[npl] / trunk / NationalProblemLibrary / WHFreeman / Rogawski_Calculus_Early_Transcendentals_Second_Edition / 10_Infinite_Series / 10.1_Sequences / 10.1.43.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

# View of /trunk/NationalProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/10_Infinite_Series/10.1_Sequences/10.1.43.pg

Tue Nov 8 15:17:41 2011 UTC (2 years, 3 months ago) by aubreyja
File size: 1489 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('43')
10 ## Author('Keith Thompson')
11 ## Institution('W.H.Freeman')
12
13 DOCUMENT();
19
20 #$showPartialCorrectAnswers=1; 21 22$num=random(2,9);
23 $den=random(2,13); 24$ans=$num/$den;
25 Context()->texStrings;
26 BEGIN_TEXT
27 \{ beginproblem() \}
28 \{ textbook_ref_exact("Rogawski ET 2e", "10.1","43") \}
29 $PAR 30 Determine the limit of the sequence or show that the sequence diverges by using the appropriate Limit Laws or theorems. If the sequence diverges, enter DIV as your answer. 31 $a_n=\frac{num n^2+n+2}{den n^2-3}$ 32 33$PAR
34 $$\lim\limits_{n\to\infty}a_n =$$  \{ans_rule()\}
35 END_TEXT
36
37 Context()->normalStrings;
38
39 #ANS(Real($ans)->cmp); 40 ANS(std_num_str_cmp($ans,['DIV']));
41
42 Context()->texStrings;
43 SOLUTION(EV3(<<'END_SOLUTION'));
44 $PAR 45$SOL
46 We have $$a_n=f(n)$$, where $$f(x)=\frac{num x^2+x+2}{den x^2-3}$$. Thus,
47
48 $\lim_{n\rightarrow \infty} \frac{num n^2+n+2}{den n^2-3} = \lim_{x\rightarrow \infty} \frac{num x^2+x+2}{den x^2-3} =\frac{num}{den}.$
49 END_SOLUTION
50
51 ENDDOCUMENT();