A importância das sequências numéricas para estudo do cálculo diferencial no ensino médio

Abstract

We know that it is in High School that the students have a first contact with the definition of function and, furthermore, we know that the main objective of Calculus is not to study limits, derivatives and integrals, but the study of functions using these tools. The introduction of some tools of the Differential Calculus on polynomials in High School, in an introductory and intuitive way, is very useful for a better understanding of the behavior of these functions, letting the formalism and the calculation applied to the most diverse functions continue being introduced in the higher education. In this work we present a proposal of activities to introduce some concepts of Differential Calculus on polynomials in high school. More specifically, we approach the concepts of sequences numeric series, and limits to support some concepts of derivative and optimization of polynomials functions. In each topic, illustrative activities will be proposed in order to introduce, in a simple way, the intuitive idea of the Differential Calculus. We also introduced some numerical methods, such as the Bisection method and Newton's method, to find zeros of polynomial functions, aiding in the search for optimal points of polynomials. We apply the concepts presented in illustrative activities, in order to facilitate the understanding of these concepts.