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| 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 : |
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