View of /trunk/NationalProblemLibrary/UMN/calculusStewartCCC/s_11_6_1.pg

    1 #DESCRIPTION
    2 ##  Calculus: Absolute convergence and the ratio and root tests
    3 ##ENDDESCRIPTION
    4 
    5 ##KEYWORDS('calculus', 'series', 'ratio test')
    6 
    7 ## DBsubject('Calculus')
    8 ## DBchapter('Infinite Sequences and Series')
    9 ## DBsection('Absolute Convergence and the Ratio and Root Tests')
   10 ## Date('04/07/2010')
   11 ## Author('Justin Sukiennik')
   12 ## Institution('University of Minnesota')
   13 ## TitleText1('Calculus: Concepts and Contexts')
   14 ## EditionText1('4 Custom UMTYMP Ed.')
   15 ## AuthorText1('Stewart')
   16 ## Section1('11.6')
   17 ## Problem1('1')
   18 
   19 #####################################################################
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23   "PGstandard.pl",
   24   "MathObjects.pl",
   25   "PGunion.pl",
   26   "parserPopUp.pl",
   27   "PGchoicemacros.pl",
   28   "PGcourse.pl",
   29 );
   30 
   31 #####################################################################
   32 install_problem_grader(~~&std_problem_grader);
   33 
   34 TEXT(beginproblem());
   35 
   36 $showPartialCorrectAnswers = 0;
   37 
   38 #####################################################################
   39 
   40 
   41 Context("Numeric");
   42 
   43 $a = list_random(2,4,5,10,20);
   44 
   45 $b = Compute("1/$a");
   46 
   47 $popup1 = PopUp(['?','Convergent', 'Divergent','Inconclusive'],'Convergent');
   48 $popup2 = PopUp(['?','Convergent', 'Divergent','Inconclusive'],'Inconclusive');
   49 $popup3 = PopUp(['?','Convergent', 'Divergent','Inconclusive'],'Divergent');
   50 
   51 #####################################################################
   52 
   53 #Title("$BITALIC Look Ahead: $EITALIC 11.6 Absolute Convergence and the Ratio and Root Tests");
   54 
   55 Context()->texStrings;
   56 BEGIN_TEXT
   57 What can you say about the series \(\sum a_n\) in each of the following cases using the Ratio Test?  Answer "Convergent," "Divergent," or "Inconclusive."$BR
   58 $HR
   59 \{$popup1->menu\} $BBOLD 1. $EBOLD  \(\displaystyle \lim_{n \to \infty} \left|\frac{a_{n+1}}{a_n} \right| = $b\)
   60 $PAR
   61 \{$popup2->menu\} $BBOLD 2. $EBOLD  \(\displaystyle \lim_{n \to \infty} \left|\frac{a_{n+1}}{a_n} \right| = 1\)
   62 $PAR
   63 \{$popup3->menu\} $BBOLD 3. $EBOLD   \(\displaystyle \lim_{n \to \infty} \left|\frac{a_{n+1}}{a_n} \right| = $a\)
   64 $HR
   65 $BBOLD Note:$EBOLD  $BITALIC You only have two attempts at this problem.$EITALIC
   66 $HR
   67 END_TEXT
   68 
   69 #####################################################################
   70 
   71 ANS($popup1->cmp);
   72 ANS($popup2->cmp);
   73 ANS($popup3->cmp);
   74 
   75 ENDDOCUMENT();        # This should be the last executable line in the problem.