View of /trunk/NationalProblemLibrary/Dartmouth/setMTWCh4S2/problem_1.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('curve' 'length')
    6 ## Tagged by tda2d
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Vector Functions')
   10 ## DBsection('Arc Length and Curvature')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Dartmouth')
   14 ## TitleText1('Basic Multivariable Calculus')
   15 ## EditionText1('3')
   16 ## AuthorText1('Marsden, Tromba, Weinstein')
   17 ## Section1('4.2')
   18 ## Problem1('')
   19 
   20 DOCUMENT();
   21 loadMacros("PG.pl",
   22            "PGbasicmacros.pl",
   23            "PGchoicemacros.pl",
   24            "PGanswermacros.pl",
   25            "PGauxiliaryFunctions.pl",
   26            "PGgraphmacros.pl",
   27            "Dartmouthmacros.pl");
   28 
   29 
   30 ## Do NOT show partial correct answers
   31 $showPartialCorrectAnswers = 1;
   32 
   33 ## Lots of set up goes here
   34 $a = non_zero_random( -5, 5, 1 );
   35 $a_t = clean_scalar_string($a, "t");
   36 $b = non_zero_random( -5, 5, 1 );
   37 $b_sin_t = clean_scalar_string($b, "\sin t");
   38 $b_cos_t = clean_scalar_string($b, "\cos t");
   39 $c = random( -5, -1, 1 );
   40 $d = random( 1, 5, 1 );
   41 
   42 
   43 ## Ok, we are ready to begin the problem...
   44 ##
   45 TEXT(beginproblem());
   46 
   47 
   48 
   49 BEGIN_TEXT
   50 $BR
   51 Find the length of the given curve:
   52 $BR
   53 
   54 \(\mathbf{r} \left( t \right) = \left( $a_t, $b_sin_t, $b_cos_t
   55 \right) \) where \($c \leq t \leq $d \).  $PAR
   56 
   57 \{ans_rule(10)\}
   58 
   59 END_TEXT
   60 
   61 
   62 $ans = ($d - $c) * sqrt( $a**2 + $b**2 );
   63 ANS(num_cmp($ans));
   64 
   65 ENDDOCUMENT();
   66 
   67 
   68 
   69