作业帮英语翻译泰勒公式及其应用 摘要 本文简要介绍了泰勒公式及其几个常见函数的展开式,针对泰勒公式的应用讨论了九个问题,即应用
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英语翻译
泰勒公式及其应用 摘要 本文简要介绍了泰勒公式及其几个常见函数的展开式,针对泰勒公式的应用讨论了九个问题,即应用泰勒公式求极限,证明不等式,判断级数的敛散性,证明根的唯一存在性,判断函数的极值,求初等函数的幂级数展开式,进行近似计算,求高阶导数在某些点的数值,球行列式的值.
关键词 泰勒公式；极限；不等式；敛散性；
泰勒公式及其应用 摘要 本文简要介绍了泰勒公式及其几个常见函数的展开式,针对泰勒公式的应用讨论了九个问题,即应用泰勒公式求极限,证明不等式,判断级数的敛散性,证明根的唯一存在性,判断函数的极值,求初等函数的幂级数展开式,进行近似计算,求高阶导数在某些点的数值,球行列式的值.
关键词 泰勒公式；极限；不等式；敛散性；
Taylor's formula and its application.
This paper briefly introduces Taylor's formula and the expansion of usual functions.Based on the application of Taylor's formula, it also discusses nine questions, which are calculating limit,proofing inequality, judging the convergence of a term series,proving the only existence root, distinguishing the extreme value,calculating the elementary function of power series expansion,doing approximate calculation, calculating the value of higher derivative in some points,calculating evaluation of determinants.
KEY WORDS:Taylor's formula, limitation, inequation, convergence
This paper briefly introduces Taylor's formula and the expansion of usual functions.Based on the application of Taylor's formula, it also discusses nine questions, which are calculating limit,proofing inequality, judging the convergence of a term series,proving the only existence root, distinguishing the extreme value,calculating the elementary function of power series expansion,doing approximate calculation, calculating the value of higher derivative in some points,calculating evaluation of determinants.
KEY WORDS:Taylor's formula, limitation, inequation, convergence