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

Sat Sep 8 05:17:01 2007 UTC (5 years, 9 months ago) by sh002i
File size: 1564 byte(s)
```Added tags for Rogawski's "Calculus: Early Transcendentals".
```

```    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();
27            "PGbasicmacros.pl",
28            "PGchoicemacros.pl",
30            "PGauxiliaryFunctions.pl",
31            "PGgraphmacros.pl",
32            "Dartmouthmacros.pl");
33
34
35 ## Do NOT show partial correct answers
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
```