View of /trunk/NationalProblemLibrary/WHFreeman/Rogawski_Calculus_Early_Transcendentals_Second_Edition/10_Infinite_Series/10.1_Sequences/10.1.16.pg

    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('16')
   10 ## Author('Keith Thompson')
   11 ## Institution('W.H.Freeman')
   12 
   13 DOCUMENT();
   14 loadMacros("PG.pl","PGbasicmacros.pl","PGanswermacros.pl");
   15 loadMacros("Parser.pl");
   16 loadMacros("freemanMacros.pl");
   17 loadMacros("PGauxiliaryFunctions.pl");
   18 loadMacros("PGgraphmacros.pl");
   19 
   20 #$showPartialCorrectAnswers=1;
   21 
   22 $b2=random(6,20,1);
   23 $b3=random(2,19,1);
   24 $power=random(2,4,1);
   25 
   26 $ans=$b2;
   27 Context()->texStrings;
   28 BEGIN_TEXT
   29 \{ beginproblem() \}
   30 \{ textbook_ref_exact("Rogawski ET 2e", "10.1","16") \}
   31 $PAR
   32 Use Theorem 1 to determine the limit of the sequence or type DIV if the sequence diverges.$PAR
   33 \(a_n=$b2-\frac{$b3}{n^{$power}}\)
   34 $PAR
   35 \(\lim\limits_{n\to\infty}a_n = \) \{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 We have \(a_n=f(n)\) where \(f(x)=$b2-\frac{$b3}{x^{$power}}\). Thus,
   47 
   48 \[
   49 \lim_{n\rightarrow \infty} \left( $b2-\frac{$b3}{n^{$power}} \right) =
   50 \lim_{x\rightarrow \infty} \left( $b2-\frac{$b3}{x^{$power}} \right) =
   51 $b2.\]
   52 END_SOLUTION
   53 
   54 ENDDOCUMENT();