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Tue Nov 8 15:17:41 2011 UTC (18 months, 2 weeks ago) by aubreyja
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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('34')
10 ## Author('Keith Thompson')
11 ## Institution('W.H.Freeman')
12
13 DOCUMENT();
19
20 #$showPartialCorrectAnswers=1; 21 22$a=random(1,3);
23 $c=random(3,5); 24$sp=random(3,5,1);
25 $sp1=$sp+1;
26 $sp2=$sp+2;
27 $sp3=$sp+3;
28 $num=2*$a;
29 $den=2*$c+1;
30 $ans1=$num**$sp/($den-$num); 31 Context()->texStrings; 32 BEGIN_TEXT 33 \{ beginproblem() \} 34 \{ textbook_ref_exact("Rogawski ET 2e", "10.2","34") \} 35$PAR
36
37 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).
38
39
40 $\frac{num^{sp}}{den}+\frac{num^{sp1}}{den^2}+\frac{num^{sp2}}{den^3}+\frac{num^{sp3}}{den^4}+\cdots$
41
42 $$S=$$ \{ans_rule()\}
43 END_TEXT
44
45 Context()->normalStrings;
46
47 ANS(std_num_str_cmp($ans1,['DIV'])). 48 49 Context()->texStrings; 50 SOLUTION(EV3(<<'END_SOLUTION')); 51$PAR
52 \$SOL
53 This is a geometric series with $$c=\frac{num^{sp}}{den}$$ and $$0<r=\frac{num}{den}<1$$. Thus,
54 $\sum_{n=0}^\infty \frac{num^{sp}}{den}\left(\frac{num}{den}\right)^n=\frac{num^{sp}}{den}\left(\frac{1}{1-\frac{num}{den}}\right)=\frac{num^{sp}}{den-num}.$
55 END_SOLUTION
56 ENDDOCUMENT();