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# View of /branches/UGA/5.2.4.pg

Sat Jul 24 17:09:50 2010 UTC (2 years, 10 months ago) by ted shifrin
File size: 1785 byte(s)
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    1 ## DESCRIPTION
2 ##   Max/min problems
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('Critical', 'Point', 'Partial', 'Multivariable')
6 ## Tagged by nhamblet
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Partial Derivatives')
10 ## DBsection('Maximum and Minimum Values')
11 ## Date('October 29, 2009')
12 ## Author('Shifrin')
13 ## Institution('UGA')
14 ## TitleText1('')
15 ## EditionText1('')
16 ## AuthorText1('')
17 ## Section1('')
18 ## Problem1('')
19
20 DOCUMENT();        # This should be the first executable line in the problem.
21
23   "PGstandard.pl",
24   "PGunion.pl",
25   "Parser.pl",
26   "parserVectorUtils.pl",
27   "PGcourse.pl"
28 );
29
30
31 TEXT(beginproblem());
32 BEGIN_PROBLEM();
33
34 ##############################################
35 #  Setup
36
37 Context("Vector");
38
39 $a = random(1,4); 40 do{$b = non_zero_random(-3,3)} until ($b!=1); 41 do{$c = non_zero_random(-4,4)} until ($c**2<4*$a);
42
43 $f = Formula("x^2 +$b y^2 + $c x")->reduce; 44$arg = '\left(\begin{array}{c} x\\y \end{array}\right)';
45
46
47 $max = max($c**2/(4*($b-1))+$a*$b,$a+sqrt($a)*$c, $a-sqrt($a)*$c, -$c**2/4);
48 $min = min($c**2/(4*($b-1))+$a*$b,$a+sqrt($a)*$c, $a-sqrt($a)*$c, -$c**2/4);
49
50
51 ##############################################
52 #  Main text
53
54 Context()->texStrings;
55 BEGIN_TEXT
56
57 The temperature of the circular plate $$D = \left\{"\{"\} arg: x^2+y^2 \le a \right\}$$ is given by the function $$f arg=f$$. Find the maximum and minimum temperatures of $$D$$.
58
59 $PAR 60 maximum temperature = \{ans_rule(10)\} 61$PAR
62 minimum temperature = \{ans_rule(10)\}
63
64 $PAR 65 66 END_TEXT 67 Context()->normalStrings; 68 69 ################################################## 70 # Answers 71 72 ANS(num_cmp($max));
73 ANS(num_cmp($min)); 74 75$showPartialCorrectAnswers = 1;
76
77 ##################################################
78
79 END_PROBLEM();
80 ENDDOCUMENT();        # This should be the last executable line in the problem.