GraphLimit Flash Applet Sample Problem

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Flash Applets embedded in WeBWorK questions GraphLimit Example

Sample Problem with GraphLimit.swf embedded

This sample problem shows how to use this versatile applet.

This applet and WeBWorK problem are based upon work supported by the National Science Foundation under Grant Number DUE-0941388.

Click here to see a problem like this in action: testcourses.webwork.maa.org/webwork2/FlashAppletDemos

A standard WeBWorK PG file with an embedded applet has six 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. An Applet link section that inserts the applet and configures it, (this section is not present in WeBWorK problems without an embedded applet)
  5. A text section, that gives the text that is shown to the student, and
  6. 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. A screenshot of the applet embedded in this WeBWorK problem is shown below:
GraphLimit.jpg
There are other example problems using this applet:
GraphLimit Flash Applet Sample Problem 2
And other problems using applets:
Derivative Graph Matching Flash Applet Sample Problem
GraphSketch Flash Applet Sample Problem 1
USub Applet Sample Problem
trigwidget Applet Sample Problem
solidsWW Flash Applet Sample Problem 1
solidsWW Flash Applet Sample Problem 2
solidsWW Flash Applet Sample Problem 3
Hint Applet (Trigonometric Substitution) Sample Problem
phasePortrait Flash Applet Sample Problem 1
autonomous solution sketch Flash Applet Sample Problem
Other useful links:
Flash Applets Tutorial
Things to consider in developing WeBWorK problems with embedded Flash applets

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);

The GraphLimits.swf applet will 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. 

#######################################
#  How to use the Graph_Test applet.
#    Purpose:  The purpose of this 
#       applet is to ask graphical 
#       limit questions
#    Use of applet:  The applet 
#       state consists of the 
#       following fields:
#     qType - question type: limits, 
#       continuity, first_derivative, 
#       second_derivative
#     hintState - context sensitive 
#       help is either on or off.  
#       Generally turned on after 
#       dueDate
#     problemSeed - the seed sets 
#       the random parameters that 
#       control which graph is 
#       chosen.  If the seed is 
#       changed, the graph is 
#       changed.
#######################################
#     qType = limits
#      right_limits - returns a 
#        list of points (a,b) 
#        such that 
#        lim_{x\to a^-}f(x)=b, 
#        but 
#        lim_{x\to a^+}f(x)\= b
#      left_limits - returns a 
#        list of points (a,b) 
#        such that
#        lim_{x\to a^+}f(x)=b, 
#        but 
#        lim_{x\to a^-}f(x)\= b
#      neither_limits - returns 
#        a list of points (a,b) 
#        such that
#        lim_{x\to a^-}f(x)\=
#          lim_{x\to a^+}f(x)\= 
#          f(a)=b
#      get_intervals returns a 
#        list of intervals on 
#        which f(x) is continuous.
#      get_f_of_x - given x value, 
#        returns f(x).  
#        returns NaN for x notin 
#        [-10,10].
#      getf_list - given x value 
#        and string returns 
#        "function" - returns f(x)
#        "leftlimit" - returns 
#           lim_{x->a^-}f(x)
#        "rightlimit" - returns 
#           lim_{x->a^+}f(x)
#        "limit" - returns 
#           lim_{x->a}f(x) or "DNE"

This is the Applet link section of the problem.


Those portions of the code that begin the line with # are comments and can be omitted or replaced with comments appropriate to your particular problem. 

#
#  What does the applet do?
#    The applet draws a graph 
#    with jumps, a cusp and 
#    discontinuities
#    When turned on, there is 
#    context sensitive help.
################################
    ############################
    # Create  link to applet 
    ############################
    $appletName = "Graph_Limit";
    $applet =  FlashApplet(
       codebase              
         => findAppletCodebase
         ("$appletName.swf"),
       appletName            
         => $appletName,
       appletId              
         => $appletName,
       setStateAlias         
         => 'setXML',
       getStateAlias         
         => 'getXML',
       setConfigAlias        
         => 'setConfig',
       maxInitializationAttempts 
         => 10,   
       height                
         => '475',
       width                 
         => '425',
       bgcolor               
         => '#e8e8e8',
       debugMode             
         =>  0,
       submitActionScript  
         =>    qq{ 
getQE("func").value=getApplet
  ("$appletName").getf_list($x1,"function");
getQE("rlimit").value=getApplet
  ("$appletName").getf_list($x2,"rightlimit");
getQE("llimit").value=getApplet
  ("$appletName").getf_list($x3,"leftlimit");
getQE("limit").value=getApplet
  ("$appletName").getf_list($x4,"limit");
   },
     );

You must include the section that

follows # Create link to applet. If you are embedding a different applet, from the Graph_Limit applet, put your applet name in place of 'Graph_Limit' in the line $appletName = "Graph_Limit";. Enter the height of the applet in the line height => '475', in place of 475 and the width in the line width => '425', in place of 425.


The code qq{ getQE("func").value=getApplet ("$appletName").getf_list($x1,"function"); getQE("rlimit").value=getApplet ("$appletName").getf_list($x2,"rightlimit"); getQE("llimit").value=getApplet ("$appletName").getf_list($x3,"leftlimit"); getQE("limit").value=getApplet ("$appletName").getf_list($x4,"limit"); } is called when the 'Submit Answers' button in the problem is pressed. There is an external interface function designed inside the applet. The function name is 'getf_list'. These lines of code call the function with javascript. getf_list, takes two arguments: the x-coordinate of a point, and a string value. The string may be any of the following four alternatives: "function", "rightlimit", "leftlimit", "limit". getf_list returns either the value of the function at the x-coordinate, or the specified limit. The line getQE("func").value=getApplet ("$appletName").getf_list($x1,"function"); gets the value of the function at $x1 and stores this value in the hidden javascript form field named "func".

