名校
解题方法
1 . 若两个函数
和
对任意
都有
,则称函数
和
在上
是疏远的.
(1)已知命题“函数
和
在
上是疏远的”,试判断该命题的真假.若该命题为真命题,请予以证明;若为假命题,请举反例;
(2)若函数
和
在
上是疏远的,求实数
的取值范围;
(3)已知常数
,若函数
与
在
上是疏远的,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68dcefc64522affe52cb23609e1ed318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b64537743379242ee87505563d3a92ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df606d4adb89b5473944bb98363a6f53.png)
(1)已知命题“函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b6e13798211ab7a313b83bb958a009.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5013206591edea029e8748159034a308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c69825660f852b3e07e21ddd804c4afb.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b6e13798211ab7a313b83bb958a009.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5013206591edea029e8748159034a308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d090c9fd3be22879e33f58e23be1bc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)已知常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e4cc00c283519973f7f8e1274b5c733.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/944d9ff34a45741697f2e5c115af1074.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30334e741241937414a7c09ba4759989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c70eceeee00d6fcc82d35d24618dcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
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2021-09-15更新
|
861次组卷
|
4卷引用:4.2指数函数C卷
名校
解题方法
2 . 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)
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