## WeBWorK Main Forum

### Help with programming a particular problem

by Dan Margalit -
Number of replies: 3
Hi,

I was wondering if someone could help me program a particular problem. Mike Gage was nice enough to point me to the description of how to deal with multi-answer problems on the wiki, but unfortunately this seems involved to me. (I'd be more comfortable mimicking an existing .pg problem if someone could point one out.)

The problem is a Riemann sum that you have to turn into an integral. The Riemann sum is the sum of:

\frac{\pi}{$a n} \tan\left(\frac{i \pi}{$p n}\right)

or, in more readable form:

pi/($a*n) tan( (i*pi) / ($p*n) )

(here, $p =$a*$b, where$b is randomly chosen).

The student is supposed to enter the left and right limits of integration and the function.

So if they enter left and right limits P and Q, the answer is:

pi/((Q-P)*$a) tan( pi/((Q-P)$a*$b) (x-P) ) (please correct me if I've screwed this up!) I'll put the text of the original .pg file below. I am guessing that this would be very easy for someone else. Any help would be greatly appreciated. Thanks! Dan ## DESCRIPTION ## Calculus: Areas and Distances ## ENDDESCRIPTION ##KEYWORDS('calculus', 'areas', 'distances') ## Tagged by XW ## DBsubject('Calculus') ## DBchapter('Integrals') ## DBsection('Area and Distance') ## Date('5/30/2005') ## Author('Jeff Holt') ## Institution('UVA') ## TitleText1('Calculus: Early Transcendentals') ## EditionText1('5') ## AuthorText1('Stewart') ## Section1('5.1') ## Problem1('19') ## TitleText2('Calculus: Early Transcendentals') ## EditionText2('6') ## AuthorText2('Stewart') ## Section2('5.1') ## Problem2('') DOCUMENT(); loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl" ); TEXT(beginproblem());$showPartialCorrectAnswers = 1;

$a = random(4,8,2);$b = random(2,5,1);
$p =$a*$b;$pi = 3.1415926535898;

TEXT(EV2(<
The value of the limit
$\lim_{n\rightarrow\infty}\sum_{i=1}^{n} \frac{\pi}{a n} \tan\left(\frac{i \pi}{p n}\right)$

is equal to the area below the graph
of a function $$f(x)$$ on an interval $$[A,B]$$. Find
$$f$$, $$A$$, and $$B$$. (Do not evaluate the limit.)
$BR$BR
$$f(x)$$ = \{ans_rule(20) \}
$BR$BR
$$A$$ = \{ans_rule(20) \}
$BR$BR
$$B$$ = \{ans_rule(20) \}
$BR EOT @ans = ( fun_cmp("tan(x/$b)", vars=>"x"), num_cmp(0), num_cmp($pi/$a));
ANS(@ans);

ENDDOCUMENT();
In reply to Dan Margalit

### Re: Help with programming a particular problem

by Davide Cervone -
Dan:

The complete problem didn't come through (because of the << that made Moodle think it was the start of an HTML tag), but I looked it up in the NPL from the tag data.

In any case, the original problem doesn't matter that much. If you are going to make a MultiAnswer problem, it has to be completely rewritten anyway. (Also, that problem uses an older approach to the text output, and should be changed anyway.)

Here is a shell for a problem that accepts P, Q, and a function and checks if the function is of the form given in your message above (depending on P and Q). You will need to write your own text for the problem, and you may want to make additional checks for values of P and Q (like Q > P) if you want those.

    loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"parserMultiAnswer.pl",
"PGcourse.pl",
);

TEXT(beginproblem);

$a = random(4,8,2);$b = random(2,5,1);

$ma = MultiAnswer(0,1,"(pi/$a) tan((pi/($a*$b))*x)")->with(
checker => sub {
my ($correct,$student,$ans) = @_; my ($P,$Q,$f) = @$student;$g = Formula("pi/(($Q-$P)*$a) * tan((pi/(($Q-$P)*$a*$b))*(x-$P))");
return $f ==$g;
}
);

BEGIN_TEXT
(a = $a, b =$b)$PAR P = \{$ma->ans_rule(5)\}$BR Q = \{$ma->ans_rule(5)\}$BR f = \{$ma->ans_rule(30)\}
END_TEXT

ANS($ma->cmp);$showPartialCorrectAnswers = 1;


See the parserMultiAnswer.pl file for more details about the options you can set for it. Note that you need to give the MultiAnswer object a correct answer, so it has something to display when students ask for correct answers.

Hope that helps.

Davide

In reply to Davide Cervone

### Re: Help with programming a particular problem

by Dan Margalit -
Thanks, Davide!

I think I have the problem working the way I want. I'll post the resulting .pg file below. I should be able to use this template in the future for similar problems.

Dan

DOCUMENT();

loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"parserMultiAnswer.pl",
"PGcourse.pl",
);

TEXT(beginproblem);

$a = random(4,8,2);$b = random(2,5,1);

$ma = MultiAnswer("(pi/$a) tan((pi/($a*$b))*x)",0,1)->with(
checker => sub {
my ($correct,$student,$ans) = @_; my ($f,$P,$Q) = @$student;$g = Formula("pi/(($Q-$P)*$a) * tan((pi/(($Q-$P)*$a*$b))*(x-$P))");
return $g ==$f;
}
);

$a = random(4,8,2);$b = random(2,5,1);
$p =$a*$b;$pi = 3.1415926535898;

BEGIN_TEXT;

The value of the limit
$\lim_{n\rightarrow\infty}\sum_{i=1}^{n} \frac{\pi}{a n} \tan\left(\frac{i \pi}{p n}\right)$

is equal to the area below the graph
of a function $$f(x)$$ on an interval $$[A,B]$$. Find
$$f$$, $$A$$, and $$B$$. (Do not evaluate the limit.)
$BR$BR
$$f(x)$$ = \{$ma->ans_rule(30) \}$BR
$BR $$A$$ = \{$ma->ans_rule(5) \}
$BR$BR
$$B$$ = \{$ma->ans_rule(5) \}$BR

END_TEXT;

ANS($ma->cmp);$showPartialCorrectAnswers = 1;

ENDDOCUMENT();
In reply to Dan Margalit

### Re: Help with programming a particular problem

by Davide Cervone -
Dan:

Looks good. Note that you don't need to set a value for $pi because you never use it. In any case, there is already a variable$PI that contains the most precise version that perl can store, and there is also a function pi that returns the same value, so there is no need ever to write it out by hand.

Davide