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Derivatives and Integrals An Annotated Discourse

Robert Beezer, A. Second Author

Section 38 Exercises, Multiple Subsections

This <section> of the sample article demonstrates a “structured division.” You are reading the introduction to the division, then there is a faux <subsection>, followed by three <exercises> divisions. Note that the three are numbered as if they are also fellow<subsection>. And a cross-reference to one of the contained <exercise> will be numbered use the number of the <subsection>, Exercise 38.3.1.
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Compare this section with the similar Section 36, previous. The following text is mostly nonsense, just for testing purposes.
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Subsection 38.1 Faux Subsection

Pellentesque nec condimentum ligula, quis interdum mauris. Ut sed urna lacinia, aliquam arcu id, faucibus nisi. Suspendisse potenti. Curabitur in erat ultricies, condimentum mi nec, vehicula mauris. Duis faucibus risus fermentum velit hendrerit, non laoreet massa maximus. Donec bibendum elit ac lectus lobortis luctus. Ut finibus, dolor ut euismod tristique, ligula tortor tempus arcu, finibus semper purus erat ut ligula. Aenean accumsan ut ante vel euismod.
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Exercises 38.2 Drill Exercises

1. Drill One.

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Cras congue urna nulla. Aliquam eget euismod tellus. Maecenas nibh libero, venenatis a laoreet in, tempor sit amet sem. Morbi sit amet justo tempor velit auctor placerat. Maecenas nec lobortis orci. Aenean dictum enim lacus, ac blandit lacus elementum nec. Mauris porttitor neque volutpat tincidunt sollicitudin. Cras porta lectus ac facilisis tempor. Suspendisse in velit nisl. Sed convallis leo at nunc aliquet fermentum. Pellentesque feugiat at ex sed elementum. In porta vulputate ipsum sit amet consectetur.
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Figure 38.5. A figure in an <exercise> in a structured division to test that it is numbered with consideration of the containing <exercises>
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2. Drill Two.

Aliquam sagittis ex at magna porttitor, quis scelerisque ligula malesuada. Vestibulum vitae mauris id nisi pretium ornare a id lectus. Nam suscipit magna id sem ultricies vestibulum. Nulla facilisi. Duis venenatis lectus massa, ac mollis nisi suscipit non. Sed et sapien vulputate, imperdiet nibh vel, lobortis nisl. Curabitur sagittis justo nibh. Nulla vulputate sodales justo at efficitur. Cras justo augue, mollis vitae nulla sed, vestibulum tincidunt ante. Vestibulum et lorem lectus. Maecenas accumsan lacus a nisi euismod rutrum eu dapibus justo. Etiam scelerisque a odio a euismod. Pellentesque vestibulum pellentesque nisi, a tempus erat cursus ac. Morbi ut auctor lectus.
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3. Drill Three.

Nam congue ex nec justo iaculis maximus. Vestibulum lobortis magna sed urna auctor, vel dignissim massa posuere. In sed venenatis elit. Vivamus congue gravida tempus. Nunc quis fermentum nisi. Nullam hendrerit lorem et tellus semper, sit amet scelerisque purus lobortis. Quisque sollicitudin quis neque eu suscipit. Praesent volutpat justo quis magna vehicula molestie.
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Exercises 38.3 Challenging Exercises

1. Challenging One.

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Cras congue urna nulla. Aliquam eget euismod tellus. Maecenas nibh libero, venenatis a laoreet in, tempor sit amet sem. Morbi sit amet justo tempor velit auctor placerat. Maecenas nec lobortis orci. Aenean dictum enim lacus, ac blandit lacus elementum nec. Mauris porttitor neque volutpat tincidunt sollicitudin. Cras porta lectus ac facilisis tempor. Suspendisse in velit nisl. Sed convallis leo at nunc aliquet fermentum. Pellentesque feugiat at ex sed elementum. In porta vulputate ipsum sit amet consectetur.
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Exercise Group.

An introduction to an exercisegroup. This is here to attempt to interrupt the flow of the counting from this division to the next.
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2. Challenging Two.
Aliquam sagittis ex at magna porttitor, quis scelerisque ligula malesuada. Vestibulum vitae mauris id nisi pretium ornare a id lectus. Nam suscipit magna id sem ultricies vestibulum. Nulla facilisi. Duis venenatis lectus massa, ac mollis nisi suscipit non. Sed et sapien vulputate, imperdiet nibh vel, lobortis nisl. Curabitur sagittis justo nibh.
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Nulla vulputate sodales justo at efficitur. Cras justo augue, mollis vitae nulla sed, vestibulum tincidunt ante. Vestibulum et lorem lectus. Maecenas accumsan lacus a nisi euismod rutrum eu dapibus justo. Etiam scelerisque a odio a euismod. Pellentesque vestibulum pellentesque nisi, a tempus erat cursus ac. Morbi ut auctor lectus.
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3. Challenging Three.
Nam congue ex nec justo iaculis maximus. Vestibulum lobortis magna sed urna auctor, vel dignissim massa posuere. In sed venenatis elit. Vivamus congue gravida tempus. Nunc quis fermentum nisi. Nullam hendrerit lorem et tellus semper, sit amet scelerisque purus lobortis. Quisque sollicitudin quis neque eu suscipit. Praesent volutpat justo quis magna vehicula molestie.
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Exercises 38.4 Impossible Exercises

