从多项式逼近函数引出泰勒公式

Introduction of the Taylor′s formula form polynomial approximation function

为便于初学者理解和掌握泰勒公式,从多项式逼近函数的角度出发引出了泰勒公式及其余项.给出了逼近函数的一次及二次多项式,分析了多项式逼近函数的误差、性质及其几何意义.在此基础上,类似逼近函数的低次多项式,利用递推公式构造了逼近函数的n次多项式,并由此引出了泰勒定理.

For the convenience of beginner to understand and master the Taylor′s formula,the Taylor′s formula and its remainder term is introduced from the point of polynomial approximation function.The polynomial of the first degree and the second degree for approximating function are given,the error,property and geometric meaning of the polynomial approximation function are analyzed.Based on this,similar with the construction of lower degree polynomial,the n-th polynomial for approximating the function is obtained by recursion formula,and then the Taylor′s theorem is introduced.