While research on the opportunity to learn about mathematics concepts provided by textbooks at the secondary level is well documented, there is still a paucity of similar research at the undergraduate level. Contributing towards addressing this knowledge gap, the present study examined opportunities to engage in quantitative and covariational…

We use Taylor's formula with Lagrange remainder to prove that functions with bounded second derivative are rectifiable in the case when polygonal paths are defined by interval subdivisions which are equally spaced. As a means for generating interesting examples of exact arc length calculations in calculus courses, we recall two large classes of…

The purpose of this article is to examine the reasoning behind the wording of the definition of the particular solution to an initial value problem. This article will be of practical importance for students taking a first year calculus course that includes the study of first order linear separable differential equations.

For most first semester students, the definition of a continuous function causes confusion. We discuss a presentation that leaves students with a better intuitive understanding of continuity, as well as an appreciation for the definition. (Contains 3 footnotes.)