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# View of /trunk/NationalProblemLibrary/Dartmouth/setMTWCh4S2/problem_1.pg

Sat Jun 3 14:39:59 2006 UTC (6 years, 11 months ago) by gage
File size: 1326 byte(s)
 Cleaned problem code using convert-functions.pl


    1 ## DESCRIPTION
2 ## Calculus
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('curve' 'length')
6 ## Tagged by tda2d
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Vector Valued Functions')
10 ## DBsection('Arc Length')
11 ## Date('')
12 ## Author('')
13 ## Institution('Dartmouth')
14 ## TitleText1('Basic Multivariable Calculus')
15 ## EditionText1('')
16 ## AuthorText1('Marsden, Tromba, and Weinstein')
17 ## Section1('4.2')
18 ## Problem1('')
19
20 DOCUMENT();
22            "PGbasicmacros.pl",
23            "PGchoicemacros.pl",
25            "PGauxiliaryFunctions.pl",
26            "PGgraphmacros.pl",
27            "Dartmouthmacros.pl");
28
29
30 ## Do NOT show partial correct answers
31 $showPartialCorrectAnswers = 1; 32 33 ## Lots of set up goes here 34$a = non_zero_random( -5, 5, 1 );
35 $a_t = clean_scalar_string($a, "t");
36 $b = non_zero_random( -5, 5, 1 ); 37$b_sin_t = clean_scalar_string($b, "\sin t"); 38$b_cos_t = clean_scalar_string($b, "\cos t"); 39$c = random( -5, -1, 1 );
40 $d = random( 1, 5, 1 ); 41 42 43 ## Ok, we are ready to begin the problem... 44 ## 45 TEXT(beginproblem()); 46 47 48 49 BEGIN_TEXT 50$BR
51 Find the length of the given curve:
52 $BR 53 54 $$\mathbf{r} \left( t \right) = \left( a_t, b_sin_t, b_cos_t 55 \right)$$ where $$c \leq t \leq d$$.$PAR
56
57 \{ans_rule(10)\}
58
59 END_TEXT
60
61
62 $ans = ($d - $c) * sqrt($a**2 + $b**2 ); 63 ANS(num_cmp($ans));
64
65 ENDDOCUMENT();
66
67
68
69