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    1 #Problem 2.3.19 ET2e
    2 
    3 DOCUMENT();
    4 
    5 # Load whatever macros you need for the problem
    6 loadMacros("PG.pl",
    7            "PGbasicmacros.pl",
    8            "PGchoicemacros.pl",
    9            "PGanswermacros.pl",
   10            "PGauxiliaryFunctions.pl",
   11            "PGgraphmacros.pl",
   12           );
   13  loadMacros("freemanMacros.pl");
   14 # Author('JustAsk!')
   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 
   53 #JustAsk 2007