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Section16Exercises

Exercises in an “exercises” section are numbered automatically. However, what if you have a busted problem and remove it? Then a bunch of problem numbers change and your list of homework for your students changes as well. What a mess. Use auto-numbering while writing and refining. Once stable, go ahead and hard-code problem numbers as you delete/add. Notice the oddly numbered problem below. Once you go down this road, you can't stop. But instructors will thank you for it.

More precisely, once you hard-code a number for a problem, you will likely need to hard-code every subsequent problem number in that section of exercises. This is because the automatic numbering is unlikely to be what you really want, or what you had before.

1An Exercise in a Section

Exercises can appear in a “section” of their own. You need to give the section a title, even if it seems obvious what to call it. Individual exercises may have titles, as you choose. Problem: How should we hide solutions?

Solution
42aAn Exercise with a Hard-Coded Problem Number

Compute the definite integral \(\definiteintegral{2}{4}{x^2}{x}\text{,}\) not as an approximate value from a Riemann sum, but as an exact value based of the limit by using the Fundamental Theorem.

Solution
3

Can you prove Corollary 4.1 directly? If not consider that a problem could have several parts, which should be formatted as a second-level list, since the problems normally get numbered at the top level.

  1. Why is this result a Corollary?

  2. Could you interchange the Theorem and Corollary?

Hint 1 Hint 2 Answer Solution