View of /trunk/rochester_problib/setDiscrete4Functions/ur_dis_4_7.pg

    1 ##DESCRIPTION
    2 ##KEYWORDS('Standard Example')
    3 ##problem 8 section 1.8 of Discrete Math by Kenneth Rosen
    4 ##ENDDESCRIPTION
    5 
    6 DOCUMENT();        # This should be the first executable line in the problem.
    7 
    8 loadMacros(
    9 "PG.pl",
   10 "PGbasicmacros.pl",
   11 "PGchoicemacros.pl",
   12 "PGanswermacros.pl",
   13 "PGauxiliaryFunctions.pl"
   14 );
   15 
   16 TEXT(&beginproblem);
   17 $showPartialCorrectAnswers=0;
   18 
   19 #Numerical Answer
   20 
   21 $a = random(3,9,1);
   22 $b = random(5,9,1);
   23 
   24 BEGIN_TEXT
   25 Find the least integer n such that f(x) is \( O(x^n) \)
   26 for each of the following functions: $PAR
   27 (a) \( f(x) = 2x^2 + x^{$a} \log(x) \) \{ ans_rule(10) \}
   28 $PAR
   29 (b) \( f(x) = 3x^{$b} + (\log x)^4 \) \{ ans_rule(10) \}
   30 $PAR
   31 (c) \( f(x) = \frac {x^4 + x^2 + 1}{x^4 + 1} \) \{ ans_rule(10) \}
   32 $PAR
   33 (d) \( f(x) = \frac {x^3 + 5\log(x)}{x^4 + 1} \) \{ ans_rule(10) \}
   34 $PAR
   35 END_TEXT
   36 
   37 $c = $a + 1;
   38 
   39 ANS( num_cmp( $c ) );
   40 ANS( num_cmp( $b ) );
   41 ANS( num_cmp( 0 ) );
   42 ANS( num_cmp( -1 ) );
   43 
   44 ENDDOCUMENT();        # This should be the last executable line in the problem.;