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# Annotation of /trunk/NationalProblemLibrary/Rochester/setComplexNumbers2AnalyticFunctions/ur_cn_2_11.pg

 1 : jjholt 184 ## DESCRIPTION 2 : ## Calculus 3 : ## ENDDESCRIPTION 4 : jj 143 5 : jjholt 184 ## KEYWORDS ('complex','imaginary','analytic') 6 : ## Tagged by cmd6a 4/20/06 7 : jj 143 8 : jjholt 184 ## DBsubject('Calculus') 9 : ## DBchapter('Appendixes') 10 : ## DBsection('Complex Analytic Functions') 11 : ## Date('') 12 : ## Author('') 13 : ## Institution('Rochester') 14 : ## TitleText1('Fundamentals of Complex Analysis for Mathematics, Science, and Engineering') 15 : ## EditionText1('') 16 : ## AuthorText1('E.B. Saff and A.D. Snider') 17 : ## Section1('2.3') 18 : ## Problem1('15') 19 : 20 : jj 143 DOCUMENT(); # This should be the first executable line in the problem. 21 : 22 : loadMacros( 23 : "PG.pl", 24 : "PGbasicmacros.pl", 25 : "PGchoicemacros.pl", 26 : "PGanswermacros.pl", 27 : "PGauxiliaryFunctions.pl", 28 : "PGcomplexmacros.pl" 29 : ); 30 : 31 : TEXT(beginproblem()); 32 : 33 : $a = 4*random(0, 2, 1) + 2; 34 :$b = 4*random(3, 4, 1) + 2; 35 : 36 : BEGIN_TEXT 37 : $PAR 38 : Use L'Hospital's rule to find $$\lim_{z\to i}{\frac{1\ +\ z^{a}}{1\ +\ z^{b}}}$$:$PAR 39 : \{ans_rule(20)\} 40 : $PAR 41 : END_TEXT 42 : 43 : 44 : ANS(cplx_cmp( new Complex($a/\$b, 0 ) )); 45 : 46 : ENDDOCUMENT(); # This should be the last executable line in the problem. 47 :