LESSON NOTES MENU
 
Course: Calculus I
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:

Terminology

Terms you should be able to define: squeeze theorem (a.k.a. sandwich theorem)

Text Notes

Special Limits

`lim_(x->0) sinx/x = 1` `lim_(x->0) tanx/x = 1`
`lim_(x->0) (1-cosx)/x = 0` `lim_(x->0) (1+x)^(1/x) = e`

Mini-Lectures and Examples

STUDY: Limits - Algebraically

Supplemental Resources (optional)

Lesson: Limit Properties, Dale Hoffman's Contemporary Calculus

Geogebra Exploration: The Limit Laws, Mark Renault

Geogebra Exploration: A Special Limit, Mark Renault

rev. 2020-10-10