View of /trunk/NationalProblemLibrary/ASU-topics/setCalculus/stef14_4p1.pg

    1 ## DESCRIPTION
    2 ## Multivariable Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('calculus','partial derivative')
    6 ## Tagged by cmd6a 3/12/06
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Partial Derivatives')
   10 ## DBsection('Tangent Planes')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('ASU')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 ## TitleText2('Calculus: Early Transcendentals')
   20 ## EditionText2('1')
   21 ## AuthorText2('Rogawski')
   22 ## Section2('14.4')
   23 ## Problem2('31')
   24 
   25 DOCUMENT();
   26 loadMacros("PG.pl",
   27            "PGbasicmacros.pl",
   28            "PGchoicemacros.pl",
   29            "PGanswermacros.pl",
   30            "PGauxiliaryFunctions.pl",
   31            "PGgraphmacros.pl",
   32            "Dartmouthmacros.pl");
   33 
   34 
   35 ## Do NOT show partial correct answers
   36 $showPartialCorrectAnswers = 0;
   37 
   38 $a = random(-9,9);
   39 $b = random(-9,9);
   40 
   41 $c = non_zero_random(-5,5);
   42 $d = non_zero_random(-5,5);
   43 $e = random(-9,9);
   44 
   45 ## Ok, we are ready to begin the problem...
   46 ##
   47 TEXT(beginproblem());
   48 
   49 
   50 BEGIN_TEXT
   51 $BR
   52 
   53 Suppose that \(f(x,y)\) is a smooth function and that its partial
   54 derivatives have the values, \(f_x($a, $b) = $c \) and \(f_y($a, $b) =
   55 $d\).  Given that \(f($a, $b) = $e \), use this information to estimate
   56 the following values: $BR
   57 Estimate of  (integer value) \(f(\{$a\}, \{$b+1\})\) \{ans_rule()\} $BR
   58 Estimate of  (integer value) \(f(\{$a+1\}, \{$b\})\) \{ans_rule()\} $BR
   59 Estimate of  (integer value) \(f(\{$a+1\}, \{$b+1\})\) \{ans_rule()\}
   60 
   61 $PAR
   62 END_TEXT
   63 
   64 ANS(num_cmp($e + $d));
   65 ANS(num_cmp($e + $c));
   66 ANS(num_cmp($e + $c + $d));
   67 
   68 ENDDOCUMENT();
   69 
   70 
   71 
   72