[npl] / trunk / NationalProblemLibrary / WHFreeman / Rogawski_Calculus_Early_Transcendentals_Second_Edition / 10_Infinite_Series / 10.2_Summing_an_Infinite_Series / 10.2.1.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

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Tue Nov 8 15:17:41 2011 UTC (18 months, 2 weeks ago) by aubreyja
File size: 1381 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('1')
10 ## Author('Keith Thompson')
11 ## Institution('W.H.Freeman')
12
13 DOCUMENT();
19
20 #$showPartialCorrectAnswers=1; 21 Context()->variables->add(n=>'Real'); 22$power=random(2,4);
23 $p2=$power ** 2;
24 $p3=$power ** 3;
25 $p4=$power ** 4;
26
27 $ans=Formula("1/($power ** n)");
28 Context()->texStrings;
29 BEGIN_TEXT
30 \{ beginproblem() \}
31 \{ textbook_ref_exact("Rogawski ET 2e", "10.2","1") \}
32 $PAR 33 34 Find a formula for the general term $$a_n$$ (not the partial sum) of the infinite series (starting with $$a_1$$). 35 $\frac{1}{power}+\frac{1}{p2}+\frac{1}{p3}+\frac{1}{p4}+\cdots$ 36 37$PAR $$a_n$$ =  \{ans_rule()\}
38 END_TEXT
39
40 Context()->normalStrings;
41
42 ANS($ans->cmp); 43 Context()->texStrings; 44 SOLUTION(EV3(<<'END_SOLUTION')); 45$PAR
46 $SOL 47 The denominators are powers of$power, starting with the first power. Hence, the general term is $$a_n=\frac{1}{power^n}$$.
48 END_SOLUTION
49
50 ENDDOCUMENT();