Symbolic Proof of Limits of Functions in Mathematica with Applications to Mathematics Education

Abstract

Although the limit of a function at a point is one of the most important concepts in mathematics, to prove symbolically its formal definition is a challenging exercise that requires a certain level of expertise usually out of the capabilities of most students. This paper introduces a new mathematica package to prove symbolically the values of limits of functions in terms of delta and epsiv. In addition to the case of finite limits at finite points, the cases of infinite limits and limits at the infinity are also considered. The package also includes additional commands for graphical output allowing the users to grasp the underlying ideas of this concept. In order to show the performance of the main commands, a comprehensive set of illustrative examples is provided. Some possible applications regarding mathematics education at the classroom are also briefly discussed.