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diff --git a/Master/texmf-dist/source/latex/probsoln/probsoln.dtx b/Master/texmf-dist/source/latex/probsoln/probsoln.dtx
index 07ecd28ba6b..0912f634e65 100644
--- a/Master/texmf-dist/source/latex/probsoln/probsoln.dtx
+++ b/Master/texmf-dist/source/latex/probsoln/probsoln.dtx
@@ -1,75 +1,140 @@
-%\def\filedate{21 Mar 2004}
-%\def\fileversion{2.0}
-%\def\filename{probsoln.dtx}
-%\def\docdate{19th Dec 2000}
%\iffalse
+% probsoln.dtx generated using makedtx version 0.9b (c) Nicola Talbot
+% Command line args:
+% -src "(.+)\.(sty)=>\1.\2"
+% -src "(.*\.tex)\Z=>\1"
+% -doc "manual.tex"
+% -author "Nicola Talbot"
+% -dir "source"
+% probsoln
+% Created on 2006/3/2 11:26
+%\fi
+%\iffalse
+%<*package>
+%% \CharacterTable
+%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+%% Digits \0\1\2\3\4\5\6\7\8\9
+%% Exclamation \! Double quote \" Hash (number) \#
+%% Dollar \$ Percent \% Ampersand \&
+%% Acute accent \' Left paren \( Right paren \)
+%% Asterisk \* Plus \+ Comma \,
+%% Minus \- Point \. Solidus \/
+%% Colon \: Semicolon \; Less than \<
+%% Equals \= Greater than \> Question mark \?
+%% Commercial at \@ Left bracket \[ Backslash \\
+%% Right bracket \] Circumflex \^ Underscore \_
+%% Grave accent \` Left brace \{ Vertical bar \|
+%% Right brace \} Tilde \~}
+%</package>
+%\fi
+% \iffalse
% Doc-Source file to use with LaTeX2e
-% Copyright (C) 2000 Nicola Talbot, all rights reserved.
+% Copyright (C) 2006 Nicola Talbot, all rights reserved.
+% \fi
+% \iffalse
+%<*driver>
+\documentclass{ltxdoc}
+\usepackage[colorlinks,
+ bookmarks,
+ hyperindex=false,
+ pdfauthor=Nicola Talbot,
+ pdftitle={probsoln.sty : a LaTeX2e package to help create problem sheets}]{hyperref}
+
+
+
+\newcommand{\sty}[1]{\textsf{#1}}\newcommand{\env}[1]{\textsf{#1}}
+\newcommand{\cmddef}[1]{\hypertarget{#1}{\cmdname{#1}}}
+\newcommand{\cmdlink}[1]{\hyperlink{#1}{\cmdname{#1}}}
+\newcommand{\problabel}[2]{\hypertarget{#1}{\texttt{#2}}}
+\newcommand{\probref}[1]{\hyperlink{#1}{\texttt{#1}}}
+\newcommand{\cmdname}[1]{\texttt{\symbol{92}#1}}
+ %hyperindex conflicts with doc
+ %(end up with |usage|hyperpage in indexentry)
+\renewcommand{\usage}[1]{\textit{\hyperpage{#1}}}
+\renewcommand{\main}[1]{\hyperpage{#1}}
+\newcommand{\see}[2]{\emph{see} #1}
+\makeatletter
+\def\index@prologue{\section*{Index}}
+\makeatother
+
+
+\OnlyDescription
+\PageIndex
+
+\begin{document}
+\DocInput{probsoln.dtx}
+\end{document}
+%</driver>
%\fi
%
-% \newsavebox{\syntaxbox}
-% \newenvironment{syntax}{\begin{lrbox}{\syntaxbox}\ttfamily}%
-%{\end{lrbox}\par\noindent\fbox{\usebox{\syntaxbox}}\\}
-% \title{probsoln.sty v\fileversion: \LaTeX\ Package to help create problem sheets}
-% \author{N.L.C. Talbot}
-% \date{\docdate}
+%
+% \title{probsoln.sty v2.02: \LaTeXe\ Package to help create problem sheets}
+% \author{Nicola L.C. Talbot}
+% \date{2nd March 2006}
% \maketitle
% \tableofcontents
%
% \section{Introduction}
-% The package |probsoln.sty| is designed for teachers or lecturers who
-% want to create problem sheets for their students. This package was
-% designed with specifically mathematics problems in mind, but can
-% be used for other subjects as well. The idea is to create a file
-% containing a large number of problems with their solutions which
-% can be read in by \LaTeX, and then select a number of problems to
-% typeset. This means that once the database has been set up, each
-% year you can easily create a new problem sheet that is sufficiently
-% different from the previous year, thus preventing the temptation
-% of current students seeking out the previous year's students,
-% and checking out their answers. There is also an option that can be
-% passed to the package to determine whether or not the solutions
-% should be printed. In this way, one file can either produce
-% the student's version or the teacher's version.
-%
-% \section{Package Options}
-% The following options may be passed to this package:
-%
-% \centerline{%
-% \begin{tabular}{@{\ttfamily}ll}
-% answers & Show the answers\\
-% noanswers & Don't show the answers (default)
-% \end{tabular}
-% }
+%The \sty{probsoln} package is designed for teachers or
+%lecturers who want to create problem sheets for their
+%students. This package was designed with specifically
+%mathematics problems in mind, but can be used for other
+%subjects as well. The idea is to create a file containing a
+%large number of problems with their solutions which can be
+%read in by \LaTeX, and then select a number of problems to
+%typeset. This means that once the database has been set up,
+%each year you can easily create a new problem sheet that is
+%sufficiently different from the previous year, thus
+%preventing the temptation of current students seeking out
+%the previous year's students, and checking out their
+%answers. There is also an option that can be passed to the
+%package to determine whether or not the solutions should be
+%printed. In this way, one file can either produce the
+%student's version or the teacher's version.
+%
+%\section{Package Options}
+%The following options may be passed to this package:
+%\begin{center}
+%\begin{tabular}{@{\ttfamily}ll}
+%answers & Show the answers\\
+%noanswers & Don't show the answers (default)
+%\end{tabular}
+%\end{center}
%
-% \section{Commands Provided}
-% \subsection{Creating a New Problem}
-% \begin{syntax}|\newproblem[|\meta{nargs}|]{|\meta{label}|}{|\meta{problem}|}{|\meta{solution}|}|\end{syntax}
-% \DescribeMacro{\newproblem}
-% A new problem is defined using the command |\newproblem|. This does not print anything,
-% but merely stores the problem. The argument \meta{label} is a unique string that is
-% assigned to this problem so that it can be used later. The argument \meta{problem}
-% is normal \LaTeX\ code that should be used to typeset the problem. The argument
-% \meta{solution} is normal \LaTeX\ code that should be used to typeset the solution,
-% if required. For example:
+%\section{Creating a New Problem}
+%\DescribeMacro{\newproblem}
+%\cmddef{newproblem}\verb|[|\meta{nargs}\verb/]{/\meta{label}\verb!}{!\meta{problem}\verb+}{+\meta{solution}\verb=}=\\[10pt]
+%A new problem is defined using the command
+%\cmdname{newproblem}. This does not print anything,
+%but merely stores the problem. The argument \meta{label} is
+%a unique string that is assigned to this problem so that it
+%can be used later. The argument \meta{problem} is normal
+%\LaTeX\ code that should be used to typeset the problem.
