how to easily write the epsilon-delta proofs for limits

TL;DR

This video explains how to prove limits using the epsilon delta definition, with linear and square root examples.

Transcript

okay this video can possibly save your gpa if you're taking a car one class at a university how to prove limits with the abstinence delta definition the first example is a linear situation check this out i would recommend you guys to always write down the pf because your professor will be really happy when he or she sees the pf which stands for pro... Read More

Key Insights

• ⛔ Writing down the proof for the epsilon delta definition is important for understanding and demonstrating your knowledge of limits.
• 💁 Following the given-choose-suppose-check format helps structure the proof and ensures it is rigorous.
• 🫚 The linear and square root examples show the application of the epsilon delta definition in different scenarios.
• 🧑‍🏭 Factoring out common factors and manipulating expressions can simplify the proof process.
• 💦 Understanding the properties of absolute values and square roots is crucial for working with the epsilon delta definition.
• 🧡 Determining the appropriate value of delta is essential to prove that the difference between the function and the limit is within the desired range.
• 👍 Proving limits using the epsilon delta definition requires attention to detail and algebraic manipulation skills.

Questions & Answers

Q: What is the importance of writing down the proof for the epsilon delta definition of a limit?

Writing down the proof helps your professor understand your thought process and shows that you have a clear understanding of the concept. It also demonstrates your ability to follow the proper format and steps.

Q: How do you start the epsilon delta definition of a limit?

Start by stating "given epsilon is greater than zero." This sets the stage for the proof and establishes the condition that we want the limit to satisfy.

Q: What should you do if you don't know the value of delta in the proof?

If you don't know the value of delta yet, simply leave it blank for the time being and continue with the other steps. It's okay to leave it blank as long as you eventually determine its value.

Q: Why is it important to check the absolute value of the function minus the limit in the proof?

Checking the absolute value of the function minus the limit allows us to show that the difference between the function and the limit is less than the desired epsilon value. This is a key step in proving that the limit exists.

Summary & Key Takeaways

• The video teaches how to use the proof format and steps for the epsilon delta definition of a limit.

• It emphasizes the importance of writing down the proof and following a specific format.

• The linear and square root examples demonstrate the application of the epsilon delta definition.