[npl] / trunk / NationalProblemLibrary / WHFreeman / Rogawski_Calculus_Early_Transcendentals_Second_Edition / 10_Infinite_Series / 10.1_Sequences / 10.1.16.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

# View of /trunk/NationalProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/10_Infinite_Series/10.1_Sequences/10.1.16.pg

Tue Nov 8 15:17:41 2011 UTC (2 years, 1 month ago) by aubreyja
File size: 1432 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('10.1')
9 ## Problem1('16')
10 ## Author('Keith Thompson')
11 ## Institution('W.H.Freeman')
12
13 DOCUMENT();
19
20 #$showPartialCorrectAnswers=1; 21 22$b2=random(6,20,1);
23 $b3=random(2,19,1); 24$power=random(2,4,1);
25
26 $ans=$b2;
27 Context()->texStrings;
28 BEGIN_TEXT
29 \{ beginproblem() \}
30 \{ textbook_ref_exact("Rogawski ET 2e", "10.1","16") \}
31 $PAR 32 Use Theorem 1 to determine the limit of the sequence or type DIV if the sequence diverges.$PAR
33 $$a_n=b2-\frac{b3}{n^{power}}$$
34 $PAR 35 $$\lim\limits_{n\to\infty}a_n =$$ \{ans_rule()\} 36 END_TEXT 37 38 Context()->normalStrings; 39 40 #ANS(Real($ans)->cmp);
41 ANS(std_num_str_cmp($ans,['DIV'])); 42 Context()->texStrings; 43 SOLUTION(EV3(<<'END_SOLUTION')); 44$PAR
45 \$SOL
46 We have $$a_n=f(n)$$ where $$f(x)=b2-\frac{b3}{x^{power}}$$. Thus,
47
48 $49 \lim_{n\rightarrow \infty} \left( b2-\frac{b3}{n^{power}} \right) = 50 \lim_{x\rightarrow \infty} \left( b2-\frac{b3}{x^{power}} \right) = 51 b2.$
52 END_SOLUTION
53
54 ENDDOCUMENT();