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

Tue Jun 18 20:27:02 2002 UTC (10 years, 11 months ago) by ad001h
File size: 997 byte(s)
added setDiscrete5Algorithms, edited problems in setDiscrete4Functions


    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
9 "PG.pl",
10 "PGbasicmacros.pl",
11 "PGchoicemacros.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.;