View of /trunk/NationalProblemLibrary/ASU-topics/setCalculus/stef13_3.pg

    1 ## DESCRIPTION
    2 ## Multivariable Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('calculus','arc length')
    6 ## Tagged by cmd6a 3/12/06
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Vector Functions')
   10 ## DBsection('Arc Length and Curvature')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('ASU')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 ## TitleText2('Calculus: Early Transcendentals')
   20 ## EditionText2('1')
   21 ## AuthorText2('Rogawski')
   22 ## Section2('13.3')
   23 ## Problem2('1 2 3 4 5 6')
   24 
   25 DOCUMENT();
   26 loadMacros("PG.pl",
   27            "PGbasicmacros.pl",
   28            "PGchoicemacros.pl",
   29            "PGanswermacros.pl",
   30            "PGauxiliaryFunctions.pl",
   31            "PGgraphmacros.pl",
   32            "Dartmouthmacros.pl");
   33 
   34 
   35 ## Do NOT show partial correct answers
   36 $showPartialCorrectAnswers = 1;
   37 
   38 ## Lots of set up goes here
   39 $b = random(2,9,1);
   40 $two_b = 2 * $b;
   41 
   42 $mult = random(2,5,1);
   43 
   44 ## Ok, we are ready to begin the problem...
   45 ##
   46 TEXT(beginproblem());
   47 
   48 
   49 BEGIN_TEXT
   50 $BR
   51 Consider the path
   52     \( \mathbf{r}(t) = ($two_b t, $b t^2, $b\ln t) \) defined for \(t > 0\).
   53 $BR
   54 Find the length of the curve between the points
   55 \( ($two_b, $b, 0)\) and \( (\{$two_b * $mult\}, \{ $b * $mult**2 \}, $b \ln($mult))\).
   56 $BR
   57     \{ans_rule(40)\}
   58 $PAR
   59 END_TEXT
   60 
   61 
   62 $ans = $b * $mult**2 + $b * ln($mult) - $b;
   63 ANS(num_cmp($ans));
   64 ENDDOCUMENT();
   65 
   66 
   67 
   68