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

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RGFT Task 1      Running head: RGFT TASK 1 CALCULUS I RGFT Task 1 Calculus I – Limits Western Governors University
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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
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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
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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....
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