## 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