{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# RGFT_Task_1 - “y” would be No matter what ∈ you give...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
RGFT Task 1      The statement , given any real number , there exists another real number δ 0 so that if δ then ∈. , In simple terms the value of δ ∈. will depend on the value of ∈. , We begin with a value for From this value we can then determine a corresponding value for δ . . 0 See the graph below L + L L - a- δ a a+ δ
RGFT Task 1      First, pick a range for values around the number L on the y axis. Then determine a range of δ values around the number a on the x-axis, but not including the actual a value. The basic concept is that we are trying to narrow down a small range of X to a small range of Y. Keep in mind that the range of “x” is given by ± δ , and the range of “y” is given by ± . Even if there is difficulty figuring out “x” right at the value it’s approaching, we can solve what

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: “y” would be. No matter what ∈ you give, there is always a distance around δ- as long as your “x” is within , where is going to be within the ∈ range. For example: For most values of x, the equation becomes simply. However, at x=1, it is undefined. This function would have a hole at x=1. The closer we get to x=1, the more precisely we can define the function at x=1. In the example, = 3, L = 3, and a = 1. We can utilize the delta-epsilon definition of a limit to show this information. The next step is to manipulate the equation to the form of . We start by canceling out the (x-1) term from the top and bottom of the equation leaving us with RGFT Task 1 This equation further simplifies as follows: Divide by 3 on both sides Therefore you have So for this example: The main point is to know that for any ∈ , we have the ability to find a δ , no matter how small ∈ gets....
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern