Algebra I / Elem. Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems
Algebra II / E&I Algebra
Exponents & Polynomials Intermediate Algebra starts here!

Factoring Rational Expressions Rational Equations and Applications
Algebra III / Inter. Algebra
Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III
Sequences and Infinite Series Power Series Vectors and Geometry of Space Vector-Valued Functions
Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis
S = contains supplemental resources
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:

• 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)