About This Chapter
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- 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 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