摘要
目的推广带有皮亚诺(Peano)型余项的泰勒公式及应用.方法应用带有皮亚诺型余项的泰勒公式,将判断函数极值性和凸凹性的定理进行推广.结果得到判断函数极值点和曲线拐点的充分条件.结论应用放宽条件的带有皮亚诺(Peano)型余项的泰勒公式扩展了其使用范围,使计算更加简捷.
In order to generalize Formula Taylor with Surplus Item Peano and its application, the application of Formula Taylor with the Peano form of the remainder was discussed in calculating the limits of indeteuminate form and analyzing the properties of functions. By generalizing the theorems used to judge such properties as local minimum and local maximum and the concave upward and downward in Higher Mathematics and Mathematical Analysis, the sufficiency conditions to judge the local minimum and maximum of functions and the inflection points of curves were obtained.
出处
《沈阳建筑大学学报(自然科学版)》
EI
CAS
2005年第6期774-776,共3页
Journal of Shenyang Jianzhu University:Natural Science
基金
辽宁省教育厅高等学校科学研究项目(2004C058)
关键词
泰勒公式
极值
保号性
拐点
Taylor formula, extreme value, the character of keep symbol, the pot of corner