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# Annotation of /trunk/NationalProblemLibrary/Rochester/setComplexNumbers2AnalyticFunctions/ur_cn_2_6.pg

 1 : jjholt 184 ## DESCRIPTION 2 : ## Calculus 3 : ## ENDDESCRIPTION 4 : jj 143 5 : jjholt 184 ## KEYWORDS ('complex','imaginary','limit') 6 : ## Tagged by cmd6a 4/20/06 7 : jj 143 8 : jjholt 184 ## DBsubject('Calculus') 9 : jjholt 449 ## DBchapter('Complex Variables') 10 : jjholt 184 ## DBsection('Complex Analytic Functions') 11 : ## Date('') 12 : ## Author('') 13 : ## Institution('Rochester') 14 : jjholt 443 ## TitleText1('Complex Analysis') 15 : jjholt 474 ## EditionText1('3') 16 : jjholt 443 ## AuthorText1('Saff, Snyder') 17 : jjholt 184 ## Section1('2.2') 18 : jjholt 474 ## Problem1('') 19 : jjholt 184 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 : $a = random( 2, 5, 1 ); 34 :$b = random( 3, 7, 1 ); 35 : $c = random( 1, 4, 1 ); 36 :$d = $c**2; 37 : 38 : 39 : BEGIN_TEXT 40 : Find each of the following limits:$PAR 41 : (1) $$\lim_{z \to a}{\frac{z^2\ +\ b}{iz}}\ =\$$\{ans_rule(10)\}$PAR 42 : (2) $$\lim_{z \to i}{\frac{z^2\ +\ 1}{z^4\ -\ 1}}\ =\$$\{ans_rule(10)\}$PAR 43 : (3) $$\lim_{z \to c+2i}{|z^2\ -\ d|}\ =\$$\{ans_rule(10)\}$PAR 44 : 45 :$PAR 46 : END_TEXT 47 : 48 : ANS(cplx_cmp( new Complex( 0, -($a**2+$b)/$a ) )); 49 : ANS(cplx_cmp( new Complex( -1/2, 0 ) )); 50 : ANS(cplx_cmp( new Complex( sqrt( (4*$c)**2 + 16 ), 0 ) )); 51 : 52 : ENDDOCUMENT(); # This should be the last executable line in the problem. 53 :