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

    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 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.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.