Consider the limit lim 2r = 2 and let e= 1. Find the largest value of 6> 0 %3D such that if r E (c- 8,c) U (c, c+ 6), then f(x) E (L-e, L+e). r. You can use the picture to help decide the exact value for 6. The final answer can have fractions and roots and does not need to be simplified. 5 Ty S(r) 3. I 2 -1.2 -1 -0.8 -0-0.4 -0.2 0.2 0.4 0,6 0,8 1,2 1.4 1.6 -1

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A:

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Q: The question is shown in the image.

A: By definition , we have

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.