曲余弦函数:
,(
是自然对数的底数).
(1)解方程:
;
(2)写出双曲正弦与两角和的正弦公式类似的展开式:
________,并证明;
(3)无穷数列
,
,
,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/9ea54f9abcfb83c1f8d4860de58d9a1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cea2c942a40975a4bed91960a217cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
(1)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/507ea92ca0fbfa95da0f01c201ff54a4.png)
(2)写出双曲正弦与两角和的正弦公式类似的展开式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6343611e15d5f379d06115077f05d2a4.png)
(3)无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.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/7268804f4cde744cf387b933409d0c33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2 . 设
我们可以证明对数的运算性质如下:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c042897ef7240e0f6039c79b4afe8176.png)
.我们将
式称为证明的“关键步骤”.则证明
(其中
)的“关键步骤”为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a08b88c327b7525f54a0c07c4cdb5f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c042897ef7240e0f6039c79b4afe8176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a5b710748a6c2604da45ba1080aaaee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c512c047783c07da1d4f4455a4033ef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c20bf29391da7eccd37b59c1898c158a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d53ee0d97877274c321928c897135c6.png)
您最近一年使用:0次
2019-12-31更新
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302次组卷
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3卷引用:上海市静安区2019-2020学年高三上学期期末数学试题
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