Acciones y expresiones de la comprensión del límite de una función en un punto, por estudiantes de cálculo diferencial

This article responds to the concern: What understandings do students who participate in a differential calculus course in which the notions of approximation and trend are explored, about the concept of limit of a function at a point?"Understanding" is taken in light of the theory of Pirie and Kieren (1989) who describe it in terms of the complementarities of action and expression.To answer the question, a sequence of activities was designed around the concept of limit of a function at a point using the notions of approximation and trend through the GeoGebra dynamic mathematics software.For the study, a student was followed as a case study, who developed and completed the designed sequence of activities.This student exhibited evidence of understanding, from the theoretical perspective in which the study is positioned, performing complementarities of action and expression that are associated with the "Formalization" level of Pirie and Kieren (1989), managing to identify the common properties of the kinds of images that he had built as he developed the activities.