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: Limits Algebraically

Overview

It is important to be able to evaluate limits graphically and numerically, but the primary approach is algebraically. The goal is to use algebraic methods to simplify the function, so that the x-value being approached can be plugged into the function producing the limit's result.

Objectives

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

• 1.3.1 Use correct mathematical notation throughout the process of evaluating a limit algebraically
• 1.3.2 Use a variety of algebraic methods to simplify and evaluate a limit
• 1.3.3 Algebraically evaluate a limit that is of the "0/0 case" including using factoring, reducing, rationalizing, or other algebraic manipulations as needed
• 1.3.4 Algebraically determine that a limit of a function does not exist

Terminology

Terms you should be able to define: limit that is of the "0/0 case"

Text Notes

• Evaluating limits algebraically is big topic which will continue to be explored as this chapter continues including the following topics: limit theorems, limits involving trig functions, and limits involving exponential or logarithmic functions.
• This is an early transcendental course so be sure to try limit problems that involve trigonometric, exponential, and logarithmic functions, not just polynomial and rational.

Mini-Lectures and Examples

STUDY: Limits - Algebraically

Supplemental Resources (recommended)

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