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    1 #DESCRIPTION
2 #Limits of sequences
3 #ENDDESCRIPTION
4
5 #Keywords('Sequences ' ,,'Limits')
6 DOCUMENT();
8 "PG.pl",
9 "PGbasicmacros.pl",
10 "PGchoicemacros.pl",
12 "PGauxiliaryFunctions.pl"
13 );
14
15 TEXT(&beginproblem);
16
17 $showPartialCorrectAnswers = 0; 18 19 20 21 22 23 @choices=(); 24 @choices = ( "F", "Z", "Z", "D", "I", "Z", "Z", "F" ); 25 26 @questions=(); 27$questions[0] = EV2( " $$\sqrt{n^{2}+4n} - \sqrt{n^{2}}$$" );
28 $questions[1] = EV2( " $$\frac{5^{n}}{n!}$$" ); 29$questions[2] = EV2( " $$\left( \frac{e}{10} \right) ^{n}$$" );
30 $questions[3] = EV2( " $$\left( -1 \right) ^{-n} \frac{2n}{ \ln(n)}$$" ); 31$questions[4] = EV2( " $$\left( 5n^{2n} \right) ^{1/n}$$" );
32 $questions[5] = EV2( " $$\frac{100n^2+1}{3n!}$$" ); 33$questions[6] = EV2( " $$\frac{(-5)^n}{n!}$$" );
34 $questions[7] = EV2( " $$\cos ^{2}(n)+ \sin ^{2}(n)$$" ); 35 36 # Now randomize the questions: 37 @slice = &NchooseK(8,8); 38 #@shuffle = &shuffle(scalar(@slice)); 39 #############################################################################TEXT(&beginproblem); 40 41 #TEXT(EV2(<<EOT)); 42 43 BEGIN_TEXT; 44 45 Match each sequence below to statement that BEST fits it.$BR
46 $BR 47 STATEMENTS$BR
48 $BR 49 Z. The sequence converges to zero; I. The sequence diverges to positive infinity;$BR
50 F. The sequence has a finite non-zero limit; D. The sequence diverges, but
51 not to infinity. $BR 52 53 SEQUENCES$BR
54
55
56
57 END_TEXT
58
59 TEXT(
60
61 &match_questions_list(@questions[@slice])
62 );
63
64
65
66 #&ANS( unordered_str_cmp_list(@ans) );
67 ANS(      str_cmp([@choices[@slice]  ]));
68 &ENDDOCUMENT;
69
70