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| 1 : | jonathan r | 1706 | gness #DESCRIPTION |
| 2 : | gness ## Calculus: Absolute convergence and the ratio and root tests | ||
| 3 : | gness ##ENDDESCRIPTION | ||
| 4 : | gness | ||
| 5 : | gness ##KEYWORDS('calculus', 'series', 'ratio test') | ||
| 6 : | gness | ||
| 7 : | gness ## DBsubject('Calculus') | ||
| 8 : | gness ## DBchapter('Infinite Sequences and Series') | ||
| 9 : | gness ## DBsection('Absolute Convergence and the Ratio and Root Tests') | ||
| 10 : | gness ## Date('04/07/2010') | ||
| 11 : | gness ## Author('Justin Sukiennik') | ||
| 12 : | gness ## Institution('University of Minnesota') | ||
| 13 : | gness ## TitleText1('Calculus: Concepts and Contexts') | ||
| 14 : | gness ## EditionText1('4 Custom UMTYMP Ed.') | ||
| 15 : | gness ## AuthorText1('Stewart') | ||
| 16 : | gness ## Section1('11.6') | ||
| 17 : | gness ## Problem1('1') | ||
| 18 : | gness | ||
| 19 : | gness ##################################################################### | ||
| 20 : | gness DOCUMENT(); # This should be the first executable line in the problem. | ||
| 21 : | gness | ||
| 22 : | gness loadMacros( | ||
| 23 : | gness "PGstandard.pl", | ||
| 24 : | gness "MathObjects.pl", | ||
| 25 : | gness "PGunion.pl", | ||
| 26 : | gness "parserPopUp.pl", | ||
| 27 : | gness "PGchoicemacros.pl", | ||
| 28 : | gness "PGcourse.pl", | ||
| 29 : | gness ); | ||
| 30 : | gness | ||
| 31 : | gness ##################################################################### | ||
| 32 : | gness install_problem_grader(~~&std_problem_grader); | ||
| 33 : | gness | ||
| 34 : | gness TEXT(beginproblem()); | ||
| 35 : | gness | ||
| 36 : | gness $showPartialCorrectAnswers = 0; | ||
| 37 : | gness | ||
| 38 : | gness ##################################################################### | ||
| 39 : | gness | ||
| 40 : | gness | ||
| 41 : | gness Context("Numeric"); | ||
| 42 : | gness | ||
| 43 : | gness $a = list_random(2,4,5,10,20); | ||
| 44 : | gness | ||
| 45 : | gness $b = Compute("1/$a"); | ||
| 46 : | gness | ||
| 47 : | gness $popup1 = PopUp(['?','Convergent', 'Divergent','Inconclusive'],'Convergent'); | ||
| 48 : | gness $popup2 = PopUp(['?','Convergent', 'Divergent','Inconclusive'],'Inconclusive'); | ||
| 49 : | gness $popup3 = PopUp(['?','Convergent', 'Divergent','Inconclusive'],'Divergent'); | ||
| 50 : | gness | ||
| 51 : | gness ##################################################################### | ||
| 52 : | gness | ||
| 53 : | gness #Title("$BITALIC Look Ahead: $EITALIC 11.6 Absolute Convergence and the Ratio and Root Tests"); | ||
| 54 : | gness | ||
| 55 : | gness Context()->texStrings; | ||
| 56 : | gness BEGIN_TEXT | ||
| 57 : | gness 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 : | gness $HR | ||
| 59 : | gness \{$popup1->menu\} $BBOLD 1. $EBOLD \(\displaystyle \lim_{n \to \infty} \left|\frac{a_{n+1}}{a_n} \right| = $b\) | ||
| 60 : | gness $PAR | ||
| 61 : | gness \{$popup2->menu\} $BBOLD 2. $EBOLD \(\displaystyle \lim_{n \to \infty} \left|\frac{a_{n+1}}{a_n} \right| = 1\) | ||
| 62 : | gness $PAR | ||
| 63 : | gness \{$popup3->menu\} $BBOLD 3. $EBOLD \(\displaystyle \lim_{n \to \infty} \left|\frac{a_{n+1}}{a_n} \right| = $a\) | ||
| 64 : | gness $HR | ||
| 65 : | jonathan r | 1815 | gness $BBOLD Note:$EBOLD $BITALIC You only have two attempts at this problem.$EITALIC |
| 66 : | gness $HR | ||
| 67 : | jonathan r | 1706 | gness END_TEXT |
| 68 : | gness | ||
| 69 : | gness ##################################################################### | ||
| 70 : | gness | ||
| 71 : | gness ANS($popup1->cmp); | ||
| 72 : | gness ANS($popup2->cmp); | ||
| 73 : | gness ANS($popup3->cmp); | ||
| 74 : | gness | ||
| 75 : | gness ENDDOCUMENT(); # This should be the last executable line in the problem. |
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