O USO DA DEFINIÇÃO FORMAL DE LIMITE FINITO PARA FUNÇÕES REAIS: UMA PROPOSTA PARA O ENSINO

Abstract

The main objective of this article is to study the following question: are there real-valued real functions, for which the study of the existence or not of the finite limit at a point is not possible, than using the formal definition of limit? For this, we first delimit the conceptual field involved in the construction of the concept of the limit of a function at a point, according to Vergnaud, in order to elaborate situations to work on our question. Next, we propose three activities whose analyses, both didactic and theoretical; illustrate the importance of the formal definition, as a relevant tool for approaching these activities. In addition, the mathematical work presented here aims to contribute to the deepening of functional thought, fundamental for mathematical analysis in general. We also provide didactic discussions and considerations, and some observations on teaching and learning, related to the formal definition of the limit, including the main concepts involved in this definition. The analyses of the activities have shown that it is possible to elaborate situations to mobilize the formal definition of the limit, to approach the concept of limit of certain functions, which appear in the manuals. As a result, it is an opportunity for students to apply this definition in situations where they cannot use the usual properties and techniques on limits. This allows them to broaden the understanding of this concept, as proposed by Vergnaud.

Keywords: Real functions, Formal definition of the limit, Finite Limit, Epsilon and delta, Mathematical course.