Topic: Limits and Continuity
Subtopic: Properties of Limits
Overview
This lesson makes formal the properties of limits (a.k.a. limit theorems). These properties govern what you can and cannot do algebraically when evaluating a limit. For instance you can rewrite a limit of a sum as a sum of limits, but you cannot rewrite a limit of a product as a product of limits.
Objectives
By the end of this topic you should know and be prepared to be tested on:
- 1.5.1 Understand the properties of limits
- 1.5.2 Evaluate limits algebraically by correctly applying the appropriate properties of limits
- 1.5.3 Understand, know when to apply, and know how to properly use the squeeze theorem
- 1.5.4 Evaluate limits of transcendental functions including trigonometric, exponential, and logarithmic
- 1.5.5 Recognize "special limits" such as the limit of (sinx)/x as x->0
Terminology
Define: squeeze theorem (a.k.a. sandwich theorem)
Text Notes
- The Squeeze Theorem, also known as The Sandwich Theorem, is so named because you are squeezing the limit between two curves like a sandwich. It is sometimes also called the Pinching Theorem so clearly there are a variety of names all based on the same squishing concept.
- About four "special limits" have been introduced (or will be soon) that are worth memorizing (below). We'll prove/justify them sometime in this chapter.
Supplemental Resources (optional)
Lesson: Limit Properties, Dale Hoffman's Contemporary Calculus