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# View of /trunk/NationalProblemLibrary/272/setStewart16_2/UR_VC_11_10.pg

Wed Jul 18 15:40:35 2007 UTC (5 years, 10 months ago) by jjholt
File size: 1520 byte(s)
Added Stew6e tags.


    1 ## DESCRIPTION
2 ##   Line Integral over Vector Field
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('Vector Fields', 'Line Integral', 'Tangent', 'Normal', 'Binormal')
6 ## Tagged by nhamblet
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Vector Calculus')
10 ## DBsection('Line Integrals')
11 ## Date('6/5/2000')
12 ## Author('Joseph Neisendorfer')
13 ## Institution('University of Rochester')
14 ## TitleText1('Calculus: Early Transcendentals')
15 ## EditionText1('5')
16 ## AuthorText1('Stewart')
17 ## Section1('16.2')
18 ## Problem1('')
19
20 ## TitleText2('Calculus: Early Transcendentals')
21 ## EditionText2('6')
22 ## AuthorText2('Stewart')
23 ## Section2('16.2')
24 ## Problem2('')
25
26 DOCUMENT();
27
29 "PG.pl",
30 "PGbasicmacros.pl",
31 "PGchoicemacros.pl",
33 "PGauxiliaryFunctions.pl"
34 );
35
36 TEXT(beginproblem());
37 $showPartialCorrectAnswers = 1; 38 39$a = random(1, 7);
40 $b = random(1, 7); 41$ba = $b+$a;
42
43 BEGIN_TEXT
44 $PAR 45 A curve C is given by a vector function $$\mathbf{r}(t), a \leq t \leq ba$$, 46 with unit tangent $$\mathbf{T}(t)$$, unit normal $$\mathbf{N}(t)$$, and unit 47 binormal $$\mathbf{B}(t)$$. Indicate whether the following line integrals are 48 positive, negative, or zero by typing P, N, or Z as appropriate: 49$PAR
50 A. $$\displaystyle \int_C \mathbf T \cdot \, d\mathbf r =$$ \{ ans_rule(10) \}
51 $PAR 52 B. $$\displaystyle \int_C \mathbf N \cdot \, d\mathbf r =$$ \{ ans_rule(10) \} 53$PAR
54 C. $$\displaystyle \int_C \mathbf B \cdot \, d\mathbf r =$$ \{ ans_rule(10) \}
55 END_TEXT
56 ANS(str_cmp('p'));
57 ANS(str_cmp('z'));
58 ANS(str_cmp('z'));
59
60 ENDDOCUMENT();