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Tue Nov 8 15:17:41 2011 UTC (2 years, 1 month 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('36')
10 ## Author('Keith Thompson')
11 ## Institution('W.H.Freeman')
12
13 DOCUMENT();
19
20 #$showPartialCorrectAnswers=1; 21 22 Context()->variables->add(D=>'Real'); 23$num=random(4,9);
24 $den=$num+1;
25 $ans1=$num**3/($den-$num);
26 $n2=$num**2;
27 $n3=$num**3;
28 $d2=$den**2;
29 $d3=$den**3;
30 $ans1=$d3/($n2*($den-$num)); 31 Context()->texStrings; 32 33 BEGIN_TEXT 34 \{ beginproblem() \} 35 \{ textbook_ref_exact("Rogawski ET 2e", "10.2","36") \} 36$PAR
37
38 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).
39
40
41 $\frac{d2}{n2}+\frac{den}{num}+1+\frac{num}{den}+\frac{n2}{d2}+\frac{n3}{d3}+\cdots$
42
43 $$S=$$  \{ans_rule()\}
44 END_TEXT
45
46 Context()->normalStrings;
47
48 ANS(std_num_str_cmp($ans1,['DIV'])); 49 50 Context()->texStrings; 51 SOLUTION(EV3(<<'END_SOLUTION')); 52$PAR
53 \$SOL
54 This is a geometric series with $$c=\left(\frac{num}{den}\right)^{-2}=\frac{d2}{n2}$$ and $$0<r=\frac{num}{den}<1$$. Thus,
55 $\sum_{n=0}^\infty \frac{d2}{n2}\left(\frac{num}{den}\right)^n=\frac{d2}{n2}\left(\frac{1}{1-\frac{num}{den}}\right)=\frac{d3}{n2(den-num)}.$
56 END_SOLUTION
57 ENDDOCUMENT();