Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / 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
Precalculus II / 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

Course: Calculus I
Topic: Limits and Continuity
Subtopic: One-Sided Limits

Overview

We have examined one-sided limits (limits from the left or from the right) graphically, but in this lesson we evaluate them algebraically.

CAUTION: Watch for limits that do not exist because the two side limits don't match.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 1.6.1 Use correct mathematical notation throughout the process of evaluating a one-sided limit algebraically
• 1.6.2 Algebraically evaluate one-sided limits, both those that do or do not exist
• 1.6.3 Algebraically evaluate a limit based on the results of its two corresponding one-sided limits

Terminology

Terms you should be able to define: one-sided limit, limit from the left, limit from the right, left-handed limit, right-handed limit

Mini-Lectures and Examples

STUDY: Limits - Algebraically

Supplemental Resources (optional)

Geogebra Exploration: Intuitive Notion of One-Sided Limit, Mark Renault

rev. 2020-10-10