Teaching Limit of a Function
This Demonstration presents the formal definition of the limit of a function, for in-class use by instructors. It allows the instructor to "challenge" students to find a suitable delta , first for some particular value of epsilon , and subsequently in general for an arbitrary epsilon (see  for an example of the intended pedagogical approach). Roman letters and are used instead of Greek letters and in order to reduce cognitive load for students encountering the concept of a limit for the first time.
 R. Smyth. "The Precise Definition of a Limit." Cooper Union. (Oct 8, 2021) faculty.cooper.edu/smyth/TechCompanion/Calc1/Ch02/PreciseDefLimit.htm.