View of /trunk/NationalProblemLibrary/Rochester/setComplexNumbers2AnalyticFunctions/ur_cn_2_9.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS ('complex','imaginary','derivative')
    6 ## Tagged by cmd6a 4/20/06
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Complex Variables')
   10 ## DBsection('Complex Analytic Functions')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Rochester')
   14 ## TitleText1('Complex Analysis')
   15 ## EditionText1('1')
   16 ## AuthorText1('Saff, Snyder')
   17 ## Section1('2.3')
   18 ## Problem1('7')
   19 
   20 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( 1, 6, 1 );
   34 $b = random( 3, 6, 1 );
   35 $c = random( 2, 5, 1 );
   36 $d = random( 1, 7, 1 );
   37 $f = random( 5, 8, 1 );
   38 
   39 $g = random( 2, 8, 1 );
   40 $h = random( 1, 5, 1 );
   41 $j = random( 3, 7, 1 );
   42 $k = random( 2, 7, 1 );
   43 
   44 BEGIN_TEXT
   45 Find the derivatives of the following functions:$PAR
   46 (1) \(f(z)\ =\ \frac{(z\ +\ $a)^$b}{(z^2\ +\ $c iz\ +\ $d)^$f}\)\{ans_rule(40)\}$PAR
   47 (2) \(f(z)\ =\ $g i(z^3\ -\ $h)^$j(z^2+$k iz)^{100}\)\{ans_rule(40)\}$PAR
   48 
   49 $PAR
   50 END_TEXT
   51 
   52 $ans = "(z+$a)**($b-1)*($b*(z**2+$c*i*z+$d)-$f*(z+$a)*(2*z+$c*i))/(z**2+$c*i*z+$d)**($f+1)";
   53 ANS(fun_cmp( $ans, var => [ 'z', 'i' ]));
   54 $ans = "$g*i*(z**3-$h)**($j-1)*(z**2+$k*i*z)**99*($j*(3*z**2)*(z**2+$k*i*z)+100*(2*z+$k*i)*(z**3-$h))";
   55 ANS(fun_cmp( $ans, var => [ 'z', 'i' ]));
   56 
   57 ENDDOCUMENT();        # This should be the last executable line in the problem.
   58