From a Fall 1982 exam of Professor Ribet:
Suppose \( \epsilon \) is a number such that \( 0< \epsilon < 1 \).
In terms of \( \epsilon \), find a positive number \( \delta \) such that
\(|1/x - 1/2| < \epsilon \) is true whenever \( |x-2| < \delta \) is true.
Tags: diff, using-a-definition, diff-at-a-point, root, absolute-value, illustrative-example, sketching, a--g, t1, c2
There are two very good features to this problem. First, it gives students practice in working with the definition of a derivative. Second, it shows students that they cannot automatically proclaim a function to be non-differentiable simply because they know one component of the function to be non-differentiable. As an additional part, it may be instructive to ask students to predict whether or not the functions in part a) will be differentiable and to give reasons for their predictions.
– Jeff Barton 1998-08-09
This one ended up in the wrong place somehow. The keywords and the comments don't match the problem. It's a limit--using a definition problem, not a derivative problem.– Concha Gomez 1999-02-19