[npl] / trunk / NationalProblemLibrary / Rochester / setComplexNumbers2AnalyticFunctions / ur_cn_2_9.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

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

Sat Jul 7 23:24:14 2007 UTC (5 years, 10 months ago) by jjholt
File size: 1461 byte(s)
Fixed text edition number. --JJH


    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
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.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