GraphLimit Flash Applet Sample Problem

Sample Problem with GraphLimit.swf embedded

This sample problem shows how to use this versatile applet.

A standard WeBWorK PG file has five sections:

1. A tagging and description section, that describes the problem for future users and authors,
2. An initialization section, that loads required macros for the problem,
3. A problem set-up section that sets variables specific to the problem,
4. A text section, that gives the text that is shown to the student, and
5. An answer and solution section, that specifies how the answer(s) to the problem is(are) marked for correctness, and gives a solution that may be shown to the student after the problem set is complete.

The sample file attached to this page shows this; below the file is shown to the left, with a second column on its right that explains the different parts of the problem that are indicated above.

PG problem file	Explanation
##DESCRIPTION ## Graphical limits ## Sample problem to illustrate the use of the GraphLimit.swf Flash applet ##ENDDESCRIPTION ## KEYWORDS('limits') ## DBsubject('Calculus') ## DBchapter('Limits') ## DBsection('Graphical limits') ## Date('7/5/2011') ## Author('Barbara Margolius') ## Institution('Cleveland State University') ## TitleText1('') ## EditionText1('2011') ## AuthorText1('') ## Section1('') ## Problem1('') ######################################################################## # This work is supported in part by the National Science Foundation # under the grant DUE-0941388. ########################################################################	This is the tagging and description section of the problem. Note that any line that begins with a "#" character is a comment for other authors who read the problem, and is not interpreted by !WeBWorK. The description is provided to give a quick summary of the problem so that someone reading it later knows what it does without having to read through all of the problem code. All of the tagging information exists to allow the problem to be easily indexed. Because this is a sample problem there isn't a textbook per se, and we've used some default tagging values. There is an on-line list of current chapter and section names and a similar list of keywords. The list of keywords should be comma separated and quoted (e.g., KEYWORDS('calculus','derivatives')).
DOCUMENT(); loadMacros( "PGstandard.pl", "AppletObjects.pl", "MathObjects.pl", );	This is the initialization section of the problem. The first executed line of the problem must be the DOCUMENT(); command. Note that every command must end with a semicolon. The loadMacros command loads information that works behind the scenes. For our purposes we can usually just load the macros shown here and not worry about things further.
# Set up problem $qtype='limits'; $showHint = 0; if(time<$dueDate){ $showHint=1; } $x1=random(-8,-2,1); $x2=$x1+random(2,4,1); $x3=$x2+random(2,3,1); $x4=random($x3+2,7,1);	This is the problem set-up section of the problem. The GraphLimits.swf applet wil accept four different question types, specified with the $qtype variable. These are: limits, continuity, first_derivative and second_derivative. This sample problem is set to 'limits'. The applet has solution/hint information embedded in it. When $hintState=0, this information is not shown. When $hintState=1, this information is revealed. The time parameter tracks the current date and time. The conditional compares that to the due date for the problem set (in the $dueDate scalar variable) and sets $hintState to 1 if the due date has passed and leaves $hintState set to 0 if the assignment is not yet due. The four variables $x1, $x2, $x3 and $x4 are the x-coordinates of four points on the graph that the applet will set to be a removable discontinuity, a jump discontinuity or a cusp. The order of these phenomena is random as are the y-values chosen. The x-coordinates must be between -10 and 10.
BEGIN_TEXT $BR The graph shown is for the function \(f(x)\). $BR Compute the following quantities: $BR a) \(f($x1)=\) \{ans_rule(35) \} $BR b) \(\lim_{x\to {$x2}^+}f(x)=\) \{ans_rule(35) \} $BR c) \(\lim_{x\to {$x3}^-}f(x)=\) \{ans_rule(35) \} $BR d) \(\lim_{x\to {$x4}}f(x)=\) \{ans_rule(35) \} $BR Enter "None" if no intervals meet this criteria. END_TEXT Context()->normalStrings;	This is the text section of the problem. The TEXT(beginproblem()); line displays a header for the problem, and the Context()->texStrings line sets how formulas are displayed in the text, and we reset this after the text section. Everything between the BEGIN_TEXT and END_TEXT lines (each of which must appear alone on a line) is shown to the student. Mathematical equations are delimited by \( \) (for inline equations) or \[ \] (for displayed equations); in these contexts inserted text is assumed to be TeX code. There are a number of variables that set formatting: $PAR is a paragraph break (like \par in TeX). This page gives a list of variables like this. Finally, \{ \} sets off code that will be executed in the problem text. Here, ans_rule(35) is a function that inserts an answer blank 35 characters wide.
ANS( $trigDeriv->cmp() ); Context()->texStrings; SOLUTION(EV3(<<'END_SOLUTION')); $PAR SOLUTION $PAR We find the derivative to this using the chain rule. The inside function is \($a x\), so that its derivative is \($a\), and the outside function is \(\sin(x)\), which has derivative \(\cos(x)\). Thus the solution is \[ \frac{d}{dx} $trigFunc = $trigDeriv. \] END_SOLUTION Context()->normalStrings; ENDDOCUMENT();	This is the answer and solution section of the problem. The problem answer is set by the ANS( $trigDeriv->cmp() ); line, which simply says that the answer is marked by comparing the student's answer with the trigonometric function derivative that we defined before. Then, we explain the solution to the student. This solution will show up when the student clicks the "show solution" checkbox after they've finished the problem set. The ENDDOCUMENT(); command is the last command in the file.