+%The argument \meta{solution} is normal \LaTeX\ code that
+%should be used to typeset the solution, if required. For
+%example, the following defines a problem with the label
+%\problabel{quaddiff}{quaddiff}:
%\begin{verbatim}
-%\newproblem{quaddiff}{%
-%%This is the problem
-%\begin{displaymath}
-%f(x) = x^2 + 3x + 4
-%\end{displaymath}
-%}{%
-%%This is the solution
-%\begin{displaymath}
-%f'(x) = 2x + 3
-%\end{displaymath}
-%}
+% \newproblem{quaddiff}{%
+% %This is the problem
+% \begin{displaymath}
+% f(x) = x^2 + 3x + 4
+% \end{displaymath}
+% }{%
+% %This is the solution
+% \begin{displaymath}
+% f'(x) = 2x + 3
+% \end{displaymath}
+% }
%\end{verbatim}
%
-% The optional argument \meta{nargs} specifies the number of parameters this
-% problem will take. By default this value is 0, but any value from 1 to 9
-% may be used. Each parameter is refered to by |#1|, |#2|, \ldots, |#9|.
-% For example, the following problem takes one parameter:
+%The optional argument \meta{nargs} specifies the number of
+%parameters this problem will take. By default this value is
+%0, but any value from 1 to 9 may be used. Each parameter is
+%referred to by \verb|#1|, \verb/#2/, \ldots, \verb!#9!.
+%For example, the following problem, labelled \problabel{sindiff}{sindiff},
+%takes one parameter:
%\begin{verbatim}
%\newproblem[1]{sindiff}{%
%\(f(x) = \sin(#1x)\)
@@ -78,7 +143,8 @@
%}
%\end{verbatim}
%
-% The |quaddiff| problem shown above can be made more generic by using parameters:
+%The \probref{quaddiff} problem shown above can be made more
+%generic by using parameters\problabel{diff:quad}{}:
%\begin{verbatim}
%\newcount\ctr
%\newproblem[3]{diff:quad}{%
@@ -115,34 +181,36 @@
%\)
%}
%\end{verbatim}
-% The three parameters correspond to the coefficients. Note that they
-% must all be integers since \TeX\ only performs integer arithmetic.
-%
-% To generate a database, simply create a |.tex| file where all the problems
-% are defined using |\newproblem|, and either |\input| it at the
-% start of your document if you want to use specific problems
-% (see Section~\ref{sec:useprob}), or
-% pass it to |\selectrandomly| (see Section~\ref{sec:selran}).
-%
-% \subsection{Displaying a Problem}
-% \label{sec:useprob}
-% \begin{syntax}|\useproblem{|\meta{label}|}|\end{syntax}
+%The three parameters correspond to the coefficients. Note
+%that they must all be integers since \TeX\ only performs
+%integer arithmetic.
+%
+%\section{Creating a Database}
+%
+%To generate a database, simply create a \texttt{.tex} file
+%where all the problems are defined using \cmdlink{newproblem},
+%and either \cmdname{input} it at the start of your document if
+%you want to use specific problems (see Section~\ref{sec:useprob}), or pass it to
+%\cmdname{selectrandomly} (see Section~\ref{sec:selran}). This package
+%comes with some sample databases, along with some sample documents
+%that use these databases.
+%
+%\section{Displaying a Problem}
+%\label{sec:useprob}
% \DescribeMacro{\useproblem}
-% Once a problem has be defined using |\newproblem|, it can be typeset
-% using the command |\useproblem|. If the problem was defined to take
-% arguments, the arguments to the problem should come after the
-% label. In the case of the |sindiff| example above, the command
-% |\useproblem{sindiff}{2}| would produce the following:\\[10pt]
-% \(f(x) = \sin(2x)\)
-% \paragraph{Solution:} \(f'(x) = 2\cos(2x)\)\\[10pt]
-% whereas the command |\useproblem{diff:quad}{3}{0}{-2}| would produce:\\[10pt]
-% \(f(x) = 3x^2 - 2\)
-% \paragraph{Solution:} \(f'(x) = 6x\)
-%
-% \vspace{10pt}
-% Suppose all the above problems are defined in the
-% file |probs.tex|, then the following code will create a problem sheet
-% with four questions in it:
+%\cmddef{useproblem}\verb|{|\meta{label}\verb/}/\\[10pt]
+%Once a problem has been defined using \cmdlink{newproblem}, it
+%can be typeset using the command \cmdname{useproblem}. If the
+%problem was defined to take arguments, the arguments to the
+%problem should come after the label. In the case of the
+%\probref{sindiff} example above, the command
+%\verb|\useproblem{sindiff}{2}| would produce the following:\\[10pt]
+% $f(x) = \sin(2x)$ \paragraph{Solution:} $f'(x) = 2\cos(2x)$\\[10pt]whereas the command \verb|\useproblem{diff:quad}{3}{0}{-2}| would produce:\\[10pt]
+% $f(x) = 3x^2 - 2$ \paragraph{Solution:} $f'(x) = 6x$\vspace{10pt}
+%
+%Suppose all the above problems are defined in the file
+%\texttt{probs.tex}, then the following code will create a
+%problem sheet with four questions in it:
%\begin{verbatim}
%\documentclass{article}
%
@@ -159,26 +227,56 @@
%\end{enumerate}
%\end{document}
%\end{verbatim}
-%The answer sheet can then be generated by passing the option |answers|
-%to the |probsoln| package.
+%The answer sheet can then be generated by passing the option
+%\texttt{answers} to the \texttt{probsoln} package.
+%
+%\section{Selecting All Problems}
+%
+%To select all problems defined in a database, in the order in
+%which they were defined, use the command:
+%\DescribeMacro{\selectallproblems}
+%\cmddef{selectallproblems}\verb|{|\meta{filename}\verb/}/
+%For example, suppose the problems are defined in the file
+%\texttt{easy.tex}, then the following will create a problem sheet
+%which uses all these problems:
+%\begin{verbatim}
+%\documentclass[a4paper]{article}
+%
+%\usepackage{probsoln}
+%
+%\begin{document}
+%Differentiate the following functions:
+%\begin{enumerate}
+%\selectallproblems{easy}
+%\end{enumerate}
+%\end{document}
+%\end{verbatim}
%
-% \subsection{Selecting Problems at Random}
-% \label{sec:selran}
-% \begin{syntax}|\selectrandomly{|\meta{filename}|}{|\meta{n}|}|\end{syntax}
+%\section{Selecting Problems at Random}
+%\label{sec:selran}
% \DescribeMacro{\selectrandomly}
-% The command |\selectrandomly| will select \meta{n} problems that are defined
-% in the file \meta{filename}. Each problem is preceeded by a |\item|, so the
-% command |\selectrandomly| should occur within one of the list-like environments,
-% such as |enumerate|. For example:
+%\cmddef{selectrandomly}\verb|{|\meta{filename}\verb/}{/\meta{n}\verb!}!\\[10pt]
+%The command \cmdname{selectrandomly} will select \meta{n}
+%problems that are defined in the file \meta{filename}. Each
+%problem is proceeded by
+%\DescribeMacro{\PSNitem}\cmddef{PSitem} which is
+%defined to be \cmdname{item}, so the command
+%\cmdname{selectrandomly} should occur within one of the
+%list-like environments, such as \texttt{enumerate}.
+%For example:
%\begin{verbatim}
%\begin{enumerate}
%\selectrandomly{easy.tex}{4}
%\end{enumerate}
%\end{verbatim}
-% will result in four numbered problems, selected at random from the
-% file |easy.tex|. (The \texttt{.tex} extension may be omitted.)
+%will result in four numbered problems, selected at random
+%from the file \texttt{easy.tex}. (The \texttt{.tex} extension
+%may be omitted.) Each problem is followed by the command
+%\cmddef{endPSNitem} which by default does nothing.
%
-% Multiple |\selectrandomly| commands may be used. For example:
+%Multiple \cmdname{selectrandomly} commands may be used, however a
+%different file must be used each time. For
+%example:
%\begin{verbatim}
%\begin{enumerate}
%\item Differentiate the following functions with respect to $x$:
@@ -193,67 +291,246 @@
%
%\end{enumerate}
%\end{verbatim}
-% This will result in a total of 6 problems, numbered 1(a), 1(b), 1(c), 1(d), 2 and 3.
+%This will result in a total of 6 problems, numbered 1(a),
+%1(b), 1(c), 1(d), 2 and 3.
