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Appendix C Solutions to Selected Exercises (Deprecated)

Exercises Exercises

Exercise 1

This is an exercise in an “Exercises” subdivision at the level of a subsubsection. There is no question other than if the numbering is appropriate. Here is a self-referential link: Exercise 4.2.1.

The subsubsection has no title in the source, so one is provided automatically, and will adjust according to the language of the document.


This solution will migrate to a list of solutions in the backmatter. We include a sidebyside as a test.

This is a skinny paragraph which should be just 30% of the width.

And another skinny paragraph which should also be just 30% of the width.

Exercises 11.3 More Exercises

Exercise 6



Addition is associative.




First, add \(3\) and \(4\) to get \(7\text{,}\) then add \(5\) to arrive at \(12\text{.}\)

Exercises Exercises, Top-Level

Exercise 10 An 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?


Maybe a global switch should be used to suppress solutions, while a separate processing regime could use them as part of a solutions manual.

Exercise 42a An 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.


An antiderivative of \(x^2\) is \(F(x)=x^3/3\text{,}\) so by the FTC,

\begin{equation*} \definiteintegral{2}{4}{x^2}{x}=F(4)-F(2)=\frac{1}{3}\left(4^3-2^3\right)=\frac{56}{3}\text{!?!} \end{equation*}

This is indeed an exciting result, but we are mostly interested in seeing that the sentence-ending punctuation is absorbed properly into the displayed equation.

Exercise 12

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 MVT

Consider the definite integral as an area function and employ the Mean Value Theorem.

Hint 2 Motivator

Think harder!

Answer Helpful
  1. It follows easily.

  2. Yes.


We could prove either result first, then obtain the other as an easy consequence.