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# Annotation of /trunk/NationalProblemLibrary/Dartmouth/setMTWCh2S2/UR_VC_5_7.pg

 1 : jjholt 156 ## DESCRIPTION 2 : ## Calculus 3 : ## ENDDESCRIPTION 4 : jj 134 5 : jjholt 156 ## KEYWORDS('vector' 'limit') 6 : ## Tagged by tda2d 7 : jj 134 8 : jjholt 156 ## DBsubject('Calculus') 9 : ## DBchapter('Differentiation') 10 : ## DBsection('Partial Derivatives and Continuity') 11 : ## Date('') 12 : ## Author('') 13 : ## Institution('Dartmouth') 14 : ## TitleText1('Basic Multivariable Calculus') 15 : ## EditionText1('') 16 : ## AuthorText1('Marsden, Tromba, and Weinstein') 17 : ## Section1('2.2') 18 : ## Problem1('') 19 : 20 : jj 134 DOCUMENT(); 21 : 22 : loadMacros( 23 : "PG.pl", 24 : "PGbasicmacros.pl", 25 : "PGchoicemacros.pl", 26 : "PGanswermacros.pl", 27 : "PGauxiliaryFunctions.pl" 28 : ); 29 : 30 : gage 269 TEXT(beginproblem()); 31 : jj 134 $showPartialCorrectAnswers = 1; 32 : 33 :$a = random(1, 5); 34 : $b = random(1, 5); 35 :$c = random(1, 5); 36 : $d = random(1, 5); 37 : 38 :$ans = ($d *$c * exp($a**2 +$b**2)) / ($a**3 +$b**3 + $c**3); 39 : 40 : BEGIN_TEXT 41 :$PAR 42 : Find the limit, if it exists, or type N if it does not exist. 43 : $PAR 44 : $$\lim_{(x, y, z) \rightarrow (a, b, c)} \frac{{d}ze^{x^2+y^2}}{{a}x^2 + 45 : {b}y^2 + {c}z^2} =$$ \{ ans_rule(40) \} 46 : END_TEXT 47 : gage 269 ANS(num_cmp($ans, strings=>['N'])); 48 : jj 134 49 : ENDDOCUMENT();