## DESCRIPTION ## Calculus ## ENDDESCRIPTION ## KEYWORDS ('complex','imaginary','limit') ## Tagged by cmd6a 4/20/06 ## DBsubject('Calculus') ## DBchapter('Appendixes') ## DBsection('Complex Analytic Functions') ## Date('') ## Author('') ## Institution('Rochester') ## TitleText1('Fundamentals of Complex Analysis for Mathematics, Science, and Engineering') ## EditionText1('') ## AuthorText1('E.B. Saff and A.D. Snider') ## Section1('2.2') ## Problem1('9') DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl", "PGcomplexmacros.pl" ); TEXT(beginproblem()); $a = random( 2, 5, 1 );$b = random( 3, 7, 1 ); $c = random( 1, 4, 1 );$d = $c**2; BEGIN_TEXT Find each of the following limits:$PAR (1) $$\lim_{z \to a}{\frac{z^2\ +\ b}{iz}}\ =\$$\{ans_rule(10)\}$PAR (2) $$\lim_{z \to i}{\frac{z^2\ +\ 1}{z^4\ -\ 1}}\ =\$$\{ans_rule(10)\}$PAR (3) $$\lim_{z \to c+2i}{|z^2\ -\ d|}\ =\$$\{ans_rule(10)\}$PAR$PAR END_TEXT ANS(cplx_cmp( new Complex( 0, -($a**2+$b)/$a ) )); ANS(cplx_cmp( new Complex( -1/2, 0 ) )); ANS(cplx_cmp( new Complex( sqrt( (4*$c)**2 + 16 ), 0 ) )); ENDDOCUMENT(); # This should be the last executable line in the problem.