Examining Opportunities to Learn Limit in Widely Used Calculus Textbooks

Abstract

We examined widely used popular calculus textbooks to explore opportunities to learn the limit concept. Definitions, worked problems, and exercise problems were coded to examine if these tasks allow students to use informal thinking to coordinate domain and range processes to understand the infinite process of limit. Results revealed many exercise problems are step 1 tasks in genetic decomposition, where students only need to evaluate a function at one point. Such tasks prevent students from using their informal thinking productively. Recommendations and implications to calculus students and instructors are also mentioned.