# Epsilons and Deltas:: Book Error? Or My Error?

Tags: book, deltas, epsilons, error
 P: 3,012 1. The problem statement, all variables and given/known data Given f(x) = mx + b, m > 0, L = (m/2) + b, xo = 1/2 , $\epsilon = c >0$ find (a) an open interval on which the inequality |f(x) - L| < $\epsilon$ holds. Then find (b) $\delta$ such that 0 < |x - xo| < $\delta\Rightarrow$ |f(x) - L| < $\epsilon$ Here is my problem with the book's solution. Since the condition $\epsilon=c>0$ was given, I only used the right-hand-side of the inequality: [itex]-c<|f(x)-L| 0 ?
 P: 1,106 The book is right, but I don't know why it introduces the unneeded term c. I'm not sure if they are trying to trick you, but epsilon, or c for that matter, is just an arbitrary positive number. Look at the inequality |f(x) - L| < e again (e is just an arbtirary positive number; we usually think of it as very small). You interpreted this correctly in the previous limit question I helped you out with. All this inequality is saying is that f(x) is within a distance e from L. Remember, |f(x) - L| < e is equivalent to L - e < f(x) < L + e. If you choose to write it in the latter form, you have to drop the absolute value signs (which I think is what tripped you up).
 P: 3,012 Oh yeah! We define epsilon to be a positive number. That wAs stupid of me! Thanks!
P: 120

## Epsilons and Deltas:: Book Error? Or My Error?

what course is this
P: 3,012
 Quote by Luongo what course is this
This from a Calculus Textbook. Self Study.

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