# RGFT_Task_1 - y would be. No matter what you give, there is...

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 - 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 , no matter how small gets....
View Full Document

## RGFT_Task_1 - y would be. No matter what you give, there is...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online