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    1 ## DBsubject('Calculus')
    2 ## DBchapter('Introduction to Differential Equations')
    3 ## DBsection('Parametric Equations')
    4 ## KEYWORDS('calculus', 'parametric', 'parametric equations')
    5 ## TitleText1('Calculus: Early Transcendentals')
    6 ## EditionText1('2')
    7 ## AuthorText1('Rogawski')
    8 ## Section1('11.1')
    9 ## Problem1('13')
   10 ## Author('Christopher Sira')
   11 ## Institution('W.H.Freeman')
   12 
   13 DOCUMENT();
   14 loadMacros("PG.pl","PGbasicmacros.pl","PGanswermacros.pl");
   15 loadMacros("Parser.pl");
   16 loadMacros("freemanMacros.pl");
   17 
   18 $context = Context("Point");
   19 $context->variables->add(t=>'Real');
   20 #$context->variables->add(x=>'Real');
   21 Context()->flags->set(reduceConstants=>0);
   22 Context()->flags->set(reduceConstantFunctions=>0);
   23 
   24 $a = Real(random(2, 8, 1));
   25 $b = Real(random(1, 10, 1));
   26 
   27 $xform = Formula("ln($a * t)")->reduce;
   28 $txform = Formula("(e**x)/$a")->reduce;
   29 
   30 $yform = Formula("$b - t")->reduce;
   31 
   32 $ans = $yform->substitute(t=>$txform)->reduce();
   33 
   34 
   35 Context()->texStrings;
   36 BEGIN_TEXT
   37 \{ beginproblem() \}
   38 \{ textbook_ref_exact("Rogawski ET 2e", "11.1","13") \}
   39 $PAR
   40 Express \( x = $xform \), \( y = $yform \) in the form \( y = f(x) \) by eliminating the parameter.
   41 $PAR
   42 y = \{ans_rule()\}
   43 END_TEXT
   44 Context()->normalStrings;
   45 
   46 ANS($ans->cmp);
   47 
   48 Context()->texStrings;
   49 SOLUTION(EV3(<<'END_SOLUTION'));
   50 $PAR
   51 $SOL
   52 We eliminate the parameter.  Since \( x = $xform \), we have \( t = $txform \).  Substituting into \( y = $yform \) we obtain
   53 $PAR
   54 \( y = $ans \)
   55 END_SOLUTION
   56 
   57 ENDDOCUMENT();