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# Annotation of /trunk/NationalProblemLibrary/Rochester/setComplexNumbers2AnalyticFunctions/ur_cn_2_9.pg

 1 : jjholt 184 ## DESCRIPTION 2 : ## Calculus 3 : ## ENDDESCRIPTION 4 : jj 143 5 : jjholt 184 ## KEYWORDS ('complex','imaginary','derivative') 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 184 ## EditionText1('') 16 : jjholt 443 ## AuthorText1('Saff, Snyder') 17 : jjholt 184 ## Section1('2.3') 18 : ## Problem1('7') 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 : $a = random( 1, 6, 1 ); 34 :$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 :