%
-% If a randomly selected problem requires arguments, a message similar to the following
-% will be displayed:
+%If a randomly selected problem requires arguments, a message
+%similar to the following will be displayed:
%\begin{verbatim}
%Problem diff:quad requires 3 argument(s), please specify (e.g. {5}{3}):
%\end{verbatim}
-% Enter the required arguments, where each argument is enclosed in braces (\{ \}).
-%
-% \subsection{Other Commands}
-% \DescribeMacro{\PSNrandseed}
-% The command |\PSNrandseed{|\meta{n}|}| specifies the seed for the random
-% number generator. For example, |\PSNrandseed{\year}| will produce a
-% different set of random problems each year, whereas |\PSNrandseed{\time}|
-% will produce a different set of problems each time you \LaTeX\ the
-% problem (as long as you leave at least a minute between runs.)
-%
-% \DescribeMacro{\showanswers}
-% The command |\showanswers| will show the solutions from that point
-% on. May be localised by placing within a group.
-%
-% \DescribeMacro{\hideanswers}
-% The command |\hideanswers| will hide the solutions from that point
-% on. May be localised by placing within a group.
-%
-% \DescribeMacro{\solutionname}
-% By default, the solution is preceeded by the text: \textbf{Solution:}. This can
-% be changed by redefining the macro |\solutionname|.
-%
-% \DescribeMacro{showanswers}
-% The boolean variable |showanswers| is defined to be true if the answers
-% are shown and false otherwise. You can therefore do something like:
+%Enter the required arguments, where each argument is
+%enclosed in braces (\{ \}).
+%
+%\section{Other Commands}
+%\DescribeMacro{\PSNrandseed}
+%The command \cmddef{PSNrandseed}\verb|{|\meta{n}\verb/}/ specifies
+%the seed for the random number generator. For example,
+%if you are using \cmdlink{selectrandomly},
+%\verb|\PSNrandseed{\year}| will produce a different set of
+%problems each year, whereas \verb|\PSNrandseed{\time}|
+%will produce a different set of problems each time you
+%\LaTeX\ the problem sheet (as long as you leave at least a
+%minute between runs.)
+%
+%\DescribeMacro{\random}
+%The command \cmddef{random}\verb|{|\meta{counter}\verb/}{/\meta{a}\verb!}{!\meta{b}\verb-}-
+%generates a random number from \meta{a} to \meta{b} and
+%stores it in the \LaTeX\ counter \meta{counter}. For example,
+%to select 2, 3 or 4 problems from the file
+%\texttt{implicit.tex}:
+%\begin{verbatim}
+%\newcounter{numproblems}
+%\begin{enumerate}
+%\random{numproblems}{2}{4}
+%\selectrandomly{implicit.tex}{\value{numproblems}}
+%\end{enumerate}
+%\end{verbatim}
+%(Note the use of \cmdname{value}.)
+%
+%This command can also be used to generate random values for
+%problems that take arguments. Consider the problem \probref{diff:quad}
+%defined earlier. Three counters can be defined to represent the
+%three coefficients:
+%\begin{verbatim}
+%\newcounter{A}
+%\newcounter{B}
+%\newcounter{C}
+%\end{verbatim}
+%Random values can now be assigned to these counters:
+%\begin{verbatim}
+%\random{A}{-5}{5}
+%\random{B}{-5}{5}
+%\random{C}{-5}{5}
+%\end{verbatim}
+%Finally, the problem can be used (note the use of \cmdname{arabic}):
+%\begin{verbatim}
+%\useproblem{diff:quad}{\arabic{A}}{\arabic{B}}{\arabic{C}}
+%\end{verbatim}
+%
+%\DescribeMacro{\doforrandN}%
+%The command
+%\cmddef{doforrandN}\verb|{|\meta{n}\verb/}{/\meta{cmd}\verb!}{!\meta{list}\verb+}{+\meta{text}\verb-}- will apply
+%\meta{text} for a random selection of \meta{n} items in the
+%comma separated \meta{list}. In each iteration the list
+%item is denoted by \meta{cmd}. For example, suppose you
+%have three files called \texttt{file1.tex},
+%\texttt{file2.tex} and \texttt{file3.tex}, and you want to
+%select 1 problem from two of the three files, then you can
+%do:
+%\begin{verbatim}
+%\doforrandN{2}{\file}{file1,file2,file3}{\selectrandomly{\file}{1}}
+%\end{verbatim}
+%Note that it is also possible to do
+%\begin{verbatim}
+%\newcounter{numproblems}
+%\random{numproblems}{1}{3}
+%\selectrandomly{file\arabic{numproblems}}{1}
+%\random{numproblems}{1}{3}
+%\selectrandomly{file\arabic{numproblems}}{1}
+%\end{verbatim}
+%however there is a possibility that the same file may be
+%selected twice which will cause an error.
+%
+%\DescribeMacro{\showanswers}
+%The command \cmddef{showanswers} will show the solutions from
+%that point on. May be localised by placing within a group.
+%
+%\DescribeMacro{\hideanswers}
+%The command \cmddef{hideanswers} will hide the solutions from
+%that point on. May be localised by placing within a group.
+%
+%The solution is placed inside the \DescribeEnv{solution}\env{solution}
+%environment. By default this environment simply does
+%\verb|\paragraph{\solutionname:}| at the start, where
+%\DescribeMacro{\solutionname}\cmddef{solutionname}
+%has the value: Solution. See the file \texttt{sample3.tex}, which
+%comes with this package, for an illustration of how to
+%customise the way in which the randomly selected problems are
+%displayed. This sample file randomly selects multiple choice
+%problems stored in the file \texttt{tabmchoice.tex}, and displays them
+%in a longtable \env{environment}.
+%
+%\DescribeMacro{showanswers}
+%The boolean variable \texttt{showanswers} is defined to be
+%true if the answers are shown and false otherwise. You can
+%therefore do something like:
%\begin{verbatim}
%\ifthenelse{\boolean{showanswers}}{\textbf{Solution Sheet}}{}
%\end{verbatim}
-% and \textbf{Solution Sheet} will be printed only if the answers are displayed.
-%(For more information on |\ifthenelse| and |\boolean| see the
-%documentation for the |ifthen| package by David Carlisle.)
+%and \textbf{Solution Sheet} will be printed only if the
+%answers are displayed. (For more information on
+%\cmdname{ifthenelse} and \cmdname{boolean} see the
+%documentation for the \texttt{ifthen} package by
+%David Carlisle.)
+%
+%The \texttt{showanswers} switch can also be used within the definition
+%of a problem, if you want the question to appear differently if the
+%solution is displayed. For example:
+%\begin{verbatim}
+%\newproblem{mc:prod}{%
+%Which of the following is the derivative of $x\sin(x)$?
+%(Circle the correct answer.)
+%\ifthenelse{\boolean{showanswers}}{}%
+%{\begin{description}
+%\item[A] $\sin(x)$
+%\item[B] $x\cos(x)$
+%\item[C] $\sin(x) + x\cos(x)$
+%\end{description}
+%}}{%
+%\begin{description}
+%\item[A] $\sin(x)$
+%\item[B] $x\cos(x)$
+%\item[\textcircled{C}] $\sin(x) + x\cos(x)$ (product rule).
+%\end{description}
+%}
+%\end{verbatim}
+%If the solutions are not displayed, the question will appear
+%as
+%\begin{description}
+%\item Which of the following is the derivative of
+%$x\sin(x)$? (Circle the correct answer.)
+%\begin{description}
+%\item[A] $\sin(x)$\item[B] $x\cos(x)$\item[C] $\sin(x) + x\cos(x)$\end{description}
+%\end{description}
+%otherwise it will appear as:
+%\begin{description}
+%\item Which of the following is the derivative of
+%$x\sin(x)$?(Circle the correct answer.)
