About This Chapter
Join us on a cross-country road trip in this video lesson series on limits. As our car travels at various speeds over time, we'll learn how to describe, understand and determine the limits of functions.
In a function, limits are used to described what happens as a variable approaches a certain number. For instance, if we hop on the interstate and start cruising along at highway speed, after we drive for 10 minutes, we could say that the limit of our function as we approach 10 minutes is 60 miles per hour. As we speed up or slow down, the limits as we approach different times will either increase or decrease. Let's hope we don't get pulled over for speeding!
Building on your understanding of limits and how they apply to the real world, you'll learn how to graph limits using proper notation. You'll learn how to 'divide and conquer' with the properties of limits, which include addition, subtraction, multiplication and division properties.
Finally, you'll understand more complex aspects of limits, such as what happens in discontinuous functions (one-sided limits), how functions relate to each other through the Squeeze Theorem and how to graph limits for asymptotes and infinity. To illustrate these concepts, we'll visit the rivers of the fictional Kingdom of Rimonn and encounter an earthquake on the way to grandma's house. So, fasten your seat belts, and let's explore the limits of functions!
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.
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Other chapters within the Math 104: Calculus course
- Graphing and Functions
- Vectors in Calculus
- Geometry and Trigonometry
- How to Use a Scientific Calculator
- Rate of Change
- Calculating Derivatives and Derivative Rules
- Graphing Derivatives and L'Hopital's Rule
- Applications of Derivatives
- Area Under the Curve and Integrals
- Integration and Integration Techniques
- Integration Applications
- Differential Equations
- Studying for Math 104