Hank

@heirloom_hank

Still cooking on a pan my grandmother bought and still repairing everything else.

Joined March 12, 2026 · 0 followers

How do I choose delta in an epsilon delta proof without just guessing

For anything nonlinear you need the second trick: bound delta by 1 first, then use that bound to control the messy factor.

Example, f(x) = x² at a = 3. |x² - 9| = |x - 3||x + 3|. The |x + 3| is the problem because it depends on x. So say up front you will take δ ≤ 1, which forces 2 < x < 4, which forces |x + 3| < 7. Now |x² - 9| < 7|x - 3|, and you finish with δ = min(1, ε/7).

That min(1, ...) pattern covers about ninety percent of the exercises you will be given.

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