1. Impossible One.

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Cras congue urna nulla. Aliquam eget euismod tellus. Maecenas nibh libero, venenatis a laoreet in, tempor sit amet sem. Morbi sit amet justo tempor velit auctor placerat. Maecenas nec lobortis orci. Aenean dictum enim lacus, ac blandit lacus elementum nec. Mauris porttitor neque volutpat tincidunt sollicitudin. Cras porta lectus ac facilisis tempor. Suspendisse in velit nisl. Sed convallis leo at nunc aliquet fermentum. Pellentesque feugiat at ex sed elementum. In porta vulputate ipsum sit amet consectetur.
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2. Impossible Two.

Aliquam sagittis ex at magna porttitor, quis scelerisque ligula malesuada. Vestibulum vitae mauris id nisi pretium ornare a id lectus. Nam suscipit magna id sem ultricies vestibulum. Nulla facilisi. Duis venenatis lectus massa, ac mollis nisi suscipit non. Sed et sapien vulputate, imperdiet nibh vel, lobortis nisl. Curabitur sagittis justo nibh. Nulla vulputate sodales justo at efficitur. Cras justo augue, mollis vitae nulla sed, vestibulum tincidunt ante. Vestibulum et lorem lectus. Maecenas accumsan lacus a nisi euismod rutrum eu dapibus justo. Etiam scelerisque a odio a euismod. Pellentesque vestibulum pellentesque nisi, a tempus erat cursus ac. Morbi ut auctor lectus.
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3. Impossible Three.

Nam congue ex nec justo iaculis maximus. Vestibulum lobortis magna sed urna auctor, vel dignissim massa posuere. In sed venenatis elit. Vivamus congue gravida tempus. Nunc quis fermentum nisi. Nullam hendrerit lorem et tellus semper, sit amet scelerisque purus lobortis. Quisque sollicitudin quis neque eu suscipit. Praesent volutpat justo quis magna vehicula molestie.
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Exercises 38.5 Layout challenge

Exercise Group.

A multicolumn exercisegroup with layout challenges. The first two should be on one row. The next two should be on one row until the hint is opened. Then one that takes up an entire row. The final row should always have two exercises.
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1.
\begin{alignat*}{3} 2x \amp {}+{} \amp y \amp {}={} \amp 10\\ x \amp \amp \amp {}={} \amp 6\\ x \amp {}+{} \amp 3y \amp {}={} \amp 13 \end{alignat*}
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2.
\begin{alignat*}{3} 2x \amp {}+{} \amp y \amp {}={} \amp 10\\ x \amp \amp \amp {}={} \amp 6\\ x \amp {}+{} \amp 3y \amp {}={} \amp 13 \end{alignat*}
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3.
\begin{alignat*}{3} 2x \amp {}+{} \amp y \amp {}={} \amp 10\\ x \amp \amp \amp {}={} \amp 6\\ x \amp {}+{} \amp 3y \amp {}={} \amp 13 \end{alignat*}
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4.
\begin{alignat*}{3} 2x \amp {}+{} \amp y \amp {}={} \amp 10\\ x \amp \amp \amp {}={} \amp 6\\ x \amp {}+{} \amp 3y \amp {}={} \amp 13 \end{alignat*}
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5.
\begin{alignat*}{6} 200t \amp {}+{} 3u \amp {}+{} 1v \amp {}+{} 3w \amp {}+{} 2x \amp {}+{} \amp y \amp {}+{} \amp 3z \amp {}={} \amp 10\\ \amp {}+{} 2u \amp {}+{} 2v \amp {}-{} 2w \amp {}+{} x \amp \amp \amp {}+{} \amp z \amp {}={} \amp 6\\ 100t \amp {}+{} 1u \amp {}-{} 3v \amp {}+{} 1w \amp {}+{} x \amp {}+{} \amp 3y \amp {}+{} \amp 2z \amp {}={} \amp 13 \end{alignat*}
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6.
\begin{alignat*}{3} 2x \amp {}+{} \amp y \amp {}={} \amp 10\\ x \amp \amp \amp {}={} \amp 6\\ x \amp {}+{} \amp 3y \amp {}={} \amp 13 \end{alignat*}
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7.
\begin{alignat*}{3} 2x \amp {}+{} \amp y \amp {}={} \amp 10\\ x \amp \amp \amp {}={} \amp 6\\ x \amp {}+{} \amp 3y \amp {}={} \amp 13 \end{alignat*}
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References 38.6 More Reading

Left intentionally blank, just checking sectioning.
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[1]
David C. Lay, Subspaces and Echelon Forms. The College Mathematics Journal, January 1993, 24 no. 1, 57–62.
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