Métodos para resolver inequações que envolvem funções elementares

Abstract

In this work, we will address some methods to resolve inequalities involving elementary functions. The two main methods we will use are: the well-known “Method of Signal Analysis of Functions”, and a method based on a valid property for continuous functions, defined in intervals, which we will call “Theme of Signal Permanence”. Although it seems to be a common theme, it is, in my opinion, rarely approached in academic works, mainly in relation to new proposals for its solutions. Therefore, we decided to build this work in the following way, first exposing all the necessary mathematical support for our object of study, that is, the numerical sets essential basics (Natural, Whole, Rational and Real) as well as their algebraic properties and order relations. More specifically, in relation to the set of real numbers, we will need the definitions of intervals, the relationship of this set with the numerical straight line, the axioms of order and their consequences: the properties of inequalities. In order to understand how inequalities work, and consequently to work with inequalities, it is essential to incorporate all concepts and properties in a comprehensive way, since this is what gives us support so as not to make mistakes. Moreover, it is important for this study to know the main elementary functions, be essential in determining the set-solutions of inequalities associated to them. Succeeding all this necessary support, we come to chapter 4: The Inequations. After defining them and showing some examples, we present the methods to solve them. Chapter 4 was divided into two sections: in section 4.1 we work with the Signal Analysis Method, and in section 4.2 we present the Signal Permanence Motto, and its application as a method for resolving inequalities. The latter is what is presented as new as a method for solving inequalities involving the known elementary functions (polynomial, rational, trigonometric, exponential, logarithmic, etc.).