Applications of a Theorem of Mathematical Analysis
Applications of a Theorem of Mathematical Analysis

Author(s): Teodor Dumitru Vălcan
Subject(s): Social Sciences, Education, School education
Published by: Editura Eikon
Keywords: function; continuity; period; limit; integral;
Summary/Abstract: Solving exercises with integrable functions, calculating limits of sequences with integrals and proving integral inequalities are quite little known to pupils, students or teachers, despite the fact that they all have numerous properties and applications. In this paper we will present two properties of some integrable functions and immediate applications of these properties. Thus, we will present here two main results regarding certain continuous (hence, integrable) functions, after which we will present a series of very interesting applications of these results, to the calculation of limits of definite integrals or to the calculation of limits of series with definite integrals. Also, with the idea of training and developing the creative capacity of attentive readers interested in these issues, I launched the idea of obtaining a series of very interesting inequalities (using the results from the paper), inequalities that would otherwise be very difficult to prove.

• Details
• Contents