Distributing three parts of a page evenly, vertically

Question

I have a page that has three big "sections," two items (in enumerate), and a note at the bottom of the page. Is there a way to get them to distribute evenly on the page without having to use all the newlines? I can't seem to find anything on the topic. \desymbol is a predefined macro. Source file is as follows:

\documentclass{article}
\usepackage{amsmath}
\newcommand\desymbol{? }
\begin{document}

\section*{Phase 3}
\begin{enumerate}
\item[1.]
Find the limit and prove using the \desymbol proof.
\begin{equation*}
\lim_{x\to a}(\text{sin}(x)) =
\end{equation*}
\\
\\
\\
\\
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\\
\\
\item[2.]
Find the limit and prove using the \desymbol proof.
\begin{equation*}
\lim_{x\to a}(\text{ln}(x)) =
\end{equation*}
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\end{enumerate}

\hrule\hspace{1mm}\\
\small{This lesson was adapted from a handout by Irena Swanson's MATH111 class at Reed College. The problems are partly my own creation, from her handout, and from D. A. Kouba at University of California, Davis.}

\end{document}

Answer 1

I suggest you use \vspace{\fill} instead of the battery of \\ directives.

Please note that \small is not a macro that takes an argument. If you want to limit the scope of this directive, write {\small ...}, not \small{...}.

I would also place \end{enumerate} directive before, not after, the second \vspace{\fill} directive.

\documentclass{article}
\usepackage{amsmath} % for 'equation*' environment
\newcommand\desymbol{xxx} %??
\begin{document}

\section*{Phase 3}
\begin{enumerate}
\item
Find the limit and prove using the \desymbol\ proof.
\begin{equation*}
\lim_{x\to a}(\text{sin}(x)) =
\end{equation*}
\vspace{\fill}
\item[2.]
Find the limit and prove using the \desymbol\ proof.
\begin{equation*}
\lim_{x\to a}(\text{ln}(x)) =
\end{equation*}
\end{enumerate}
\vspace{\fill}

\hrule
\smallskip\noindent%
{\small This lesson was adapted from a handout by Irena Swanson's MATH111 class at Reed College. The problems are partly my own creation, from her handout, and from D. A. Kouba at University of California, Davis.\par}

\end{document}

Answer 2

Something like this?

Note that the point of enumerate is that it numbers the items automatically. You don't need to specify them and it is better by far not to in case you want to change the order or add items in the middle later.

\documentclass{article}
\usepackage{amsmath,amssymb}
\begin{document}
\section*{Phase 3}
\begin{enumerate}
  \item
  Find the limit and prove using the \maltese{} proof.
  \begin{equation*}
    \lim_{x\to a}(\text{sin}(x)) =
  \end{equation*}
  \vfill
  \item
  Find the limit and prove using the \maltese{} proof.
  \begin{equation*}
    \lim_{x\to a}(\text{ln}(x)) =
  \end{equation*}
  \vfill
\end{enumerate}

\hrule\hspace{1mm}

\noindent\small{This lesson was adapted from a handout by Irena Swanson's MATH111 class at Reed College. The problems are partly my own creation, from her handout, and from D. A. Kouba at University of California, Davis.}

\end{document}

However, that is probably not the best way to typeset the acknowledgement.

If the acknowledgement applies just to this section, I'd suggest a footnote:

\section*{Phase 3\footnote{...}}

If the acknowledgement applies the the whole document, I'd suggest using \thanks instead.

\documentclass{article}
\usepackage{amsmath,amssymb}
\title{Phase 3\thanks{%
    This lesson was adapted from a handout by Irena Swanson's MATH111 class at Reed College.
    The problems are partly my own creation, from her handout, and from D. A. Kouba at University of California, Davis.}%
}
\date{}
\begin{document}
\maketitle
\begin{enumerate}
  \item
  Find the limit and prove using the \maltese{} proof.
  \begin{equation*}
    \lim_{x\to a}(\text{sin}(x)) =
  \end{equation*}
  \vfill
  \item
  Find the limit and prove using the \maltese{} proof.
  \begin{equation*}
    \lim_{x\to a}(\text{ln}(x)) =
  \end{equation*}
  \vfill
\end{enumerate}

\end{document}

Answer 3

You should never use \\ at the start, end or between paragraphs, each one in the original version generates

Underfull \hbox (badness 10000) in paragraph at lines 33--50

10000 is the maximum badness that TeX ever assigns, so this usage (and the resulting output) is (according to TeX's built in checks) as bad as it gets....

Also \text{sin} has the wrong spacing and, depending on the context outside the math, may use the wrong font, use \sin

also you should avoid \item[1.] it is almost always better to let latex number things.

\small does not take an argument so it should be \small ... not \small{...} (or just use \footnote which will add the rule, change the font, and position the text at the bottom automatically)

I would simplify the markup to

\documentclass{article}
\usepackage{amsmath}
\usepackage{enumitem}
\newcommand\desymbol{? }
\begin{document}

\section*{Phase 3\footnote{%
This lesson was adapted from a handout by Irena Swanson's MATH111 class at Reed College. The problems are partly my own creation, from her handout, and from D. A. Kouba at University of California, Davis.}}

\begin{enumerate}[label={[\arabic*.]},
topsep=\textheight minus\textheight,
itemsep=\textheight minus\textheight
]
\item
Find the limit and prove using the \desymbol proof.
\begin{equation*}
\lim_{x\to a}(\sin(x)) =
\end{equation*}

\item
Find the limit and prove using the \desymbol proof.
\begin{equation*}
\lim_{x\to a}(\ln(x)) =
\end{equation*}

\end{enumerate}


\end{document}