【摘要】 泰勒公式是高等数学的重要内容,借助它可以解决很多问题.本文针对泰勒公式的应用讨论了9个问题,即应用泰勒公式定义某些非初等函数,近似计算和误差估计,对某些定积分进行近似计算,求某些复合函数的极限,求高阶导数在某些点的数值,研究函数的极值,证明不等式,利用泰勒公式判断级数的敛散性,求行列式的值。更多还原

【Abstract】 Talyor Formula is of great importance in advanced mathematics,and very helpful to the solutions of many other mathematical problems.This article will discuss some applications of Talyor Formula,i.e.defining some elementary functions,approximate calculation and error estimation,approximately calculating of some definite integrals,getting the limits of some composite functions,getting the numerical value of some points in higher derivatives,studying the extremums of functions,proving the inequalities,testing of convergence and divergence of series,and getting the values of determinants.更多还原