[rochester] / trunk / rochester_problib / setLinearAlgebra9Dependence / ur_la_9_5.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

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

Wed Jun 4 19:10:29 2003 UTC (9 years, 11 months ago) by voloshin
File size: 2309 byte(s)
minor changes

1 ## DESCRIPTION
2 ## KEYWORDS('functions', 'dependent', 'independent')
3 ##
4 ## ENDDESCRIPTION
5
6
7 DOCUMENT();        # This should be the first executable line in the problem.
9         "PGbasicmacros.pl",
10         "PGchoicemacros.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();