ABSTRACT
This chapter has four sections which focus on: the place of limits and continuity in elementary calculus curricula, an overview of education research on limits and continuity, a short history of limits and continuity and ways that limits and continuity can be introduced. There are many ways that limits and continuity can be introduced in an elementary calculus course. Limits may be explored numerically or graphically. Numerical explorations usually use tables to express values in the domain of a function and corresponding images. The construct of continuity (of a function at a point) has been a poor relation to the construct of limit in the chapter. One reason for this is that continuity of a function at a point can be defined in terms of the limit existing at this point. Functions like f are made up by mathematics teachers to illustrate a specific mathematical feature.
