Question

Can someone help me with this limit problem? It involves definition of a limit/values of epsilon and delta. The problem is in the attachment.

Answer 1

Please see below.

Explanation:

Let `color(blue)epsi` `> 0` be given. Then with `delta =` _ __`epsilon`, and with `x` satisfying `abs(x-color(blue)6)` `< color(blue)delta`, (after some algebra), we arrive at `abs(f(x)-color(blue)(31)) < epsilon`

The problem is not well posed (In the source).

(1) The definition requires "`x` satisfying `color(red)(0 < )abs(x-color(blue)6)` `< color(blue)delta`"

(2) We cannot simply make `delta` a constant multiple of `epsilon`

We could use `delta = min{1,epsilon/13}` or we could use `delta = min{4, epsilon/16}`