名校
解题方法
1 . 在高等数学中,我们将
在
处可以用一个多项式函数近似表示,具体形式为:
(其中
表示
的n次导数),以上公式我们称为函数
在
处的泰勒展开式.
(1)分别求
,
,
在
处的泰勒展开式;
(2)若上述泰勒展开式中的x可以推广至复数域,试证明:
.(其中
为虚数单位);
(3)若
,
恒成立,求a的范围.(参考数据
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69c15b525ef8e6ca5281ba79454ad6e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33cfe27fd2276a7c542f062c17b4d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
(1)分别求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad040ae0fab73f5dd7b1af48cd3b5f93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a48345d239aaf8e9ca1ff2846c08a99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66db91bb3be9e2b6ad567774e3699758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)若上述泰勒展开式中的x可以推广至复数域,试证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6d931430b1f41235a04287471c5098e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69fbf62426f2cc9fe0db2b0567b7037a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0da8f0351e47d68e95fb13727bf1a1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99e4c6d95c2ae50836b6c596b6df911d.png)
您最近一年使用:0次