View of /trunk/webwork2/doc/parser/problems/sample03.pg

    1 ###########################################################
    2 #
    3 #  Example showing how to use the Parser's differentiation
    4 #  capabilities.
    5 #
    6 
    7 DOCUMENT();        # This should be the first executable line in the problem.
    8 
    9 loadMacros(
   10   "PGbasicmacros.pl",
   11   "PGanswermacros.pl",
   12   "Parser.pl",
   13   "Differentiation.pl",
   14 );
   15 
   16 TEXT(beginproblem());
   17 
   18 ###########################################################
   19 #
   20 #   Use standard numeric mode
   21 #
   22 Context('Numeric');
   23 $x = Formula('x');  # used to construct formulas below.
   24 
   25 #
   26 #   Define a function and its derivative and make them pretty
   27 #
   28 $a = random(1,8,1);
   29 $b = random(-8,8,1);
   30 $c = random(-8,8,1);
   31 
   32 $f = ($a*$x**2 + $b*$x + $c) -> reduce;
   33 $df = $f->D('x');
   34 
   35 $x = random(-8,8,1);
   36 
   37 ###########################################################
   38 #
   39 #  The problem text
   40 #
   41 BEGIN_TEXT
   42 
   43 Suppose \( f(x) = \{$f->TeX\}\).
   44 $PAR
   45 Then \(f'(x)=\) \{ans_rule(20)\},$BR
   46 and \(f'($x)=\) \{ans_rule(20)\}.
   47 $PAR
   48 (Same as previous problem, but using the formal differentiation package.
   49 Note that automatic differentiation does not always produce the simples form.)
   50 
   51 END_TEXT
   52 
   53 ###########################################################
   54 #
   55 #  The answers
   56 #
   57 ANS(fun_cmp($df->string));
   58 ANS(num_cmp($df->eval(x=>$x)));
   59 $showPartialCorrectAnswers = 1;
   60 
   61 ###########################################################
   62 
   63 ENDDOCUMENT();        # This should be the last executable line in the problem.