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# View of /trunk/NationalProblemLibrary/Union/setMVderivatives/an14_6_1.pg

Thu Jun 1 18:19:46 2006 UTC (6 years, 11 months ago) by jj
File size: 1334 byte(s)
```New files.
```

```    1 DOCUMENT();        # This should be the first executable line in the problem.
2
4   "PGstandard.pl",
5   "PGunion.pl",
6   "Parser.pl",
7   "parserVectorUtils.pl",
8   "PGcourse.pl"
9 );
10
11
12 TEXT(beginproblem());
13 BEGIN_PROBLEM();
14
15 ##############################################
16 #  Setup
17
18 Context("Vector")->flags->set(
19   reduceConstants => 0,
20   reduceConstantFunctions => 0,
21 );
22
23 #
24 #  The function
25 #
26 \$a = random(1,5,1);
27 \$b = random(2,5,1);
28
29 \$f = Formula("(\$a + \$b x y)^(3/2)");
30
31 #
32 #  The point
33 #
34 (\$x,\$y) = (random(1,5,1),random(1,5,1));
35
36 #
37 #  The unit vector
38 #
39 \$u = non_zero_vector2D(-2,2);
40 \$d = (\$u.\$u); \$U = \$u->TeX."/".Formula("sqrt(\$d)")->TeX;
41
42 #
43 #  The derivatives
44 #
45 \$fx = \$f->D('x');
46 \$fy = \$f->D('y');
47
49 \$Duf = \$gradf->eval(x=>\$x,y=>\$y) . unit(\$u);
50
51 ##############################################
52 #  Main text
53
54 \$uu = BoldMath('u');
55
56 Context()->texStrings;
57 BEGIN_TEXT
58
59 Let \(f(x,y) = \$f\).
60 Then \(\$GRAD\!f\) = \{ans_rule(50)\}, and \(D_{\$uu} f(\$x,\$y)\) for
61 \(\$uu = \$U\) is \{ans_rule(30)\}.
62
63 END_TEXT
64 Context()->normalStrings;
65
66 ##################################################
68
69 ANS(