## 泰勒公式及其在解题中的应用

The Taylor formula and its application in solving problems
Abstract: the Taylor formula is an important formula in mathematical analysis, and is also a basic theory of the calculus of one variable, and an important tool for solving problems in Higher Mathematics and it is also the theoretical method, it has become a research estimation error and the limit of function and other aspects of the indispensable tool, in approximate calculation there is a unique advantage, it can be used to simplify complex problems. It is the extension of the calculus mean value theorem, Taylor formula in various fields in calculus has important applications. In addition to this introduction to Lagrange and Taylor formula with remainder wear Asian remainder outside, also commonly used for the infinitive, power series expansion, the inequality proof, judge the convergence of series of applications to do a simple introduction, this paper not only introduces the Taylor formula of a binary function, also the Taylor formula of function of two variables is briefly introduced.

Keywords: Taylor formula; Lagrange remainder term; Pei Jarno remainder；Maclaurin formula

1.泰勒公式•2
1.1一元函数泰勒公式理论2
1.2二元函数泰勒公式理论• 4
2.泰勒公式在解题中的应用5
2.1一元函数泰勒公式在解题中的应用5
2.1.1利用泰勒公式求不定式•5
2.1.2利用泰勒公式进行幂级数展开7
2.1.3利用泰勒公式判断级数的敛散性•7
2.1.4利用泰勒公式证明不等式9
2.1.5利用泰勒公式求行列式的值•11
2.2二元函数泰勒公式在解题中的应用12
2.2.1求二元函数的泰勒展开式•12
2.2.2泰勒公式在极值方面的应用•13
2.2.3利用泰勒公式判定极限存在性13
2.2.4利用泰勒公式求极限14
2.2.5利用泰勒公式判别级数的敛散性•14

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