+%\begin{description}
+%\item[A] $\sin(x)$\item[B] $x\cos(x)$\item[\textcircled{C}] $\sin(x) + x\cos(x)$ (product rule)\end{description}
+%\end{description}
+%
+%\section{Troubleshooting}
+%\subsection{Unexpected Output}
+%\begin{itemize}
+%\item I have lots of blank space before the first problem when
+%using \cmdlink{selectrandomly}.
+%
+%This is probably because you have lots of extraneous white space
+%in your database. \cmdlink{selectrandomly} will input the entire
+%file, so any extra space will be included. Try commenting out the
+%extra space using \%.
+%\end{itemize}
%
-% \section{Error Messages}
+%\subsection{Error Messages}
+%\begin{itemize}
+%\item
%\begin{ttfamily}
%! Package probsoln Error: Label \ldots\ already used.
-%\end{ttfamily}\\[10pt]
-% Each label identifier used in |\newproblem| must be unique.
-% Check to make sure you haven't used the same label more than once.
-% Also check to make sure you haven't |\input|ed or randomly selected
-% from the same file more than once. (Or |\input|ed and randomly
-% selected from the same file.)
-%\\[10pt]
+%\end{ttfamily}
+%
+%Each label identifier used in \cmdlink{newproblem} must be
+%unique. Check to make sure you haven't used the same label
+%more than once. Also check to make sure you haven't
+%\cmdname{input}ed or randomly selected from the same file more
+%than once. (Or \cmdname{input}ed and randomly selected from
+%the same file.)
+%
+%\item
%\begin{ttfamily}
%! Package probsoln Error: Label \ldots\ undefined.
-%\end{ttfamily}\\[10pt]
-% You need to define a problem before you can use it. Check to
-% make sure you haven't mis-spelt it.
-%\\[10pt]
+%\end{ttfamily}
+%
+%You need to define a problem before you can use it. Check to
+%make sure you haven't mis-spelt it, and check to make sure you
+%have \cmdname{input}ed the file in which it is defined.
+%
+%\item
%\begin{ttfamily}
%! Package probsoln Error: Requested number too large.
%\end{ttfamily}
-%\\[10pt]
-% You have asked for more problems than are defined within
-% the specified file. All problems in that file will be selected.
+%
+%You have asked for more problems than are defined within the
+%specified file. All problems in that file will be selected.
+%
+%\item
+%\begin{ttfamily}
+%! Package probsoln Error: Can't randomly select \meta{n}
+%item(s)
+%\end{ttfamily}
+%
+%You have asked to randomly select \meta{n} items from a list
+%that has less than \meta{n} elements. For example, the
+%following will generate this error:
+%\begin{verbatim}
+%\doforrandN{10}{\file}{file1,file2,file3}{%
+%\selectrandomly{\file}{1}}
+%\end{verbatim}
+%In this case the list, \texttt{file1,file2,file3} has only 3
+%elements, but the user has asked for 10 elements. If you type
+%`h' at the \LaTeX\ prompt it will tell you how many items it thinks
+%there are in the list. Remember that each item must be separated by a
+%comma.
+%
+%\item
+%\begin{ttfamily}
+%! LaTeX Error: Lonely \cmdname{item}--perhaps missing list
+%environment.
+%\end{ttfamily}
+%
+%Each problem selected using \cmdlink{selectrandomly} is
+%proceeded by \cmdlink{PSNitem} which by default is defined
+%as \cmdname{item}, and should therefore be
+%placed in one of the list environments, such as
+%\texttt{enumerate}. Alternatively, redefine \cmdlink{PSNitem}.
+%
+%\item I get an error when I put a command definition in my database
+%when using \cmdname{selectrandomly}.
+%
+%\cmdlink{selectrandomly} inputs the database twice, so any
+%command definition will be read twice, causing an error. You
+%can use the switch \cmdname{iffirstpass} to prevent the error. For
+%example:
+%\begin{verbatim}
+%\iffirstpass
+%\newcommand{\mycmd}{}
+%\fi
+%\end{verbatim}
+%It is generally not a good idea to put anything other than
+%\cmdlink{newproblem} commands within the database.
+%
+%\end{itemize}
%
%\section{Contact Details}
%Dr Nicola Talbot\\
@@ -262,26 +539,17 @@
%Norwich. NR4 7TJ\\
%\url{http://theoval.cmp.uea.ac.uk/~nlct/}
%
-% \StopEventually{}
-% \section{The Code}
-% \iffalse
-% First we have the driver to get the documentation
+%\StopEventually{\PrintIndex}
+%
+%\section{The Code}
% \begin{macrocode}
-%<*driver>
-\documentclass{ltxdoc}
-\usepackage[colorlinks,bookmarks]{hyperref}
-\begin{document}
-\OnlyDescription
-\DocInput{probsoln.dtx}
-\end{document}
-%</driver>
+%<*probsoln.sty>
% \end{macrocode}
-% \fi
-% At the start of the package, specify that the \LaTeX2e format is
+% At the start of the package, specify that the \LaTeXe\ format is
% required. And specify the package provided.
% \begin{macrocode}
\NeedsTeXFormat{LaTeX2e}
-\ProvidesPackage{probsoln}[2004/03/21 Problems and their Solutions Package]
+\ProvidesPackage{probsoln}[2006/03/02 v2.02 Problems and their Solutions Package (NLCT)]
\RequirePackage{ifthen}
% \end{macrocode}
% Define newif to determine whether or not to show the answers.
@@ -298,11 +566,6 @@
\ExecuteOptions{noanswers}
\ProcessOptions
% \end{macrocode}
-% Create a newif to determine whether a command has already been defined
-% \begin{macrocode}
-\newif\ifdefined
-\def\checkdefined#1{\ifx#1\relax \definedfalse \else \definedtrue \fi}
-% \end{macrocode}
% Create newifs for selecting randomly and parsing through file
% \begin{macrocode}
\newif\ifselectrandom \selectrandomfalse
@@ -311,93 +574,93 @@
% \end{macrocode}
% Define the command that creates a new problem
% \begin{macrocode}
-\newcommand{\solutionname}{Solution:}
+\newcommand{\solutionname}{Solution}
\newcommand{\newproblem}[4][0]{%
\ifselectrandom
\iffirstpass
% on the first pass, just store the label, and increment \@probN
\global\advance\@probN by 1
-\expandafter\gdef\csname @problabel\romannumeral\@probN\endcsname{#2}
+\expandafter\gdef\csname @problabel\romannumeral\@probN\endcsname{#2}%
\else
% check to see if this problem has been selected
-\checkselected{#2}
+\checkselected{#2}%
\ifselected
-\expandafter\checkdefined\csname @prob@#2\endcsname
-\ifdefined
-\PackageError{probsoln}{Label #2 already used}%
-{Each problem must have a unique label identifier}
-\else
+\@ifundefined{@prob@#2}{%
\ifnum#1=0
% this problem has no arguments
-\expandafter\newcommand\csname @prob@#2\endcsname[#1]{%
-#3 \ifshowanswers\paragraph{\solutionname} #4\fi}
+\expandafter\gdef\csname @prob@#2\endcsname{%
+#3 \ifshowanswers\begin{solution}#4\end{solution}\fi}%
+\expandafter\gdef\csname @prob@#2@arg\endcsname{\relax}%
\else
-\message{Problem #2 requires #1 argument(s), please specify (e.g. {5}{3}):}
+\message{Problem #2 requires #1 argument(s), please specify (e.g. {5}{3}):}%
\read-1to\@tmp
-\expandafter\let\csname @prob@#2@arg\endcsname=\@tmp
-\expandafter\newcommand\csname @prob@#2\endcsname[#1]{%
-#3 \ifshowanswers\paragraph{\solutionname} #4\fi}
-\fi
+\expandafter\xdef\csname @prob@#2@arg\endcsname{\@tmp}%
+\expandafter\global\expandafter\newcommand\csname @prob@#2\endcsname[#1]{%
+#3 \ifshowanswers\solution #4\fi}%
\fi
+}{%
+\PackageError{probsoln}{Label #2 already used}%
+{Each problem must have a unique label identifier}%
+}%
\fi
\fi
\else
-\expandafter\checkdefined\csname @prob@#2\endcsname
-\ifdefined
+\@ifundefined{@prob@#2}{%
+\expandafter\global\expandafter\newcommand\csname @prob@#2\endcsname[#1]{%
+#3 \ifshowanswers\begin{solution}#4\end{solution}\fi}%
+}{%
\PackageError{probsoln}{Label #2 already used}%
-{Each problem must have a unique label identifier}
-\else
-\expandafter\newcommand\csname @prob@#2\endcsname[#1]{%
-#3 \ifshowanswers\paragraph{\solutionname} #4\fi}
-\fi
+{Each problem must have a unique label identifier}%
+}
\fi
}
% \end{macrocode}
% Define the command that uses a problem
% \begin{macrocode}
\newcommand{\useproblem}[1]{%
-\expandafter\checkdefined\csname @prob@#1\endcsname
-\ifdefined
-\def\doprob{\csname @prob@#1\endcsname}
-\else
+\@ifundefined{@prob@#1}{%
\PackageError{probsoln}{Label #1 undefined}%
-{Can't find problem defined with label identifier '#1'}
-\def\doprob{\relax}
-\fi
-\doprob
+{Can't find problem defined with label identifier '#1'}%
+}{\csname @prob@#1\endcsname}%
}
% \end{macrocode}
% Now deal with the stuff for random selection.
