View of /trunk/NationalProblemLibrary/Dartmouth/setStewartCh14S3/problem_2.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('arc 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('Calculus')
   15 ## EditionText1('5')
   16 ## AuthorText1('Stewart')
   17 ## Section1('14.3')
   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 = 0;
   32 
   33 $a = random(2,10);
   34 
   35 
   36 ## Ok, we are ready to begin the problem...
   37 ##
   38 TEXT(beginproblem());
   39 
   40 
   41 BEGIN_TEXT
   42 $BR
   43 Find the arclength of the curve
   44 \(\mathbf r(t) =  \langle $a \sqrt2$SPACE t, e^{$a t}, e^{-$a t}\rangle\),
   45 \(0 \le t \le 1\)
   46 $BR
   47 \{ans_rule()\}
   48 
   49 $PAR
   50 END_TEXT
   51 
   52     ANS(num_cmp(exp($a) - exp(- $a)));
   53 
   54 ENDDOCUMENT();
   55 
   56 
   57 
   58