View of /trunk/NationalProblemLibrary/Dartmouth/setMTWCh2S6/problem_2.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('tangent' 'slope')
    6 ## Tagged by tda2d
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Partial Derivatives')
   10 ## DBsection('Directional Derivatives and the Gradient Vector')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Dartmouth')
   14 ## TitleText1('Basic Multivariable Calculus')
   15 ## EditionText1('3')
   16 ## AuthorText1('Marsden, Tromba, Weinstein')
   17 ## Section1('2.6')
   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 = 1;
   32 
   33 ## Lots of set up goes here
   34 $x1 = random(1,8,1);
   35 $y1 = random(1,8,1);
   36 
   37 $a = random(1,4,1);
   38 $a_x = clean_scalar_string($a, "x");
   39 
   40 $b = random(1,4,1);
   41 $b_y = clean_scalar_string($b, "y");
   42 
   43 $c = random(1,4,1);
   44 $c_xy = clean_scalar_string($c, "xy");
   45 
   46 #$d = sqrt($a*$x1+$b*$y1) + sqrt($c*$x1*$y1);
   47 
   48 $num = $a/(2*sqrt($a*$x1 + $b*$y1) ) + $c*$y1/(2*sqrt($c*$x1*$y1) );
   49 $denom = $b/(2*sqrt($a*$x1+$b*$y1) ) + $c*$x1/(2*sqrt($c*$x1*$y1) );
   50 
   51 $yp = - $num/$denom;
   52 
   53 #
   54 ## Ok, we are ready to begin the problem...
   55 ##
   56 TEXT(beginproblem());
   57 
   58 
   59 BEGIN_TEXT
   60 $BR
   61 Find the slope of the tangent line to the curve
   62 $BR
   63 \(\displaystyle \sqrt{$a_x +$b_y}  + \sqrt{$c_xy} =
   64     \sqrt{\{$a*$x1+$b*$y1\}} + \sqrt{\{$c*$x1*$y1\}} \)
   65 at the point \( ( $x1,$y1 ) \). $BR
   66 
   67 The slope is \{ ans_rule(70) \}.
   68 
   69 END_TEXT
   70 
   71 ANS(num_cmp($yp));
   72 ENDDOCUMENT();
   73 
   74 
   75 
   76