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# Annotation of /trunk/NationalProblemLibrary/Rochester/setComplexNumbers/ur_cn_1_25.pg

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 1 : jjholt 184 ## DESCRIPTION 2 : ## Calculus 3 : ## ENDDESCRIPTION 4 : jj 143 5 : jjholt 184 ## KEYWORDS ('complex','imaginary','exponential') 6 : ## Tagged by cmd6a 4/20/06 7 : jj 143 8 : jjholt 184 ## DBsubject('Calculus') 9 : ## DBchapter('Appendixes') 10 : ## DBsection('Complex Analytic Functions') 11 : ## Date('') 12 : ## Author('') 13 : ## Institution('Rochester') 14 : ## TitleText1('Fundamentals of Complex Analysis for Mathematics, Science, and Engineering') 15 : ## EditionText1('') 16 : ## AuthorText1('E.B. Saff and A.D. Snider') 17 : ## Section1('1.4') 18 : ## Problem1('11') 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 : ); 29 : 30 : TEXT(beginproblem()); 31 : $showPartialCorrectAnswers = 0; 32 : 33 : @questions =( "$$e^x$$ is never zero.", 34 : "$$e^x$$is a one-to-one function.", 35 : "$$e^x$$ is defined for all $$x$$.", 36 : "$$e^{-x} = \frac{1}{e^x}$$." 37 : ); 38 : @answers =( 'T', 'F', 'T', 'T'); 39 : 40 : @slice = NchooseK(scalar(@questions), 4); 41 : 42 : BEGIN_TEXT 43 : Determine which of the following properties of the real exponential function 44 : remain true for the complex exponential ( i.e., for $$x$$ replaced by $$z$$ 45 : ).$PAR Answer T or F:\$PAR 46 : END_TEXT 47 : 48 : ## Next we output the 4 chosen questions. #match_ 49 : TEXT( 50 : &match_questions_list(@questions[@slice]) 51 : ); 52 : 53 : ANS(str_cmp([ @answers[@slice] ] )); 54 : ENDDOCUMENT(); # This should be the last executable line in the problem.

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