View of /trunk/rochester_problib/setLinearAlgebra9Dependence/ur_la_9_5.pg

    1 ## DESCRIPTION
    2 ## KEYWORDS('functions', 'dependent', 'independent')
    3 ##
    4 ## ENDDESCRIPTION
    5 
    6 
    7 DOCUMENT();        # This should be the first executable line in the problem.
    8 loadMacros(
    9         "PGbasicmacros.pl",
   10         "PGchoicemacros.pl",
   11         "PGanswermacros.pl",
   12         "PGgraphmacros.pl",
   13         "PGmatrixmacros.pl"
   14         );
   15 
   16 TEXT(beginproblem());
   17 # Do not show which answers are incorrect.
   18 $showPartialCorrectAnswers = 0;
   19 
   20 $a = random(2,5,1);
   21 
   22 # Make a new checkbox multiple choice
   23 $tf = new_pop_up_select_list();
   24 $tf->ra_pop_up_list(["?"=>"NO_ANSWER", "Linearly independent" => "Linearly independent",
   25                         "Linearly dependent" => "Linearly dependent"]);
   26 # $cmc now "contains" the checkbox multiple choice object.
   27 
   28 # Insert some  questions and matching answers in the q/a list
   29 $b=7*$a;
   30 $c=2*$a;
   31 $tf -> qa ( "\( f(t) = ${a}t^2+${b}t \quad,\quad g(t)=${a}t^2-${b}t\)",
   32                         "Linearly independent",
   33                  "\(f(\theta) = \cos(3\theta) \quad,\quad g(\theta)=$a\cos^3(\theta)-${c}\cos(\theta) \)",
   34                         "Linearly dependent",
   35                  "\(f(\theta) = \cos(3\theta)\quad,\quad g(\theta)=$a\cos^3(\theta)-$a\cos(\theta) \)",
   36                         "Linearly independent",
   37                  "\(f(t)=e^{\lambda t}\cos(\mu t)\quad,\quad g(t)=e^{\lambda t}\sin(\mu t)\quad,\mu\ne 0 \)",
   38                         "Linearly independent",
   39                  "\(f(x)=e^{${a}x}\quad, \quad g(x) = e^{${a}(x-3)} \)",
   40                         "Linearly dependent",
   41                  "\(f(x) = x^3\quad , \quad g(x)=|x|^3\)",
   42                         "Linearly independent",
   43                  "\(f(x) = x^2\quad, \quad g(x) = 4|x|^2\)",
   44                         "Linearly dependent",
   45                  "\(f(t) = 3t \quad, \quad g(t) = |t|\)",
   46                         "Linearly independent",
   47 
   48 
   49 
   50 );
   51 
   52 $tf->choose(4);
   53 
   54 # Insert some incorrect answers
   55 
   56 # Print the text using $mc->print_q for the questions and
   57 # $mc->print_a to print the answers.
   58 BEGIN_TEXT
   59 
   60 Determine which of the following pairs of functions are linearly independent.
   61 
   62 $BR
   63 
   64  \{ $tf -> print_q \}
   65 
   66 END_TEXT
   67 
   68 # Enter the correct answers to be checked against the answers to the students.
   69 ANS( str_cmp( $tf->ra_correct_ans )   ) ;
   70 
   71 ENDDOCUMENT();