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

Sun Mar 26 04:58:01 2006 UTC (7 years, 1 month ago) by jj
File size: 1520 byte(s)
Initial import


    1 ##DESCRIPTION
2 #
3 # File Created: 5/30/2000
5 # Problem Author: Joseph Neisendorfer
6 # WeBWorK Entry: Eva Culakova
7 # Location: University of Rochester
8 # derivative and integral of a vector function
9 #
10 ##ENDDESCRIPTION
11
12 #KEYWORDS('derivative','vector function','parametric','integral')
13
14 DOCUMENT();        # This should be the first executable line in the problem.
15
17 "PG.pl",
18 "PGbasicmacros.pl",
19 "PGchoicemacros.pl",
21 "PGauxiliaryFunctions.pl"
22 );
23
24 TEXT(beginproblem());
25 $showPartialCorrectAnswers = 1; 26 27$a1 = non_zero_random(-5,5,1);
28 $b1 = random(-5,5,1); 29$b2 = 2*$b1; 30$pi = arccos(-1);
31
32
33 BEGIN_TEXT
34
35
36
37  If
38  $$\mathbf{r}(t)= \cos(a1 t)\mathbf{i}+\sin( a1 t)\mathbf{j}+b2 t 39 \mathbf{k}$$ $BR 40 compute $$\mathbf{r}'(t)$$= \{ans_rule(15)\} $$\mathbf{i}+$$ 41 \{ans_rule(15)\}$$\mathbf{j}+$$ \{ans_rule(15)\} $${\bf{k}}$$$BR
42
43  and $$\int{\bf{r}}(t)\, dt$$= \{ans_rule(15)\} $$\mathbf{i}+$$
44  \{ans_rule(15)\}$$\mathbf{j}+$$ \{ans_rule(15)\} $$\mathbf{k}$$
45  $BR 46 END_TEXT 47 48 49$ans0 =  "- $a1*sin($a1*t)";
50 $ans1 = "$a1*cos($a1*t)"; 51$ans2 =   "2*$b1"; 52$ans3 =   "(1/$a1)*sin($a1*t)";
53 $ans4 = "(-1/$a1)*cos($a1*t)"; 54$ans5 =  "$b1*t*t"; 55 56 57 ANS(fun_cmp($ans0, vars=>"t"));
58 ANS(fun_cmp($ans1, vars=>"t")); 59 ANS(fun_cmp($ans2, vars=>"t"));
60 ANS(fun_cmp($ans3, mode=>"antider", vars=>"t")); 61 ANS(fun_cmp($ans4, mode=>"antider", vars=>"t"));
62 ANS(fun_cmp(\$ans5, mode=>"antider", vars=>"t"));
63
64 ENDDOCUMENT();        # This should be the last executable line in the problem.