View of /branches/UGA/2.2.5.pg

    1 ## DESCRIPTION
    2 ##   Recursive Sequence
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Convergent Sequence')
    6 ##
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('')
   10 ## DBsection('')
   11 ## Date('8/22/2009')
   12 ## Author('Ted Shifrin')
   13 ## Institution('UGA')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT(); # This should be the first executable line in the problem.
   21 
   22 loadMacros("PG.pl",
   23            "PGbasicmacros.pl",
   24            "PGchoicemacros.pl",
   25            "PGanswermacros.pl",
   26            "PGauxiliaryFunctions.pl"
   27           );
   28 
   29 TEXT(beginproblem());
   30 $showPartialCorrectAnswers = 1;
   31 
   32 $a = random(1, 10, 1);
   33 $b = random(1,10,1);
   34 $x0 = random (1,20,1);
   35 
   36 $ans = ($a+sqrt($a**2+4*$b))/2;
   37 
   38 BEGIN_TEXT
   39 Given \(x_0=$x0\) and the recursive formula \(x_k = $a + \dfrac{$b}{x_{k-1}}\), assuming the sequence \( (x_k) \) converges, find its limit. $BR
   40 \{ans_rule(10)\} $BR
   41 END_TEXT
   42 
   43 ANS(num_cmp($ans));
   44 
   45 
   46 ENDDOCUMENT();  # This should be the last executable line in the problem.