-% Syntax: |\selectrandomly{|\meta{filename}|}{|\meta{n}|}|.
+% First define some registers for later use.
% \begin{macrocode}
\newcount\@probN \newcount\@probselN \newcount\@rndselctr
-
-% \PSNrandom{<count>}{<n>} stores a random number from 1 to <n>
-% in the TeX count register <count>
\newcount\r@ndcur
+\newcount\@ps@randtmp
\r@ndcur=1\relax
+% \end{macrocode}
+% Set the random generator seed
+% \begin{macrocode}
\newcommand{\PSNrandseed}[1]{%
-\ifnum#1=0
-\typeout{Can't have 0 as random seed, changing to 1}
+\ifnum#1=0\relax
+\PackageWarning{probsoln}{Can't have 0 as random seed, changing to 1}%
\r@ndcur=1\relax
\else
\r@ndcur=#1\relax
\fi
-\typeout{Random Seed = \the\r@ndcur}
+\PackageInfo{probsoln}{Random Seed = \the\r@ndcur}%
}
-
-\newcount\@ps@randtmp
-\newcommand{\PSNrand}{
+% \end{macrocode}
+% Generate a random integer.
+% \begin{macrocode}
+\newcommand{\PSNrand}{%
\@ps@randtmp=\r@ndcur
\multiply\@ps@randtmp by 16807\relax
\r@ndcur=\@ps@randtmp
-\divide\r@ndcur by 120001
-\multiply\r@ndcur by 120001
+\divide\r@ndcur by 120001\relax
+\multiply\r@ndcur by 120001\relax
\advance\@ps@randtmp by -\r@ndcur
\r@ndcur = \@ps@randtmp
\ifnum\r@ndcur=0\relax\r@ndcur=1\fi
}
-
+% \end{macrocode}
+% |\PSNrandom{|\meta{count}|}{|\meta{n}|}| stores a random number
+% from 1 to \meta{n}
+% in the TeX count register \meta{count}
+% \begin{macrocode}
\newcommand{\PSNrandom}[2]{%
% generate new random number.
\PSNrand
@@ -409,33 +672,83 @@
\advance#1 by -\@ps@randtmp
\advance#1 by 1\relax
}
-
+% \end{macrocode}
+% |\random{|\meta{counter}|}{|\meta{a}|}{|\meta{b}|}|:
+% Generate a random number in the range $[a,b]$, and store this
+% number in the \LaTeX\ counter \meta{counter}.
+% \begin{macrocode}
+\newcommand{\random}[3]{%
+\ifnum#2=1\relax
+\PSNrandom{\value{#1}}{#3}%
+\else
+\@rndselctr=#3%
+\advance\@rndselctr by -#2\relax
+\advance\@rndselctr by 1\relax
+\PSNrandom{\value{#1}}{\@rndselctr}%
+\addtocounter{#1}{#2}%
+\addtocounter{#1}{-1}%
+\fi
+}
+% \end{macrocode}
+% Define command to use all problems from a given file.
+% Syntax: |\selectallproblems{|\meta{filename}|}|.
+% \begin{macrocode}
+\newcommand*{\selectallproblems}[1]{%
+\global\@probN=0\relax
+\selectrandomtrue
+\firstpasstrue
+\input{#1}%
+\firstpassfalse
+\selectrandomfalse
+\input{#1}%
+\global\@rndselctr=1\relax
+\whiledo{\@rndselctr < \@probN \TE@or \@rndselctr = \@probN}{%
+\edef\@tmp{\csname @problabel\romannumeral\@rndselctr\endcsname}%
+\edef\@probargs{{\@tmp}\csname @prob@\@tmp @arg\endcsname}%
+\PSNitem \expandafter\useproblem\@probargs \endPSNitem
+\global\advance\@rndselctr by 1\relax
+}}
+% \end{macrocode}
+% Now define command to randomly select \meta{n} problems from
+% a given file.
+% Syntax: |\selectrandomly{|\meta{filename}|}{|\meta{n}|}|.
+% \begin{macrocode}
\newcommand{\selectrandomly}[2]{%
-\global\@probselN=#2
-\global\@probN=0
+\global\@probselN=#2\relax
+\global\@probN=0\relax
\selectrandomtrue
\firstpasstrue
-\input{#1}
+\input{#1}%
\ifnum\@probselN>\@probN
\PackageError{probsoln}{Requested number too large}%
{You have asked for \the\@probselN \space problems, but there are only
\the\@probN \space problems defined in the file #1. I will only select \the\@probN \space
-problems.}
+problems.}%
\global\@probselN=\@probN
\fi
-\shuffle{@problabel}{\@probN}
+\shuffle{@problabel}{\@probN}%
\firstpassfalse
-\input{#1}
+\input{#1}%
\selectrandomfalse
-\@rndselctr=1\relax
+\global\@rndselctr=1\relax
\whiledo{\@rndselctr < \@probselN \TE@or \@rndselctr = \@probselN}{%
-\edef\@tmp{\csname @problabel\romannumeral\@rndselctr\endcsname}
-\edef\@probargs{{\@tmp}\csname @prob@\@tmp @arg\endcsname}
-\item \expandafter\useproblem\@probargs
-\advance\@rndselctr by 1\relax
-}
+\edef\@tmp{\csname @problabel\romannumeral\@rndselctr\endcsname}%
+\edef\@probargs{{\@tmp}\csname @prob@\@tmp @arg\endcsname}%
+\PSNitem \expandafter\useproblem\@probargs \endPSNitem
+\global\advance\@rndselctr by 1\relax
+}%
}
% \end{macrocode}
+% What to do at start and end of each randomly selected item:
+% \begin{macrocode}
+\newcommand{\PSNitem}{\item}
+\@ifundefined{endPSNitem}{\def\endPSNitem{}}{%
+\PackageError{probsoln}{\string\endPSitem\ already defined}{}}
+% \end{macrocode}
+% How to display each solution
+% \begin{macrocode}
+\newenvironment{solution}{\paragraph{\solutionname:}}{}
+% \end{macrocode}
% Check to see if label has been selected
% \begin{macrocode}
\newcount\@ckselctr
@@ -444,30 +757,531 @@ problems.}
\@ckselctr=1\relax
\whiledo{\@ckselctr < \@probselN \TE@or \@ckselctr = \@probselN}{%
\ifthenelse{\equal{#1}{\csname @problabel\romannumeral\@ckselctr\endcsname}}%
-{\global\selectedtrue \global\@ckselctr=\@probselN}{}
+{\global\selectedtrue \global\@ckselctr=\@probselN}{}%
\advance\@ckselctr by 1\relax
-}
+}%
}
% \end{macrocode}
-% Shuffle contents of pseudo-array
+% Shuffle contents of pseudo-array. For example, suppose you have
+% the following definitions: |\def\fooi{A}|, |\def\fooii{B}| and
+% |\def\fooiii{C}|, then |\shuffle{foo}{3}| will shuffle the
+% definitions, so you may end up with, e.g.\ |\def\fooi{C}|,
+% |\def\fooii{A}|, |\def\fooiii{B}|, or some other variation.
