## DESCRIPTION ## Calculus ## ENDDESCRIPTION ## KEYWORDS ('complex','imaginary','exponential') ## Tagged by cmd6a 4/20/06 ## DBsubject('Calculus') ## DBchapter('Appendixes') ## DBsection('Complex Analytic Functions') ## Date('') ## Author('') ## Institution('Rochester') ## TitleText1('Fundamentals of Complex Analysis for Mathematics, Science, and Engineering') ## EditionText1('') ## AuthorText1('E.B. Saff and A.D. Snider') ## Section1('1.4') ## Problem1('11') DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl" ); TEXT(beginproblem()); $showPartialCorrectAnswers = 0; @questions =( "$$e^x$$ is never zero.", "$$e^x$$is a one-to-one function.", "$$e^x$$ is defined for all $$x$$.", "$$e^{-x} = \frac{1}{e^x}$$." ); @answers =( 'T', 'F', 'T', 'T'); @slice = NchooseK(scalar(@questions), 4); BEGIN_TEXT Determine which of the following properties of the real exponential function remain true for the complex exponential ( i.e., for $$x$$ replaced by $$z$$ ).$PAR Answer T or F:\$PAR END_TEXT ## Next we output the 4 chosen questions. #match_ TEXT( &match_questions_list(@questions[@slice]) ); ANS(str_cmp([ @answers[@slice] ] )); ENDDOCUMENT(); # This should be the last executable line in the problem.