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**

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.

**Supplemental Resources (recommended)**

Need a complete trig review sheet?

Download/Print: Paul Dawkin's Trigonometry Cheat Sheet

Need a one-page basic trig formulas sheet?

Download/Print: Prof. Keely's Trigonometric Identities Sheet

**Supplemental Resources (optional)**