% \begin{macrocode}
\newcount\@shfctr \newcount\@shfA \newcount\@shfB
\newcommand{\shuffle}[2]{%
\@shfctr=1\relax
\whiledo{\@shfctr < 101}{%
-\PSNrandom{\@shfA}{#2}\PSNrandom{\@shfB}{#2}
+\PSNrandom{\@shfA}{#2}\PSNrandom{\@shfB}{#2}%
\ifnum\@shfA=\@shfB
\else
-\edef\@@tmpA{\csname#1\romannumeral\@shfA\endcsname}
+\edef\@@tmpA{\csname#1\romannumeral\@shfA\endcsname}%
\let\@tmpA=\@@tmpA
-\edef\@@tmpB{\csname#1\romannumeral\@shfB\endcsname}
+\edef\@@tmpB{\csname#1\romannumeral\@shfB\endcsname}%
\let\@tmpB=\@@tmpB
-\expandafter\xdef\csname#1\romannumeral\@shfA\endcsname{\@tmpB}
-\expandafter\xdef\csname#1\romannumeral\@shfB\endcsname{\@tmpA}
+\expandafter\xdef\csname#1\romannumeral\@shfA\endcsname{\@tmpB}%
+\expandafter\xdef\csname#1\romannumeral\@shfB\endcsname{\@tmpA}%
\fi
\advance\@shfctr by 1\relax
+}%
+}
+% \end{macrocode}
+% Syntax: |\doforrandN{|\meta{n}|}{|\meta{cmd}|}{|\meta{list}|}{|\meta{text}|}|.
+% A bit like |\@for| but only for a random subset of the given list.
+% For example,
+%\begin{verbatim}
+%\doforrandN{2}{\tmp}{file1,file2,file3}{%
+%\selectrandomly{\tmp}{1}}
+%\end{verbatim}
+%This will select one problem each from two out of the three listed
+%files.
+% \begin{macrocode}
+\newcount\@ps@forrand
+\newcommand{\doforrandN}[4]{%
+{\@ps@forrand=0\relax
+\@for#2:=#3\do{%
+\advance\@ps@forrand by 1\relax
+\expandafter\edef\csname @doforrandN@\romannumeral\@ps@forrand\endcsname{#2}}%
+\ifnum\@ps@forrand<#1\relax
+\PackageError{probsoln}{Can't randomly select \number#1 item(s)}{You
+have requested \number#1 item(s), but there
+are only \number\@ps@forrand item(s) in the list}%
+\else
+\shuffle{@doforrandN@}{\@ps@forrand}%
+\ifnum#1>0\relax
+\@ps@forrand=0\relax
+\loop
+\advance\@ps@forrand by 1\relax
+\edef#2{\csname @doforrandN@\romannumeral\@ps@forrand\endcsname}%
+#4%
+\ifnum\@ps@forrand<#1\relax
+\repeat
+\fi
+\fi
+}}
+% \end{macrocode}
+% \begin{macrocode}
+%</probsoln.sty>
+% \end{macrocode}
+% \begin{macrocode}
+%<*1stprncp.tex>
+% \end{macrocode}
+% These all involve differentiating from 1st principles
+
+\newproblem{dfp:xcube}{%
+Differentiate $f(x) = x^3$ with respect to $x$ by first principles.}{%
+\begin{eqnarray*}
+\frac{dy}{dx} & = & \lim_{\Delta x\rightarrow 0}\frac{f(x+\Delta x) - f(x)}{\Delta x}\\
+ & = & \lim_{\Delta x\rightarrow 0}\frac{(x+\Delta x)^3-x^3}{\Delta x}\\
+ & = & \lim_{\Delta x\rightarrow 0}\frac{(x+\Delta x)(x^2+2x\Delta x+(\Delta x)^2)-x^3}{\Delta x}\\
+ & = & \lim_{\Delta x\rightarrow 0}\frac{x^3+3x^2\Delta x+3x(\Delta x)^2+(\Delta x)^3-x^3}{\Delta x}\\
+ & = & \lim_{\Delta x\rightarrow 0}\frac{3x^2\Delta x+3x(\Delta x)^2+(\Delta x)^3}{\Delta x}\\
+ & = & \lim_{\Delta x\rightarrow 0}3x^2+3x\Delta x + (\Delta x)^2\\
+ & = & 3x^2
+\end{eqnarray*}}
+
+\newproblem{dfp:Ioverxsq}{%
+Differentiate $\displaystyle f(x) = \frac{1}{x^2}$ with respect to $x$ by first principles.}{%
+\begin{eqnarray*}
+\frac{df}{dx} & = & \lim_{\Delta x\rightarrow 0}\frac{\frac{1}{(x+\Delta x)^2}-\frac{1}{x^2}}{\Delta x}\\
+ & = & \lim_{\Delta x\rightarrow 0}\frac{\frac{x^2-(x+\Delta x)^2}{x^2(x+\Delta x)^2}}{\Delta x}\\
+ & = & \lim_{\Delta x\rightarrow 0}\frac{x^2-(x^2+2x\Delta x+(\Delta x)^2)}{x^2\Delta x(x+\Delta x)^2}\\
+ & = & \lim_{\Delta x\rightarrow 0}\frac{-2x\Delta x-(\Delta x)^2}{x^2\Delta x(x+\Delta x)^2}\\
+ & = & \lim_{\Delta x\rightarrow 0}\frac{-2x-\Delta x}{x^2(x+\Delta x)^2}\\
+ & = & \frac{-2x}{x^2x^2}\\
+ & = & -\frac{2}{x^3}
+\end{eqnarray*}}
+
+\newproblem{dfp:sqrtx}{%
+Differentiate from first principles $f(x) = \surd x$}{%
+\begin{eqnarray*}
+\frac{df}{dx} & = & \lim_{\Delta x\rightarrow 0}\frac{\sqrt{x+\Delta x}-\surd x}{\Delta x}\\
+ & = & \lim_{\Delta x\rightarrow 0}\frac{(\sqrt{x+\Delta x}-\surd x)(\sqrt{x+\delta x}+\surd x)}{\Delta x(\sqrt{x+\Delta x}+\surd x)}\\
+ & = & \lim_{\Delta x\rightarrow 0}\frac{x+\Delta x - x}{\Delta x(\sqrt{x+\Delta x}+\surd x)}\\
+ & = & \lim_{\Delta x\rightarrow 0}\frac{\Delta x}{\Delta x(\sqrt{x+\Delta x}+\Delta x)}\\
+ & = & \lim_{\Delta x\rightarrow 0}\frac{1}{\sqrt{x+\Delta x}+\surd x}\\
+ & = & \frac{1}{2\surd x}
+\end{eqnarray*}}
+
+\newproblem{dfp:cons}{%
+Differentiate from first principles $f(x) = c$ where $c$ is a constant.}{%
+\begin{eqnarray*}
+\frac{df}{dx} & = & \lim_{\Delta x\rightarrow 0}\frac{c-c}{\Delta x}\\
+ & = & \lim_{\Delta x\rightarrow 0}0\\
+ & = & 0
+\end{eqnarray*}}
+
+\newproblem{dfp:cosx}{%
+Given
+\begin{eqnarray*}
