## DESCRIPTION
## Multivariable differential calculus: interactive graph of 3D function in cylindrical coordinates
## ENDDESCRIPTION

## KEYWORDS('multivariable differential calculus', '3D graph', 'cylindrical coordinates')

## DBsubject('WeBWorK')
## DBchapter('WeBWorK Tutorial')
## DBsection('Fort Lewis Tutorial 2011')
## Date('01/30/2011')
## Author('Paul Pearson')
## Institution('Fort Lewis College')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')


####################################
#  Initialization

DOCUMENT();

loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"LiveGraphicsCylindricalPlot3D.pl",
);

TEXT(beginproblem());


##################################
#  Set-up

Context("Numeric");
Context()->variables->are(x=>"Real",y=>"Real",r=>"Real",t=>"Real");

$a = random(4,6,1);

$plot = CylindricalPlot3D(
function => Formula("$a/e^r"),
rvar => "r",
tvar => "t",
rmin =>  0,
rmax =>  3,
tmin =>  0,
tmax =>  2*pi,
rsamples => 20,
tsamples => 15,
axesframed => 1,
xaxislabel => "X",
yaxislabel => "Y",
zaxislabel => "Z",
outputtype => 4,
);


####################################
#  Main text

Context()->texStrings;
BEGIN_TEXT
\{ 
Live3Ddata(
$plot,
image => "wavy-surface.png", 
size => [400,400],
tex_size => 600,
tex_center => 1,
scale => 1.1,
);
\}
END_TEXT
Context()->normalStrings;


#####################################
#  Answer evaluation

$showPartialCorrectAnswers = 1;



#####################################
#  Solution

Context()->texStrings;
BEGIN_SOLUTION
${PAR}SOLUTION:${PAR}
Solution explanation goes here.
END_SOLUTION
Context()->normalStrings;

COMMENT("MathObject version.");

ENDDOCUMENT();