Considerações a respeito das formas indeterminadas do cálculo para o ensino básico

Abstract

The indeterminate forms in Calculus refers to the expressions that appear during the calculation of specific types of limits of functions. Although this topic is restricted to higher education level, it can appear in other educational levels, such as primary and secondary school, in the topics of arithmetic operations and exponential function. In the absence of Differential Calculus tools, such as limits and derivatives, delineating this field of mathematical expressions without mentioning those tools is challenging. The purpose of this essay is to explain, under the circumstances forementioned, the reason why 0/0 and 00 are named indeterminate forms. Therefore, a literature review in the area of Algebra was made, researching Fields of fractions, and in the area of Analysis, researching exponentiation. At the end of this work, discussions regarding the indeterminability of those forms were realized using the aforementioned literature review. Besides that, a sequence of activities to delineate the subject in primary and secondary education was created, alongside a script containing steps that justify why those forms are called indeterminate. Through the creation of both the activities and the script, that use exclusively elementary concepts available to students, we determined that it is possible to discuss the indeterminate forms without recurring to higher education elements.