View of /trunk/NationalProblemLibrary/UCSB/Stewart5_4_7/Stewart5_4_7_15.pg

    1 ## DBsubject('Calculus')
    2 ## DBchapter('Applications of Differentiation')
    3 ## DBsection('Optimization Problems')
    4 ## KEYWORDS('Optimization','Differentiation')
    5 ## TitleText1('Calculus: Early Transcendentals')
    6 ## EditionText1('5')
    7 ## AuthorText1('Stewart')
    8 ## Section1('4.7')
    9 ## Problem1('15')
   10 ## Author('')
   11 ## Institution('UCSB')
   12 
   13 DOCUMENT();
   14 
   15 loadMacros(
   16 "PG.pl",
   17 "PGbasicmacros.pl",
   18 "PGchoicemacros.pl",
   19 "PGanswermacros.pl",
   20 "PGauxiliaryFunctions.pl"
   21 );
   22 
   23 TEXT(&beginproblem);
   24 $showPartialCorrectAnswers = 1;
   25 $a=random(1,10,1);
   26 $b=random(1,10,1);
   27 #$c=2*$b*$a*$a*$a/15;
   28 #while ($b==$a) $b=random(1,10,1);
   29 #$c=random(1,10,1)*random(-1,1,2);
   30 
   31 # Insert problem text between the $PAR, and space for the
   32 # answer, like this   \(y =\) \{ans_rule(50)\}
   33 # just before the END_TEXT.
   34 
   35 BEGIN_TEXT
   36 
   37 $PAR
   38 
   39 Find the point on the line \(y=$a x+$b\) that is closest to the origin.
   40 
   41 $PAR
   42 
   43 x = \{ans_rule(20)\}
   44 
   45 $PAR
   46 
   47 y = \{ans_rule(20)\}
   48 
   49 END_TEXT
   50 
   51 ANS(num_cmp(-2*$a*$b/(2*$a*$a+2)));
   52 ANS(num_cmp($a*2*$a*$b/(-2*$a*$a-2)+$b));
   53 
   54 
   55 ENDDOCUMENT();