Unit 1

Intro

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.

Unit 1 Podcast

1.1 Determining Limits

    • Defining Limits
    • Limit Notation
    • Estimating Limits Graphically
    • Estimating Limits Numerically

    • Limit Properties
    • Direct Substitution
    • Dividing Out Technique
    • Rationalizing Technique

1.2 Limits and Graphing

    • Infinite Limits and Vertical Asymptotes
    • Limits at Infinity and Horizontal Asymptotes

    • Types of Discontinuities
    • Defining Continuity at a Point
    • Confirming Continuity over an Interval
    • Removing Discontinuities
    • Intermediate Value Theorem