利用函数的幂级数展开式求下列不定式极限：

A .https://assets.asklib.com/psource/2015103008541736328.jpg B .https://assets.asklib.com/psource/2015103008543025282.jpg C .https://assets.asklib.com/psource/2015103008544162569.jpg D .https://assets.asklib.com/psource/2015103008545413665.jpg

<img src='https://img2.soutiyun.com/ask/2020-12-20/977328821805932.png' />

<img src='https://img2.soutiyun.com/ask/2020-12-22/977479103761578.png' />

<img src='https://img2.soutiyun.com/ask/2021-01-25/98044366648261.png' />

<img src='https://img2.soutiyun.com/ask/2020-12-10/976481945992252.png' />

是 否

函数<img src='https://img2.soutiyun.com/shangxueba/ask/17670001-17673000/17671257/2015102914165070741.jpg' />在x=2处的泰勒级数展开式为（）． A．<img src='https://img2.soutiyun.com/shangxueba/ask/17670001-17673000/17671257/2015102914171256962.jpg' /> B．<img src='https://img2.soutiyun.com/shangxueba/ask/17670001-17673000/17671257/2015102914172646978.jpg' /> C．<img src='https://img2.soutiyun.com/shangxueba/ask/17670001-17673000/17671257/2015102914174241489.jpg' /> D．<img src='https://img2.soutiyun.com/shangxueba/ask/17670001-17673000/17671257/2015102914180033916.jpg' />

已知<img src='https://img2.soutiyun.com/ask/2020-12-01/975701179868315.png' />,求对应的序列x(n). [利用级数展开式<img src='https://img2.soutiyun.com/ask/2020-12-01/975701192867058.png' />]

将下列函数展开成(x-3)的幕级数： <img src='https://img2.soutiyun.com/ask/2020-08-12/966088220653753.png' />

将函数<img src='https://img2.soutiyun.com/ask/2020-12-14/97678986011847.png' />展开成简单幂级数,并指出它收敛的区间.

求幂级数<img src='https://img2.soutiyun.com/ask/2020-12-11/976533602465549.png' />的收敛域及和函数,并求常数项级数<img src='https://img2.soutiyun.com/ask/2020-12-11/976533633968351.png' />的和.

将下列各周期函数f(x)展开成傅里叶级数，如果f(x)在一个周期的表达式为： <img src='https://img2.soutiyun.com/ask/2021-01-14/979481711875738.jpg' />

以z₀为展开中心,把下列各函数展开成洛朗级数(包括泰勒级数作为它的特殊情形),并指出展开式成立的区域: (1)<img src='https://img2.soutiyun.com/ask/2021-01-15/979557772361073.png' />; (2)<img src='https://img2.soutiyun.com/ask/2021-01-15/979557781103573.png' />; (3)<img src='https://img2.soutiyun.com/ask/2021-01-15/979557792907248.png' />.

将下列函数展成麦克劳林级数(可用已知的展开公式): <img src='https://img2.soutiyun.com/ask/2020-11-13/974119543727273.png' />

<img src='https://img2.soutiyun.com/ask/2020-12-22/977477173109151.png' />

<img src='https://img2.soutiyun.com/ask/2020-08-04/965409790910194.png' />

<img src='https://img2.soutiyun.com/ask/2020-08-21/966869110386338.png' />

将函数<img src='https://img2.soutiyun.com/ask/2020-08-10/96591628820966.png' />展开成关于x-1的泰勒级数。