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Tue Nov 8 15:17:41 2011 UTC (2 years, 1 month ago) by aubreyja
File size: 1560 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('51')
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=ln($num/$den);
25 Context()->texStrings;
26 BEGIN_TEXT
27 \{ beginproblem() \}
28 \{ textbook_ref_exact("Rogawski ET 2e", "10.1","51") \}
29 $PAR 30 31 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. 32 $c_n=\ln\left(\frac{num n-7}{den n+4}\right)$ 33 34$PAR
35 $$\lim\limits_{n\to\infty}c_n =$$  \{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 Because $$f(x)=\ln x$$ is a continuous function, it follows that
47
48
49 $\lim_{n\rightarrow \infty} c_n = \lim_{x\rightarrow \infty}\ln\left(\frac{num x-7}{den x+4}\right)=\ln\left(\lim_{x\rightarrow \infty}\frac{num x-7}{den x+4}\right)=\ln \left(\frac{num}{den}\right).$
50 END_SOLUTION
51
52 ENDDOCUMENT();