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

    1 ##DESCRIPTION
    2 #
    3 # File Created: 5/30/2000
    4 # Last Modified: 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 
   16 loadMacros(
   17 "PG.pl",
   18 "PGbasicmacros.pl",
   19 "PGchoicemacros.pl",
   20 "PGanswermacros.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.