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# View of /trunk/NationalProblemLibrary/Rochester/setVecFunction1Curves/urvc_3_14.pg

Thu Jul 19 14:16:05 2007 UTC (5 years, 10 months ago) by jjholt
File size: 1596 byte(s)
Updated tags.


    1 ## DESCRIPTION
2 ## Calculus
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('vector' 'integral' 'derivative')
6 ## Tagged by tda2d
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Vector Functions')
10 ## DBsection('Derivatives and Integrals of Vector Functions')
11 ## Date('')
12 ## Author('')
13 ## Institution('Rochester')
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 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.pl",
27 "PGauxiliaryFunctions.pl"
28 );
29
30 TEXT(beginproblem());
31 $showPartialCorrectAnswers = 1; 32 33$a1 = non_zero_random(-5,5,1);
34 $b1 = random(-5,5,1); 35$b2 = 2*$b1; 36$pi = arccos(-1);
37
38
39 BEGIN_TEXT
40
41
42
43  If
44  $$\mathbf{r}(t)= \cos(a1 t)\mathbf{i}+\sin( a1 t)\mathbf{j}+b2 t 45 \mathbf{k}$$ $BR 46 compute $$\mathbf{r}'(t)$$= \{ans_rule(15)\} $$\mathbf{i}+$$ 47 \{ans_rule(15)\}$$\mathbf{j}+$$ \{ans_rule(15)\} $${\mathbf{k}}$$$BR
48
49  and $$\int{\mathbf{r}}(t)\, dt$$= \{ans_rule(15)\} $$\mathbf{i}+$$
50  \{ans_rule(15)\}$$\mathbf{j}+$$ \{ans_rule(15)\} $$\mathbf{k}$$
51  $BR 52 END_TEXT 53 54 55$ans0 =  "- $a1*sin($a1*t)";
56 $ans1 = "$a1*cos($a1*t)"; 57$ans2 =   "2*$b1"; 58$ans3 =   "(1/$a1)*sin($a1*t)";
59 $ans4 = "(-1/$a1)*cos($a1*t)"; 60$ans5 =  "$b1*t*t"; 61 62 63 ANS(fun_cmp($ans0, vars=>"t"));
64 ANS(fun_cmp($ans1, vars=>"t")); 65 ANS(fun_cmp($ans2, vars=>"t"));
66 ANS(fun_cmp($ans3, mode=>"antider", vars=>"t")); 67 ANS(fun_cmp($ans4, mode=>"antider", vars=>"t"));
68 ANS(fun_cmp(\$ans5, mode=>"antider", vars=>"t"));
69
70 ENDDOCUMENT();        # This should be the last executable line in the problem.


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