# Ch 35: Limits in Precalculus

### About This Chapter

## Limits in Precalculus - Chapter Summary and Learning Objectives

Refresh your understanding of how limits are used, described and calculated in mathematics as you study these lessons. Take a look at the squeeze theorem, what it means and how to use it, and explore how graphing can help you define and understand limits. The lessons in the chapter cover the following material:

- What limits and asymptotes are
- How to annotate and describe limits
- Definition and explanation of the squeeze theorem
- Description of the properties of limits
- Equation for a tangent line

## Course Topics

Lesson | Objective |
---|---|

Using a Graph to Define Limits | Create graphic illustrations to define limits. |

Understanding Limits: Using Notation | Use notation to distinguish limits numerically. |

One-Sided Limits and Continuity | Rewrite and connect one-sided limits to continuity. |

How to Determine the Limits of Functions | Verify function limits. |

How to Approximate Limits From Graphs & Data Tables | Employ graphing to approximate limits. |

Understanding the Properties of Limits | Recognize properties of limits. |

Squeeze Theorem: Definition and Examples | Explain and illustrate the squeeze theorem. |

Graphs and Limits: Defining Asymptotes and Infinity | Delineate limits for infinity and asymptotes. |

Tangent Line: Definition & Equation | Describe and calculate a tangent line. |

### 1. Using a Graph to Define Limits

My mom always said I tested the limits of her patience. Use graphs to learn about limits in math. You won't get grounded as we approach limits in this lesson.

### 2. Understanding Limits: Using Notation

Join me on a road trip as we define the mathematical notation of limits. As time goes by and I traverse hills and highways, the limit of my speed changes. Learn how to write these limits in this lesson.

### 3. One-Sided Limits and Continuity

Over the river and through the woods is only fun on a continuous path. What happens when the path has a discontinuity? In this lesson, learn about the relationship between continuity and limits as we walk up and down this wildlife path.

### 4. How to Determine the Limits of Functions

You know the definition of a limit. You know the properties of limits. You can connect limits and continuity. Now use this knowledge to calculate the limits of complex functions in this lesson.

### 5. How to Approximate Limits From Graphs & Data Tables

In this lesson, we will review what limits are, and then we will look at how to approximate limits from graphs and how to approximate limits from data tables. We will use real-world examples to explore these methods.

### 6. Understanding the Properties of Limits

Graphically we can see limits, but how do we actually calculate them? Three words: Divide and Conquer. In this lesson, explore some of the properties that we can use to find limits.

### 7. Squeeze Theorem: Definition and Examples

In the Kingdom of Rimonn there are three rivers. In this lesson, learn how these waterways demonstrate the power of the squeeze theorem for finding the limits of functions.

### 8. Graphs and Limits: Defining Asymptotes and Infinity

Infinity is a hard concept to understand and the word asymptote is pretty intimidating. But this fun lesson will make both seem like a walk in the park as it defines both and shows their relationship using a graph.

### 9. Tangent Line: Definition & Equation

In this lesson, we explore the idea and definition of a tangent line both visually and algebraically. After learning how to calculate a tangent line to a curve, you will find a short quiz to test your knowledge.

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### Other Chapters

Other chapters within the Honors Precalculus Textbook course

- Working with Linear Equations
- Working With Inequalities
- Absolute Value Equations
- Working with Complex Numbers
- Systems of Linear Equations
- Mathematical Modeling for Precalculus
- Introduction to Quadratics
- Working with Quadratic Functions
- Geometry Basics for Precalculus
- Types of Functions in Precalculus
- Understanding Function Operations
- Graphing Functions in Precalculus
- Graph Symmetry
- Rate of Change
- Polynomial Function Basics in Precalculus
- Higher-Degree Polynomial Functions
- Rational Functions & Difference Quotients
- Rational Expressions & Function Graphs in Precalculus
- Exponential Functions & Logarithms in Precalculus
- Using Trigonometric Functions
- Trigonometric Graphs
- Solving Trigonometric Equations
- Trigonometric Identities
- Trigonometric Applications
- Graphing Piecewise Functions in Precalculus
- Vectors in Precalculus
- Matrices and Determinants in Algebra
- Understanding Arithmetic Sequences & Series
- Understanding Geometric Sequences & Series
- Analytic Geometry and Conic Sections
- Polar Coordinates and Parameterizations
- Working with Sequences & Series
- Sets & Probability
- Continuity