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Tue Nov 8 15:17:41 2011 UTC (2 years, 5 months ago) by aubreyja
File size: 1772 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('10.7')
9 # Problem1('3')
10 # Author('Emily Price')
11 # Institution('W.H.Freeman')
12 DOCUMENT();
13
14
15
17
21
22
24
25 #Book Values
26 #$constant = -2 27 28$constant = random(2, 9);
29 $sign = list_random(-1, 1); 30$coef = $sign*$constant;
31
32 $denominator = Formula("1 -$coef*x")->reduce;
33 #$mcterms = Formula("($coef*x)^n")->reduce;
34 $mcterms = Formula("($coef*x)^n");
35 $mcterms->{test_points}=[[1,0.1],[2,0.2],[3,0.3]]; 36 37$interval = Interval("(-1/$constant,1/$constant)");
38
39 Context()->texStrings;
40
41 BEGIN_TEXT
42 \{ beginproblem() \}
43 \{ textbook_ref_exact("Rogawski ET 2e", "10.7", "3") \}
44 $PAR 45 Find the Maclaurin series and corresponding interval of convergence of the following function. 46$PAR
47 $f(x) = \frac{1}{denominator}$
48 $PAR 49 $$f(x) = \sum\limits_{n=0}^{\infty}$$ \{ ans_rule() \} 50$PAR
51 The interval of convergence is: \{ans_rule() \}
52 END_TEXT
53
54 Context()->normalStrings;
55
57 ANS($mcterms->cmp); 58 ANS($interval->cmp);
59
60 Context()->texStrings;
61 SOLUTION(EV3(<<'END_SOLUTION'));
62 $PAR 63$SOL
64
65 Substituting $$coef x$$ for $$x$$ in the Maclaurin series for $$\frac{1}{1-x}$$ gives
66 $\frac{1}{denominator} = \sum_{n=0}^{\infty} mcterms$
67 This series is valid for $$|constant x| < 1$$, or $$|x| < \frac{1}{constant}$$.  Thus, the interval of convergence is $$(-\frac{1}{constant},\frac{1}{constant})$$.
68
69
70 END_SOLUTION
71
72 ENDDOCUMENT()