View of /trunk/NationalProblemLibrary/UVA-Stew5e/setUVA-Stew5e-C03S11-LinApprox/3-11-24.pg

    1 ## DESCRIPTION
    2 ##  Calculus: Linear Approximations and Differentials
    3 ## ENDDESCRIPTION
    4 
    5 ##KEYWORDS('derivatives', 'linear approximation')
    6 ## Tagged by YL
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Differentiation')
   10 ## DBsection('Linear Approximation and Differentials')
   11 ## Date('5/29/2005')
   12 ## Author('Jeff Holt')
   13 ## Institution('UVA')
   14 ## TitleText1('Calculus: Early Transcendentals')
   15 ## EditionText1('5')
   16 ## AuthorText1('Stewart')
   17 ## Section1('3.11')
   18 ## Problem1('24')
   19 
   20 ## TitleText2('Calculus: Early Transcendentals')
   21 ## EditionText2('6')
   22 ## AuthorText2('Stewart')
   23 ## Section2('3.10')
   24 ## Problem2('')
   25 
   26 DOCUMENT();        # This should be the first executable line in the problem.
   27 
   28 loadMacros(
   29 "PG.pl",
   30 "PGbasicmacros.pl",
   31 "PGchoicemacros.pl",
   32 "PGanswermacros.pl",
   33 "PGauxiliaryFunctions.pl"
   34 );
   35 
   36 TEXT(beginproblem());
   37 $showPartialCorrectAnswers = 1;
   38 
   39 $a = random(5,8,1);
   40 $x1 = random(1,4,1);
   41 $d1 = random(.1,.5,.1);
   42 $d2 = random(.01,.05,.01);
   43 $deriv1 = ((-1/2)*($a - $x1)**(-1/2));
   44 TEXT(EV2(<<EOT));
   45 Let \( y = \sqrt{$a - x}  \). $BR
   46 Find the differential \( dy \)
   47 when \( x= $x1 \) and \( dx = $d1 \)
   48 \{ans_rule(20) \}
   49 $BR
   50 EOT
   51 
   52 $ans = $deriv1*$d1;
   53 ANS(num_cmp($ans));
   54 TEXT(EV2(<<EOT));
   55 Find the differential \( dy \)
   56 when \( x= $x1 \) and \( dx = $d2 \)
   57 \{ans_rule(20) \}
   58 EOT
   59 
   60 $ans = $deriv1*$d2;
   61 ANS(num_cmp($ans));
   62 ENDDOCUMENT();        # This should be the last executable line in the problem.