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Tue Nov 8 15:17:41 2011 UTC (2 years, 1 month ago) by aubreyja
File size: 2140 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('Infinite Sequences and Series')
3 ## DBsection('Infinite Sequences and Series')
4 ## KEYWORDS('calculus', 'series')
5 ## TitleText1('Calculus: Early Transcendentals')
6 ## EditionText1('2')
7 ## AuthorText1('Rogawski')
8 ## Section1('10.1')
9 ## Problem1('23')
10 ## Author('Danny Glin')
11 ## Institution('W.H.Freeman')
12
13 DOCUMENT();
17
18 Context()->texStrings;
20
21 #$p=1; 22 #$q=1;
23 #$r=1; 24$p=random(1,9,1);
25 $q=random(1,9,1); 26$qq=$q**2; 27$r=random(1,9,1);
28
29 ##for variation in answer, if $pn is 2 nonzero, if$pn is 3, zero
30 $pn = random(2,3,1); 31 32$an=Formula("($p n)/sqrt($qq n^($pn)+$r)")->reduce;
33 $ax =$an->substitute(n=>x);
34 if($pn==3){ 35$ans=0;
36   Context()->flags->set(reduceConstants=>0);
37   $ax1=Formula("($p x/x^(3/2))/(sqrt($qq x^($pn)+$r)/(x^(3/2)))"); 38$ax2=Formula("($p/sqrt(x))/sqrt($qq+$r/x^3)"); 39$solText = "
40 We have $$a_n=f(n)$$ where $$f(x)= ax$$.  Thus
41 $42 \lim_{n\to\infty}an = 43 \lim_{x\to\infty}ax = 44 \lim_{x\to\infty}ax1 45$
46 $47 = \lim_{x\to\infty}ax2 = 48 \frac{0}{\sqrt{qq+0}} = 49 \frac{0}{q} = 50 ans. 51$
52 "
53
54
55 }
56 else{
57   $ans =$p/$q; 58$ax1=Formula("(($p x)/x)/(sqrt($qq x^($pn)+$r)/x)");
59   $ax2 = Formula("$p /(sqrt($qq +$r/x^($pn)))"); 60$solText = "
61 We have $$a_n=f(n)$$ where $$f(x)=ax$$.  Thus
62 $63 \lim_{n\to\infty}a_n = 64 \lim_{x\to\infty}f(x) = 65 \lim_{x\to\infty} ax 66$
67 $68 = \lim_{x\to\infty} ax1 = 69 \lim_{x\to\infty} ax2 = 70 \frac{p}{q} = ans. 71$
72
73
74 ";
75
76 }
77
78
79
80 BEGIN_TEXT
81 \{ beginproblem() \}
82 \{ textbook_ref_exact("Rogawski ET 2e", "10.1","23") \}
83 $PAR 84 Use Theorem 1 to determine the limit of the sequence or type DIV if the sequence diverges.$PAR
85 $$a_n=an$$
86 $PAR 87 $$\lim\limits_{n\to\infty}a_n =$$ \{ans_rule()\}$BR
88 END_TEXT
89 Context()->normalStrings;
90
91 ANS(std_num_str_cmp($ans,['DIV'])); 92 93 Context()->texStrings; 94 Context()->flags->set(reduceConstants=>0); 95 96 97 SOLUTION(EV3(<<'END_SOLUTION')); 98$PAR
99 $SOL 100$solText
101
102 END_SOLUTION
103
104 ENDDOCUMENT();