View of /trunk/NationalProblemLibrary/ma122DB/set5/s3_6_5.pg

    1 ##DESCRIPTION
    2 ##  Find a derivative of y at a point using implicit differentiation
    3 ##ENDDESCRIPTION
    4 ##KEYWORDS('derivatives', 'implicit')
    5 
    6 ## Shotwell cleaned
    7 ## tcao , PAID on 11-24-2003
    8 
    9 ## DBsubject('Calculus')
   10 ## DBchapter('Differentiation Rules')
   11 ## DBsection('Implicit Differentiation')
   12 ## Date('6/3/2002')
   13 ## Author('')
   14 ## Institution('')
   15 ## TitleText1('Calculus Early Transcendentals')
   16 ## EditionText1('4')
   17 ## AuthorText1('Stewart')
   18 ## Section1('3.6')
   19 ## Problem1('1')
   20 
   21 DOCUMENT();        # This should be the first executable line in the problem.
   22 
   23 loadMacros(
   24 "PGbasicmacros.pl",
   25 "PGanswermacros.pl",
   26 "PGauxiliaryFunctions.pl"
   27 );
   28 
   29 TEXT(beginproblem());
   30 $showPartialCorrectAnswers = 0;
   31 
   32 $a1 = random(2,5,1);
   33 $b1 = random(2,5,1);
   34 $c1 = random(1,4,5);
   35 $x1 = random(1,5,1);
   36 $c2 = $c1*$x1;
   37 $y1 = $c1-$a1*$x1-$b1;
   38 $deriv1 = "-((2*$a1*$x1+$b1+$y1)/$x1)";
   39 
   40 BEGIN_TEXT
   41 Let \( $a1 x^2+ $b1 x + xy = $c2  \) and \( y( $x1 ) = $y1 \). Find
   42 \( y'( $x1 ) \) by implicit differentiation.
   43 $BR $BR Answer: \{ans_rule(30) \}
   44 $BR
   45 END_TEXT
   46 
   47 ANS(num_cmp($deriv1));
   48 ENDDOCUMENT();        # This should be the last executable line in the problem.
   49