###################################
# Configure applet
###################################
# configuration consists of 
# hintState, question type, and 
# random seed, and x-coordinates of 
# four points where jumps, 
# discontinuities or cusps 
# occur.
$applet->configuration(qq{<xml>
<hintState>$hintState</hintState>
<qtype>limits</qtype>
<seed>$problemSeed</seed>
<xlist x1='$x1' x2='$x2' 
x3='$x3' x4='$x4' /></xml>});
$applet->initialState(qq{<xml>
<hintState>$hintState</hintState>
<qtype>limits</qtype>
<seed>$problemSeed</seed>
<xlist x1='$x1' x2='$x2' 
x3='$x3' x4='$x4' /></xml>});

TEXT( MODES(TeX=>'object code', 
  HTML=>$applet->insertAll(
  debug=>0,
  includeAnswerBox=>0,
   )));

TEXT(MODES(TeX=>"", HTML=><<'END_TEXT'));
<input type="hidden" 
  name="func" id="func" />
<input type="hidden" 
  name="llimit" id="llimit" />
<input type="hidden" 
  name="rlimit" id="rlimit" />
<input type="hidden" 
  name="limit" id="limit" />
END_TEXT

$answerString1 = 
$inputs_ref->{func};
my $correctAnswer1 = 
Compute("$answerString1");

$answerString2 = 
$inputs_ref->{rlimit};
my $correctAnswer2 = 
Compute("$answerString2");

$answerString3 = 
$inputs_ref->{llimit};
my $correctAnswer3 = 
Compute("$answerString3");

$answerString4 = 
$inputs_ref->{limit};
my $correctAnswer4 = 
Compute("$answerString4");

The lines $applet->configuration

(qq{<xml><hintState>$hintState</hintState> <qtype>$qtype</qtype> <seed>$problemSeed</seed> <xlist x1='$x1' x2='$x2' x3='$x3' x4='$x4' /> </xml>}); and $applet ->initialState(qq{<xml> <hintState>$hintState</hintState> <qtype>$qtype</qtype><seed>$problemSeed</seed> <xlist x1='$x1' x2='$x2' x3='$x3' x4='$x4' /> </xml>}); configure the applet. The configuration of the applet is done in xml. The hintState is set to the variable $hintState, the question type is set to $qtype and the problem seed is the WeBWorK environmental variable $problemSeed. The variables $x1, $x2, $x3 and $x4 are also passed to the applet.


The hidden form fields are created in the code block: TEXT(MODES(TeX=>"", HTML=><<'END_TEXT')); <input type="hidden" name="func" id="func" /> <input type="hidden" name="llimit" id="llimit" /> <input type="hidden" name="rlimit" id="rlimit" /> <input type="hidden" name="limit" id="limit" /> END_TEXT The line TEXT(MODES(TeX=>"", HTML=><<'END_TEXT')); prevents the hidden fields from becoming part of the hard copy.


TEXT( MODES(TeX=>'object code', HTML=>$applet->insertAll( debug=>0, includeAnswerBox=>0, reinitialize_button=>$permissionLevel>=10, ))); actually embeds the applet in the WeBWorK problem.


When the submit button is pressed, the hidden form fields defined in this block are filled with information from the applet.

The data from the hidden form fields is used in these simple perl subroutines to define the correct answers to the four questions that are part of this WeBWorK problem.

The WeBWorK variable $answerString1 is the content of the hidden form field "func". $correctAnswer1 is the solution to the first question. The solutions for the next two questions are defined in a similar way. The final question also has 'DNE' as a possible correct answer for the student to enter. The way that the applet is designed, the left and right limits always exist.

TEXT(MODES(TeX=>"", HTML=><<'END_TEXT'));
<script>
if (navigator.appVersion.indexOf("MSIE") > 0) {
    document.write("<div width='3in' 
    align='center' style='background:yellow'>
    You seem to be using Internet Explorer.
    <br/>It is recommended that another 
    browser be used to view this page.</div>");
}
</script>
END_TEXT

The text between the <script> tags detects whether the student is using Internet Explorer. If the student is using this browser, a warning is issued and the student is advised to use another browser. IE mis-sizes the applets. Some will work correctly when displayed at the wrong size, but others will fail. We do not recommend using IE with WeBWorK problems with Flash embedded.

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
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. 

#############################
#
#  Answers
#
## answer evaluators

ANS( $correctAnswer1->cmp() );   
#checks AnSwEr00001
ANS( $correctAnswer2->cmp() );   
#checks AnSwEr00002
ANS( $correctAnswer3->cmp() );   
#checks AnSwEr00003
ANS(num_cmp($correctAnswer4,
strings=>['DNE']));   
#checks AnSwEr00004


ENDDOCUMENT();

This is the answer section of the problem. The problem answer is set by the ANS( $correctAnswer1->cmp() );, ANS( $correctAnswer2->cmp() );, ANS( $correctAnswer3->cmp() );, and ANS(num_cmp ($correctAnswer4, strings=>['DNE'])); lines. These compare the student's answer with the answers returned from the applet. Answers 1-3 follow the same basic structure. The fourth answer allows for either a numeric answer or the string 'DNE' for limits that do not exist.

The solution is embedded in the applet and becomes available when the due date has passed.

The ENDDOCUMENT(); command is the last command in the file.

License

The Flash applets developed under DUE-0941388 are protected under the following license: Creative Commons Attribution-NonCommercial 3.0 Unported License.

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