+\lim_{x \rightarrow 0} \frac{\cos x - 1}{x} & = & 0\\
+\lim_{x \rightarrow 0} \frac{\sin x}{x} & = & 1
+\end{eqnarray*}
+differentiate from first principles $f(x) = \cos x$.}{%
+\begin{eqnarray*}
+\frac{df}{dx} & = & \lim_{\Delta x \rightarrow 0}\frac{f(x + \Delta x) - f(x)}{\Delta x}\\
+ & = & \lim_{\Delta x \rightarrow 0} \frac{\cos(x + \Delta x) - \cos(x)}{\Delta x}\\
+ & = & \lim_{\Delta x \rightarrow 0} \frac{\cos x\cos\Delta x - \sin x\sin\Delta x - \cos x}{\Delta x}\\
+ & = & \lim_{\Delta x \rightarrow 0} \frac{\cos x(\cos\Delta x - 1) - \sin x\sin\Delta x}{\Delta x}\\
+ & = & \cos x\lim_{\Delta x \rightarrow 0}\frac{\cos\Delta x - 1}{\Delta x}
+ - \sin x\lim_{\Delta x \rightarrow 0}\frac{\sin\Delta x}{\Delta x}\\
+ & = & -1 \qquad\mbox{(using given results)}
+\end{eqnarray*}}
+% \begin{macrocode}
+%</1stprncp.tex>
+% \end{macrocode}
+% \begin{macrocode}
+%<*args.tex>
+% \end{macrocode}
+% These problems require arguments
+
+% Arguments: #1->a_2, #2->a_1 and #3->a_0
+% (Arguments must be integers)
+\newcount\ctr
+\newproblem[3]{diff:quad}{%
+\(f(x) =
+\ifnum#1=0
+\else
+\ifnum#1=1\else#1\fi x^2
+\fi
+\ifnum#2=0
+\else
+\ifnum#2>0 \ifnum#1=0 \else + \fi \fi
+\ifnum#2=1\else#2\fi x
+\fi
+\ifnum#3=0
+\else
+\ifnum#3>0 \ifnum#2=0 \ifnum#1=0 \else + \fi \else + \fi\fi
+#3
+\fi\)
+}{%
+\(f'(x) =
+\ifnum#1=0
+\else
+\ctr=2
+\multiply\ctr by #1
+\the\ctr x
+\fi
+\ifnum#2=0
+\else
+\ifnum#2>0 \ifnum#1=0 \else + \fi \fi
+#2
+\fi
+% print 0 if both #1 and #2 are 0
+\ifnum#1=0 \ifnum#2=0 0 \fi\fi
+\)
}
+
+\newproblem[1]{diff:sin}{%
+\(f(x) = \sin(#1x)\)
+}{%
+\(f'(x) = #1\cos(#1x)\)
}
+
+% \begin{macrocode}
+%</args.tex>
+% \end{macrocode}
+% \begin{macrocode}
+%<*easy.tex>
+% \end{macrocode}
+% These are all easy differentiation problems
+
+\newproblem{diffeasy:gpowh}{%
+\(f(x) = g(x)^{h(x)}.\)}{%
+\begin{eqnarray*}
+f(x) & = & e^{\ln g(x)^{h(x)}}\\
+ & = & e^{h(x)\ln g(x)}\\
+f'(x) & = & e^{h(x)\ln g(x)}(h'(x)\ln g(x) + h(x)\frac{g'(x)}{g(x)})\\
+ & = & g(x)^{h(x)}(h'(x)\ln g(x) + \frac{h(x)g'(x)}{g(x)})
+\end{eqnarray*}}
+
+\newproblem{diffeasy:arcsin}{%
+\(y = \arcsin(x)\)}{%
+\[\sin(y) = x\]
+diff. w.r.t. $x$:
+\begin{eqnarray*}
+\cos y \frac{dy}{dx} & = & 1\\
+\frac{dy}{dx} & = & \frac{1}{\cos y}\\
+ & = & \frac{1}{\sqrt{1 - \sin^2y}}\\
+ & = & \frac{1}{\sqrt{1-x^2}}.
+\end{eqnarray*}}
+
+\newproblem{diffeasy:arccos}{%
+$y = \arccos x$.}{%
+\(\cos y = x\)
+diff. w.r.t. $x$:
+\begin{eqnarray*}
+-\sin y \frac{dy}{dx} & = & 1\\
+\frac{dy}{dx} & = & \frac{-1}{\sin y}\\
+ & = & \frac{-1}{\sqrt{1-\cos^2y}}\\
+ & = & \frac{-1}{\sqrt{1-x^2}}
+\end{eqnarray*}}
+
+\newproblem{diffeasy:tan}{%
+\(y = \tan x\)}{%
+\begin{eqnarray*}
+y & = & \tan x\\
+ & = & \frac{\sin x}{\cos x}\\
+\frac{dy}{dx} & = & \frac{\cos x}{\cos x} + \sin x\times\frac{-1}{\cos^2x}\times -\sin x\\
+ & = & 1 + \tan^2x\\
+ & = & \sec^2x.
+\end{eqnarray*}}
+
+\newproblem{diffeasy:arctan}{%
+\(y = \arctan x = \tan^{-1}x\)}{%
+\[\tan y = x\]
+diff w.r.t. $x$:
+\begin{eqnarray*}
+\sec^2y\frac{dy}{dx} & = & 1\\
+\frac{dy}{dx} & = & \frac{1}{\sec^2y}\\
+ & = & \frac{1}{1+\tan^2y}\\
+ & = & \frac{1}{1+x^2}
+\end{eqnarray*}}
+
+\newproblem{diffeasy:cot}{%
+\(y = (\tan x)^{-1} = \cot x\)}{%
+\begin{eqnarray*}
+\frac{dy}{dx} & = & -(\tan x)^{-2}\sec^2x\\
+ & = & -\frac{\cos^2x}{\sin^2x}\cdot\frac{1}{\cos^2x}\\
+ & = & \frac{-1}{\sin^2x}\\
+ & = & -\csc^2x.
+\end{eqnarray*}}
+
+\newproblem{diffeasy:cosxsqsinx}{%
+$y = \cos(x^2)\sin x$.}{%
+\[\frac{dy}{dx} = -\sin(x^2)2x\sin x + \cos(x^2)\cos x\]}
+
+\newproblem{diffeasy:xlnx}{%
+$y = (x+1)\ln(x+1)$.}{%
+\begin{eqnarray*}
+\frac{dy}{dx} & = & \ln(x+1) + \frac{x+1}{x+1}\\
+ & = & 1 + \ln(x+1).
+\end{eqnarray*}}
+
+\newproblem{diffeasy:glng}{%
+$f(x) = g(x)\ln(g(x))$.}{%
+\begin{eqnarray*}
+f'(x) & = & g'(x)\ln(g(x)) + \frac{g(x)}{g(x)}g'(x)\\
+ & = & g'(x)(1+\ln(g(x))).
+\end{eqnarray*}}
+
+\newproblem{diffeasy:sinx/x}{%
+$y = \frac{\sin x}{x}$.}{%
+\[\frac{dy}{dx} = \frac{\cos x}{x} - \frac{\sin x}{x^2}\]}
+
+% \begin{macrocode}
+%</easy.tex>
+% \end{macrocode}
+% \begin{macrocode}
+%<*implicit.tex>
+% \end{macrocode}
+% These are all implicit differentiation problems
+
+\newproblem{imd:circ}{%
+Find the gradient of the unit circle ($x^2 + y^2 = 1$).}{%
+Differentiating with respect to $x$ gives:
+\begin{eqnarray*}
+2x + 2y\frac{dy}{dx} & = & 0\\
+\frac{dy}{dx} & = & \frac{-2x}{2y}\\
+ & = & \frac{-x}{\sqrt{1-x^2}}.
