The Application of Taylor formula in Limits and Approximation
DOI:
https://doi.org/10.54097/a2nzcd87Keywords:
Taylor formula, limits, approximation.Abstract
In higher mathematics, the extremely significant content is Taylor’s formula. Simple polynomial functions can be translated from complex functions by this formula. The Taylor formula can be seen as a useful tool to analyze and study many problems in mathematics because of its ability to reduce complexity. The Taylor Formula is an essential mathematical process for solving some problems about limits and approximation and has a unique advantage in rough calculation. The Taylor formula is an important tool in calculus, as it can transform nonlinear problems into linear ones with high accuracy. The topic of this paper is researching the application of the Taylor formula in different fields. In this paper, it will talk about the introduction of the Taylor formula, the expansion of the Taylor formula, and its remainders. It also would talk about the application of the Taylor formula in limits and approximation. As a broad mathematical formulation, the Taylor formula can be used to approximate function singularities, non-analytic behavior, or to simplify complex functions. It can be used in a variety of disciplines, including engineering, physics, and mathematics.
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