The limit of a function is the main concept that distinguishes calculus from algebra and geometry (and all other math). Limits are fundamental to the study of calculus. Thus, it is beyond important to acquire a working understanding of limits before moving on to other topics in calculus such as derivatives and integrals.
In order to discover and create important ideas, definitions, formulas, and theorems in calculus, a firm understanding of limits is needed. Furthermore, limits can be used to understand the behavior of functions including concepts such as asymptotes (vertical and horizontal) and continuity.
1.A. Finding Limit Graphically and Numerically
1.B. Finding Limits Algebraically
- Limit Properties - Direct Substitution (example problem)
- Limit Properties - Dividing Out Technique (example problem)
- Limit Properties - Rationalizing Technique (example problem)
- Epsilon-Delta Limit Definition (conceptual)
- Epsilon-Delta Limit Definition (example problem)
- Infinite Limits (conceptual)
- Infinite Limits and Vertical Asymptotes (conceptual and example problems)
- Limits at Infinity (conceptual)