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    1 #Problem 2.3.16 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', 'polynomial functions')
   20 ## TitleText1('Calculus: Early Transcendentals')
   21 ## EditionText1('2')
   22 ## AuthorText1('Rogawski')
   23 ## Section1('2.3')
   24 ## Problem1('16')
   25 ## Institution('W.H.Freeman')
   26 
   27 $showPartialCorrectAnswers = 0;
   28 TEXT(beginproblem());
   29 
   30 $n=random(1,6,1);
   31 $a=random(2,7,1);
   32 $b=$a+1;
   33 
   34 BEGIN_TEXT
   35 \{ textbook_ref_exact("Rogawski ET 2e", "2.3","16") \}$BR
   36 Evaluate the limit using the Limit Laws: $BR
   37 \( \lim\limits_{x \to $n} x (x+$a) (x+$b)  = \)  \{ ans_rule(4) \}
   38 
   39 END_TEXT
   40 
   41 $answ=$n*($n+$a)*($n+$b);
   42 
   43 SOLUTION(EV3(<<'END_SOLUTION'));
   44 $BR$BBOLD Solution:$EBOLD
   45 $BR
   46 We apply the Product Law and Sum Law: $BR
   47 \( \lim\limits_{x \to $n} x (x+$a) (x+$b) = \Large( \normalsize\lim\limits_{x \to $n} x \Large) (\normalsize \lim\limits_{x \to $n} (x+$a) \Large) ( \normalsize \lim\limits_{x \to $n} (x+$b)\Large )\normalsize =\) $BR \(=$n \Large ( \normalsize \lim\limits_{x \to $n} x + \lim\limits_{x \to $n} $a \Large ) ( \normalsize \lim\limits_{x \to $n} x + \lim\limits_{x \to $n} $b \Large ) \normalsize = $n ($n+$a)($n+$b) = $answ \).
   48 
   49 END_SOLUTION
   50 
   51 ANS( num_cmp( $answ ) );
   52 
   53 ENDDOCUMENT();
   54 
   55 #JustAsk 2007