## 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.