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几种微积分解题定式解析

Analysis of several calculus solutions

Theoretical Mathematics Study / 2020,2(1): 1-7 / 2020-05-14 2749 3798

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• Authors: 蒋欣
• Information:

  苏州大学，苏州

• Keywords:
  Calculus; Typical problems; Method; Problem-solving formula
  微积分; 典型问题; 解题定式
• Abstract: It is no doubt how to problem-solving for the importance to learn calculus. It is more common phenomenon for the beginners not to start to solve questions. In this paper, for the types of typical problems in calculus, systematically summed up the general method of solution, and gives some typical examples. 无穷小量阶的问题用等价无穷小代换定阶法、泰勒公式（Taylor）定阶 法、求导定阶法解题；函数零点或方程实根或两曲线交点的存在性问题，要先 找函数再定区间，然后用介值定理或罗尔定理；积分区间关于原点对称的定积分， 要想到考查被积函数及其代数和的每一部分是否具有奇偶性；被积函数为周期 函数的定积分，要想到考查积分区间是否为整数倍的周期，以简化计算。
• DOI: https://doi.org/10.35534/tms.0201001c
• Cite: 蒋欣．几种微积分解题定式解析［J］．理论数学前沿，2020，2（1）：1-7．