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It generally follows the algorithm from this website:http://www.milefoot.com/math/calculus/limits/DeltaEpsilonProofs03.htm

focusing on the first example(example using linear functions)

The first table I get, but is the second table necessary, it basically restates the given?

it seems analogous to x + 1 = 3

x = 2

and then subbing 2 in for x