FORMATION OF THE CONCEPT OF THE LIMIT OF A FUNCTION AMONG STUDENTS OF HIGHER EDU CATION INSTITUTIONS

Abstract

The article is devoted to the methodology of forming the concept of a limit of a function for students of higher education institutions. The relevance of the study is determined by the fact that modern society is developing under conditions of the active application of mathematical methods in various spheres of human activity. This leads to increased requirements for the level of mathematical training of specialists in different fields. An important component of such training is students’ mastery of fundamental mathematical concepts. Among these concepts, in particular, is the concept of a limit of a function. Mastering this concept contributes to a better understanding by students of other key concepts of mathematical analysis, such as function continuity, the derivative, and the definite integral, which are based on the idea of a limiting process. The article analyzes domestic and foreign publications on the research topic. The developed methodology for forming the concept of a limit of a function involves introducing students to three definitions of the limit of a function at a point in the following sequence: in terms of sequences (according to Heine), in terms of neighborhoods, and in terms of the «ε–δ» definition (according to Cauchy). The chosen sequence makes it possible to implement the principle of moving from a definition that is more accessible for students’ understanding to a more complex one. Given the complexity of the formal definitions of the concept of a limit of a function at a point, their introduction is carried out using a concrete–inductive method with the involvement of appropriate graphical illustrations. In order to enhance students’ understanding of the more complex definitions of the limit of a function at a point (in terms of neighborhoods and the «ε–δ» definition), dynamic visualizations implemented using GeoGebra were employed. The proposed methodology for introducing the concept of a limit of a function is based on combining visual reasoning with subsequent analytical justification, which enables students to independently arrive at the formulation of various definitions of a function limit. This approach promotes the conscious and meaningful acquisition of the concept of a function limit by students.