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Question about epsilon - delta proofs?
I have a page of examples of solving epsilon - delta proofs. Upon proving that lim x -> 2 (x^2 + x - 2) = 4, the page says " the right hand side is at the minimum when x + 3 is at its maximum. Since the maximum of x + 3 is 6, we know that,
|x - 2| < e / |x + 3| < e / 6
My question is if the maximum of x + 3 is 6, wouldnt all values of x make that inequality false (e / 2 < e / 6 is false for example)?
This is the page (example 4) for reference.
1 Answer
- 5 years agoFavorite Answer
Yes it is a mistake on the part of the example. The example should have proceeded as follows " the right hand side is at the *maximum* when x + 3 is at its *minimum*. Since the minimum of x + 3 is 4, we know that,
|x - 2| < e / |x + 3| < e / 4
