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Tue Nov 8 15:17:41 2011 UTC (2 years, 5 months ago) by aubreyja
File size: 1697 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('Limits and Derivatives')
3 ## DBsection('Definition of the Derivative')
4 ## KEYWORDS('calculus', 'derivatives', 'slope')
5 ## TitleText1('Calculus: Early Transcendentals')
6 ## EditionText1('2')
7 ## AuthorText1('Rogawski')
8 ## Section1('10.2')
9 ## Problem1('25')
10 ## Author('Keith Thompson')
11 ## Institution('W.H.Freeman')
12
13 DOCUMENT();
19
20 #$showPartialCorrectAnswers=1; 21 22$num=random(3,7,2); #force odd
23 $den=random(10,14,2); #force even 24$n0 = random(2,6,1);
25 $den_num =$den-$num; 26 27$ans1=($num**$n0)/($den**$n0)*($den/($den-$num)); 28 Context()->texStrings; 29 BEGIN_TEXT 30 \{ beginproblem() \} 31 \{ textbook_ref_exact("Rogawski ET 2e", "10.2","25") \} 32$PAR
33
34 Use the formula for the sum of a geometric series to find the sum or state that the series diverges (enter DIV for a divergent series).
35
36 $\sum_{n=n0}^\infty \frac{num^n}{den^n}$
37
38 $PAR $$S=$$ \{ans_rule()\} 39 END_TEXT 40 41 Context()->normalStrings; 42 43 ANS(std_num_str_cmp($ans1,['DIV']));
44
45 Context()->texStrings;
46 SOLUTION(EV3(<<'END_SOLUTION'));
47 $PAR 48$SOL
49 This is a geometric series with $$c=\left(\frac{num}{den}\right)^{n0}$$ and $$0<r=\frac{num}{den}<1$$. Thus,
50 $\sum_{n=n0}^\infty \frac{num^n}{den^n}= 51 \left(\frac{num}{den}\right)^{n0}\sum_{n=0}^\infty\left( \frac{num}{den}\right)^n= 52 \left(\frac{num}{den}\right)^{n0}\left(\frac{1}{1-\frac{num}{den}}\right)=\left(\frac{num}{den}\right)^{n0}\left(\frac{den}{den_num}\right).$
53 END_SOLUTION
54 ENDDOCUMENT();