[npl] / trunk / NationalProblemLibrary / WHFreeman / Rogawski_Calculus_Early_Transcendentals_Second_Edition / 10_Infinite_Series / 10.5_The_Ratio_and_Root_Tests / 10.5.37.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

# View of /trunk/NationalProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/10_Infinite_Series/10.5_The_Ratio_and_Root_Tests/10.5.37.pg

Tue Nov 8 15:17:41 2011 UTC (2 years, 5 months ago) by aubreyja
File size: 2014 byte(s)
Rogawski problems contributed by publisher WHFreeman. These are a subset of the problems available to instructors who use the Rogawski textbook. The remainder can be obtained from the publisher.

    1 # DBsubject('Calculus')
2 # DBchapter('')
3 # DBsection('')
4 # KEYWORDS('')
5 # TitleText1('Calculus: Early Transcendentals')
6 # EditionText1('2')
7 # AuthorText1('Rogawski')
8 # Section1('10.5')
9 # Problem1('37')
10 # Author('Emily Price')
11 # Institution('W.H.Freeman')
12 DOCUMENT();
13
14
15
17
21
22
24
25 #Book Values
26 #$rho = 1 27 28$exp = random(2, 9);
29 $base = random(5,15,1); 30 31 ($an, $den,$result, $L,$compare, $answer,$trueanswer,) = @{list_random(
32   [ "\frac{1}{n^{$exp n}}", "n^{$exp}", "0", Real(0), "<", "converges", 'convergent'],
33   [ "\frac{1}{$base^n}", "$base",  "\frac{1}{$base}", Real(1/$base), "<", "converges", 'convergent'] )};
34
35
36
37 #Let's try to make a multiple choice question
38 $question = new_multiple_choice(); 39$question->qa(' $$\sum\limits_{n=1}^{\infty} an$$ is:', $trueanswer); 40$question->makeLast( 'convergent', 'divergent', 'The Root Test is inconclusive');
41
42
43 Context()->texStrings;
44
45 BEGIN_TEXT
46 \{ beginproblem() \}
47 \{ textbook_ref_exact("Rogawski ET 2e", "10.5", "37") \}
48 $PAR 49 Use the Root Test to determine the convergence or divergence of the given series or state that the Root Test is inconclusive. 50 $\sum\limits_{n=1}^{\infty} an$ 51 $$L = \lim\limits_{n \to \infty} \sqrt[n]{\left| a_n \right|} =$$ \{ans_rule()\} (Enter 'inf' for $$\infty$$.) 52$PAR
53 \{ $question->print_q() \} 54 \{$question->print_a() \}
55 END_TEXT
56
57 Context()->normalStrings;
58
60 ANS($L->cmp); 61 ANS(radio_cmp($question->correct_ans));
62
63 Context()->texStrings;
64 SOLUTION(EV3(<<'END_SOLUTION'));
65 $PAR 66$SOL
67 With $$a_n = an$$,
68 $\sqrt[n]{a_n} = \sqrt[n]{an} = \frac{1}{den}$ and $L = \lim_{n \to \infty} \sqrt[n]{a_n} = result compare 1.$
69 Therefore, the series $$\sum\limits_{n=1}^{\infty} an$$ \$answer by the Root Test.
70
71 END_SOLUTION
72
73 ENDDOCUMENT()