+\end{eqnarray*}}
+
+\newproblem{imd:ysq:xcuov2mx}{%
+Find $\frac{dy}{dx}$, given
+\begin{displaymath}
+y^2 = \frac{x^3}{2-x}
+\end{displaymath}}{%
+Differentiating both sides w.r.t.\ $x$:
+\begin{eqnarray*}
+2y\frac{dy}{dx} & = & \frac{(2-x)3x^2 - x^3(-1)}{(2-x)^2}\\
+ & = & \frac{3x^2(2-x) + x^3}{(2-x)^2}\\
+ & = & \frac{6x^2 - 3x^3 + x^3}{(2-x)^2}\\
+ & = & \frac{6x^2-2x^3}{(2-x)^2}\\
+ & = & 2x^2\frac{3-x}{(2-x)^2}
+\end{eqnarray*}
+Therefore
+\begin{displaymath}
+y\frac{dy}{dx} = x^2\frac{3-x}{(2-x)^2}
+\end{displaymath}}
+
+\newproblem{imd:exy:IIxay}{%
+Differentiate w.r.t.\ $x$:
+\begin{displaymath}
+e^{xy} = 2x + y
+\end{displaymath}}{%
+Differentiating both sides w.r.t.\ $x$:
+\begin{eqnarray*}
+e^{xy}(1y + x\frac{dy}{dx}) & = & 2 + \frac{dy}{dx}\\
+xe^{xy}\frac{dy}{dx} - \frac{dy}{dx} & = & 2 - ye^{xy} \\
+\frac{dy}{dx}(xe^{xy}-1) & = & 2 - ye^{xy}\\
+\frac{dy}{dx} & = & \frac{2-ye^{xy}}{xe^{xy}-1}
+\end{eqnarray*}}
+% \begin{macrocode}
+%</implicit.tex>
+% \end{macrocode}
+% \begin{macrocode}
+%<*mchoice.tex>
+% \end{macrocode}
+\newproblem{mc:prod}{%
+Which of the following is the derivative of $x\sin(x)$?
+(Circle the correct answer.)
+\ifthenelse{\boolean{showanswers}}{}%
+{\begin{description}
+\item[A] $\sin(x)$
+\item[B] $x\cos(x)$
+\item[C] $\sin(x) + x\cos(x)$
+\end{description}
+}}{%
+\begin{description}
+\item[A] $\sin(x)$
+\item[B] $x\cos(x)$
+\item[\textcircled{C}] $\sin(x) + x\cos(x)$ (product rule).
+\end{description}
+}
+
+\newproblem{mc:quot}{%
+Which of the following is the derivative of $\frac{\sin(x)}{x}$?
+(Circle the correct answer.)
+\ifthenelse{\boolean{showanswers}}{}%
+{\begin{description}
+\item[A] $\sin(x)$
+\item[B] $\cos(x)$
+\item[C] $\frac{\cos(x)x-\sin(x)}{x^2}$
+\end{description}
+}}{%
+\begin{description}
+\item[A] $\sin(x)$
+\item[B] $\cos(x)$
+\item[\textcircled{C}] $\frac{\cos(x)x-\sin(x)}{x^2}$
+(quotient rule)
+\end{description}
+}
+% \begin{macrocode}
+%</mchoice.tex>
+% \end{macrocode}
+% \begin{macrocode}
+%<*sample.tex>
+% \end{macrocode}
+\documentclass[a4paper]{article}
+
+\usepackage{probsoln}
+%uncomment the following line to display the answers
+\showanswers
+
+% The following will generate a different set of
+% problems in subsequent years
+\PSNrandseed{\year}
+
+\begin{document}
+\title{Sample Problem Sheet}
+\author{Nicola Talbot}
+\maketitle
+
+\begin{enumerate}
+% Differentiation from first principles
+\selectrandomly{1stprncp}{1}
+
+\item Differentiate the following functions:
+\begin{enumerate}
+\selectrandomly{easy}{5}
+\end{enumerate}
+
+% Implicit differentiation
+\selectrandomly{implicit}{2}
+
+% Multiple choice question
+\selectrandomly{mchoice}{1}
+\end{enumerate}
+\end{document}
+% \begin{macrocode}
+%</sample.tex>
+% \end{macrocode}
+% \begin{macrocode}
+%<*sample2.tex>
+% \end{macrocode}
+\documentclass[a4paper]{article}
+
+\usepackage{probsoln}
+%uncomment the following line to display the answers
+\showanswers
+
+% The following will generate a different set of
+% problems in subsequent years
+%\PSNrandseed{\year}
+
+% The following will generate a different set of
+% problems on every run (where each run is at
+% least a minute apart from the previous one)
+\PSNrandseed{\time}
+
+\begin{document}
+\title{Sample Problem Sheet}
+\author{Nicola Talbot}
+\maketitle
+
+\begin{enumerate}
+
+\newcounter{numproblems}
+% store a random number from 1 to 3 in the counter numproblems
+\random{numproblems}{1}{3}
+
+% selects 1,2 or 3 problems from 1 of the given files:
+\doforrandN{1}{\file}{1stprncp,implicit}{\selectrandomly{\file}{\value{numproblems}}}
+
+\item Differentiate the following functions:
+\input{args}% load database
+\begin{enumerate}
+\newcounter{A}
+\newcounter{B}
+\newcounter{C}
+\random{A}{-4}{5}
+\random{B}{-3}{3}
+\random{C}{-1}{10}
+\item \useproblem{diff:quad}{\arabic{A}}{\arabic{B}}{\arabic{C}}
+
+\random{A}{-5}{5}
+% make sure its not 0
+\whiledo{\value{A}=0}{\random{A}{-5}{5}}
+\item \useproblem{diff:sin}{\arabic{A}}
+\end{enumerate}
+\end{enumerate}
+\end{document}
+% \begin{macrocode}
+%</sample2.tex>
+% \end{macrocode}
+% \begin{macrocode}
+%<*sample3.tex>
+% \end{macrocode}
+\documentclass[a4paper]{article}
+
+\usepackage{longtable}
+\usepackage{probsoln}
+
+%\showanswers
+
+\newcounter{problem}
+\renewcommand{\PSNitem}{\refstepcounter{problem}%
+\theproblem. }
+\renewcommand{\endPSNitem}{\\}
+
+\renewenvironment{solution}{}{}
+
+\newcommand{\selected}{\fbox{$\times$}}
+\newcommand{\notselected}{\fbox{\phantom{$\times$}}}
+
+\begin{document}
+\begin{longtable}{lrrrl}
+\bfseries Question & \bfseries A & \bfseries B &
+\bfseries C & \ifshowanswers \bfseries Reason\fi\\
+\selectrandomly{tabmchoice}{2}
+\end{longtable}
+\end{document}
+% \begin{macrocode}
+%</sample3.tex>
+% \end{macrocode}
+% \begin{macrocode}
+%<*sample4.tex>
+% \end{macrocode}
+\documentclass[a4paper]{article}
+
+\usepackage{probsoln}
+
+% Sample file illustrating use of \selectallproblems
+% All problems defined in specified file will be used
+% in order of definition
+
+\showanswers
+
+\begin{document}
+Differentiate the following functions:
+\begin{enumerate}
+\selectallproblems{easy}
+\end{enumerate}
+\end{document}
+% \begin{macrocode}
+%</sample4.tex>
+% \end{macrocode}
+% \begin{macrocode}
+%<*tabmchoice.tex>
+% \end{macrocode}
+% These problems are designed to be placed in a
+% tabular environment
+%
+\newproblem{tab:1}{%
+What is $(3+2)\times5$? &
+25 \ifshowanswers\selected\else\notselected\fi &
+13 \notselected &
+10 \notselected &
+}{Brackets come first}%
+%
+\newproblem{tab:2}{%
+What is $-1+2\times3$? &
+3 \notselected &
+-7 \notselected &
+5 \ifshowanswers\selected\else\notselected\fi &
+}{Multiplication comes first}%
+% \begin{macrocode}
+%</tabmchoice.tex>
% \end{macrocode}
%\Finale
\endinput