Irrational Powers: perspectives for Higher Education
DOI:
https://doi.org/10.5902/2179460X65837Keywords:
Irrational exponents, Exponential function, Logarithmic function, Mathematics teachingAbstract
The set of real numbers has a fundamental role in the teaching of mathematics, both in Elementary and Higher Education levels, and should not be ignored the difficulties that students have in relation to such elements, especially the irrational. Thus, with the objective of seeking to produce knowledge on this topic, we developed ways to address the power function, exponential, their inverses and their respective derived functions, seeking to clarify the continuity. Therefore, we sought to know how textbooks present the exponential function and the rules of derivation the power functions, emphasizing the case of irrational exponents and, based on reflections, many of them inspired by the work Cálculo Diferencial and Integral by Courant (1951), we have prepared a material that resume discussions about the basic properties and expand the arguments regarding the continuity of such functions, in addition to an appropriate definition for the value a raised to the exponent x. As a result, we present two perspectives for working with this functions, as well as alternatives for defining powers of irrational exponents. We believe that this meeting of different interpretations enables a rethinking of the concepts, allowing achieve new perception on such matters.
Downloads
References
Aragona, J. (2010). Números Reais, 1º edn. Livraria da Física.
Avila, G. (1999). Introdução a Análise Matemática, 1º edn. Blücher.
Broetto, G. C. (2019). O ensino de números irracionais na educação básica e na licenciatura em matemática: um círculo vicioso está em curso? Bolema, 33, 728–747.
Courant, R. (1951). Cálculo Diferencial e Integral, 1º edn. Globo.
Courant, R., Robbins, H. (2000). O que é a Matemática?, 1º edn. Ciência Moderna.
Dante, L. R. (2013). Matemática: contexto e aplicações, 2º edn. Ática.
Demana, F. D., Waits, B. K., Foley, G. D., Kennedy, D. (2009). Pré-Cálculo, 1º edn. Addison Wesley.
Figueiredo, D. G. (2013). Análise, 1º edn. LTC.
Gil, A. C. (2008). Métodos e Técnicas de Pesquisa Social, 6º edn. Atlas.
Guidorizzi, H. L. (2008). Um curso de Cálculo, 5º edn. LTC.
Iezzi, G., Dolce, O., Murakami, C. (2013). Fundamentos da Matemática Elementar, 2, Logaritmos, 10º edn. Atual.
Leithold, L. (1994). O cálculo com geometria analítica, 3º edn. Harbra.
Lima, E. L. (2017). Curso de Análise, 14º edn. IMPA.
Lima, E. L., Carvalho, P., Wagner, E., Morgado, A. (2006). A Matemática do Ensino Médio. Volume 1., 1º edn. SBM.
Medeiros, V. Z., Caldeira, A. M., Silva, L. M. O., Machado, M. A. S. (2006). Pré-Cálculo, 1º edn. Pioneira Thomson Learning.
Monteiro, J. (1971). Elementos de Álgebra, 1º edn. Ao Livro Técnico.
Moreira, P. C., Vianna, C. R. (2016). Por que análise real na licenciatura?: um paralelo entre as visões de educadores matemáticos e de matemáticos. Bolema, 30, 515–534.
Oliveira, M. M. (2014). Como fazer pesquisa qualitativa, 6º edn. Vozes.
Ribenboim, P. (2012). Funções, limites e continuidade, 1º edn. SBM.
Silva, P. L. D. d., Spolaor, S. d. L. G. (2015). Um irracional: o número de euler. Ciência e Natura, 37(7), 89–94.
Souza, J. R. d., Garcia, J. R. d. S. (2016). Contato Matemática, 1º edn. FTD.
Stewart, J. (2013). Cálculo, 7º edn. Cengage Learning.
Swokowski, E. (1994). Cálculo com geometria analítica, 2º edn. Makron Books.
Thomas, G. B. (2002). Cálculo, 10º edn. Addison Wesley.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Ciência e Natura
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
To access the DECLARATION AND TRANSFER OF COPYRIGHT AUTHOR’S DECLARATION AND COPYRIGHT LICENSE click here.
Ethical Guidelines for Journal Publication
The Ciência e Natura journal is committed to ensuring ethics in publication and quality of articles.
Conformance to standards of ethical behavior is therefore expected of all parties involved: Authors, Editors, Reviewers, and the Publisher.
In particular,
Authors: Authors should present an objective discussion of the significance of research work as well as sufficient detail and references to permit others to replicate the experiments. Fraudulent or knowingly inaccurate statements constitute unethical behavior and are unacceptable. Review Articles should also be objective, comprehensive, and accurate accounts of the state of the art. The Authors should ensure that their work is entirely original works, and if the work and/or words of others have been used, this has been appropriately acknowledged. Plagiarism in all its forms constitutes unethical publishing behavior and is unacceptable. Submitting the same manuscript to more than one journal concurrently constitutes unethical publishing behavior and is unacceptable. Authors should not submit articles describing essentially the same research to more than one journal. The corresponding Author should ensure that there is a full consensus of all Co-authors in approving the final version of the paper and its submission for publication.
Editors: Editors should evaluate manuscripts exclusively on the basis of their academic merit. An Editor must not use unpublished information in the editor's own research without the express written consent of the Author. Editors should take reasonable responsive measures when ethical complaints have been presented concerning a submitted manuscript or published paper.
Reviewers: Any manuscripts received for review must be treated as confidential documents. Privileged information or ideas obtained through peer review must be kept confidential and not used for personal advantage. Reviewers should be conducted objectively, and observations should be formulated clearly with supporting arguments, so that Authors can use them for improving the paper. Any selected Reviewer who feels unqualified to review the research reported in a manuscript or knows that its prompt review will be impossible should notify the Editor and excuse himself from the review process. Reviewers should not consider manuscripts in which they have conflicts of interest resulting from competitive, collaborative, or other relationships or connections with any of the authors, companies, or institutions connected to the papers.
