Understanding Epsilon Delta Limits Relationship in Calculus

In summary, the process of finding the derivative of a function involves approaching a specific point, X, from points to the left and right, with delta(y) and delta(x). As delta x and delta y approach zero, the values of x and y for the points also approach the values of X. This is represented by the shrinking of delta and epsilon around X.
  • #1
Miike012
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Homework Statement



Is my understanding correct?

As delta(y) and delta(x) approach X from points to the left and points to the right of X (x is what we wish to find the derivative of) then the x and y values of points to the left and right approach the x and y values of X.
And as the approach... delta x and delta y approach zero thus... the delta and epsilon shrink and shrink around X.

hope that isn't confusing.

Homework Equations





The Attempt at a Solution

 
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  • #2
There is a lot of abitrary phrasing in your explanation; the same sort of phrasing that makes the typical definitions in calculus non-rigorous.

Try putting it into more solid terms and state clearly the relationship between delta and epsilon.
 

What is the "Epsilon Delta Limits Applet"?

The "Epsilon Delta Limits Applet" is a computer program or application that helps visualize the concept of limits in calculus. It is a helpful tool for students and teachers to better understand and practice finding limits of functions.

How does the "Epsilon Delta Limits Applet" work?

The applet works by allowing the user to input a function and choose a specific limit point. It then displays a graph of the function and visually shows how the limit is calculated using the epsilon-delta definition. The user can also adjust the values of epsilon and delta to better understand their relationship to the limit.

What are the benefits of using the "Epsilon Delta Limits Applet"?

The applet provides a visual aid for understanding the concept of limits, which can be a challenging topic in calculus. It allows for interactive exploration and practice, making it a useful learning tool for students. It also helps teachers in explaining the concept to their students.

Is the "Epsilon Delta Limits Applet" accurate?

Yes, the applet utilizes the standard mathematical definition of limits, so the results are accurate. However, it is important to note that the applet is meant to supplement learning and not replace the understanding of the underlying concepts.

Is the "Epsilon Delta Limits Applet" free to use?

Yes, the applet is typically free to use and can be accessed online through various websites. Some versions may require a small fee or subscription, but there are plenty of free options available.

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