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Tue Nov 8 15:17:41 2011 UTC (18 months, 2 weeks ago) by aubreyja
File size: 1399 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 #Problem 2.3.19 ET2e
2
3 DOCUMENT();
4
5 # Load whatever macros you need for the problem
7            "PGbasicmacros.pl",
8            "PGchoicemacros.pl",
10            "PGauxiliaryFunctions.pl",
11            "PGgraphmacros.pl",
12           );
15
16 ## DBsubject('Calculus')
17 ## DBchapter('Limits and Derivatives')
18 ## DBsection('Calculating Limits Using the Limit Laws')
19 ## KEYWORDS('calculus', 'limits', 'basic limit laws', 'rational functions')
20 ## TitleText1('Calculus: Early Transcendentals')
21 ## EditionText1('2')
22 ## AuthorText1('Rogawski')
23 ## Section1('2.3')
24 ## Problem1('19')
25 ## Institution('W.H.Freeman')
26
27 $showPartialCorrectAnswers = 0; 28$solutionexits=1;
29
30 TEXT(beginproblem());
31 $n=random(2,10,1); 32 33 BEGIN_TEXT 34 \{ textbook_ref_exact("Rogawski ET 2e", "2.3","19") \}$BR
35 Evaluate the limit using the Limit Laws: $BR 36 $$\lim\limits_{t \to n} t^{-1} =$$ \{ ans_rule(4) \} 37$PAR
38 END_TEXT
39
40 $answ="1/$n";
41
42 SOLUTION(EV3(<<'END_SOLUTION'));
43 $BR$BBOLD Solution:$EBOLD 44$BR
45 We apply the definition of $$t^{-1}$$, and then the Quotient Law: $BR 46 $$\lim\limits_{t \to n} t^{-1} = \lim\limits_{t \to n} \frac {1}{t} = \frac {\lim\limits_{t \to n} 1} {\lim\limits_{t \to n} t} = \frac {1}{n}$$. 47 END_SOLUTION 48 49 ANS( num_cmp($answ ) );
50
51 ENDDOCUMENT();
52