# Ch 5: Limits: Tutoring Solution

### About This Chapter

## How it works:

- Begin your assignment or other calculus work.
- Identify the limits concepts that you're stuck on.
- Find fun videos on the topics you need to understand.
- Press play, watch and learn!
- Complete the quizzes to test your understanding.
- As needed, submit a question to one of our instructors for personalized support.

## Who's it for?

This chapter of our calculus tutoring solution will benefit any student who is trying to learn limits and earn better grades. This resource can help students including those who:

- Struggle with understanding properties of limits, the Squeeze Theorem, asymptotes or any other limits topic
- Have limited time for studying
- Want a cost effective way to supplement their math learning
- Prefer learning math visually
- Find themselves failing or close to failing their limits unit
- Cope with ADD or ADHD
- Want to get ahead in calculus
- Don't have access to their math teacher outside of class

## Why it works:

**Engaging Tutors:**We make learning limits simple and fun.**Cost Efficient:**For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.**Consistent High Quality:**Unlike a live calculus tutor, these video lessons are thoroughly reviewed.**Convenient:**Imagine a tutor as portable as your laptop, tablet or smartphone. Learn limits on the go!**Learn at Your Pace:**You can pause and rewatch lessons as often as you'd like, until you master the material.

## Learning Objectives

- Define limits using graphs.
- Using proper notation, identify limits numerically.
- Understand how one-sided limits relate to continuity.
- Calculate the limits of functions.
- Describe the properties of limits.
- Explain the Squeeze Theorem.
- Understand how asymptotes and infinity relate to limits.

### 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. 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.

### 6. 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.

### 7. 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.

### 8. Solving 1 Divided by Infinity

In this lesson, we will analyze the expression 1 divided by infinity through the use of limits, tables, and graphs. We will see how to work with the abstract concept of infinity within a mathematical expression.

### 9. Finding the Limit of (1-cos(x))/x

We will see how to find the limit of (1 - cos(x)) / x, as x approaches a, for the case when a is 0 and when a is not equal to zero. We will see two different methods for when a is 0, so you can choose which method you like better.

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### Other Chapters

Other chapters within the Calculus: Tutoring Solution course

- Graphing and Functions: Tutoring Solution
- Continuity: Tutoring Solution
- Geometry and Trigonometry in Calculus: Tutoring Solution
- Using Scientific Calculators in Calculus: Tutoring Solution
- Rate of Change: Tutoring Solution
- Calculating Derivatives and Derivative Rules: Tutoring Solution
- Graphing Derivatives and L'Hopital's Rule: Tutoring Solution
- Applications of Derivatives: Tutoring Solution
- Area Under the Curve and Integrals: Tutoring Solution
- Integration and Integration Techniques: Tutoring Solution
- Integration Applications: Tutoring Solution
- Differential Equations: Tutoring Solution