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| 1 : | ted shifri | 1457 | ## DESCRIPTION |
| 2 : | ## Calculating directional derivative | ||
| 3 : | ## ENDDESCRIPTION | ||
| 4 : | |||
| 5 : | ## KEYWORDS('Directional Derivative', 'homogeneous function') | ||
| 6 : | ## | ||
| 7 : | |||
| 8 : | ## DBsubject('Calculus') | ||
| 9 : | ## DBchapter('') | ||
| 10 : | ## DBsection('') | ||
| 11 : | ## Date('8/22/2009') | ||
| 12 : | ## Author('Ted Shifrin') | ||
| 13 : | ## Institution('UGA') | ||
| 14 : | ## TitleText1('') | ||
| 15 : | ## EditionText1('') | ||
| 16 : | ## AuthorText1('') | ||
| 17 : | ## Section1('') | ||
| 18 : | ## Problem1('') | ||
| 19 : | |||
| 20 : | DOCUMENT(); # This should be the first executable line in the problem. | ||
| 21 : | |||
| 22 : | loadMacros("PG.pl", | ||
| 23 : | "PGbasicmacros.pl", | ||
| 24 : | "PGchoicemacros.pl", | ||
| 25 : | "PGanswermacros.pl", | ||
| 26 : | "PGauxiliaryFunctions.pl", | ||
| 27 : | "PGstandard.pl", | ||
| 28 : | "PGunion.pl", | ||
| 29 : | "Parser.pl", | ||
| 30 : | "MathObjects.pl" | ||
| 31 : | ); | ||
| 32 : | |||
| 33 : | |||
| 34 : | TEXT(beginproblem()); | ||
| 35 : | BEGIN_PROBLEM(); | ||
| 36 : | |||
| 37 : | ############################################## | ||
| 38 : | # Setup | ||
| 39 : | |||
| 40 : | Context("Vector")->variables->are( | ||
| 41 : | x=>'Real', y=>'Real', | ||
| 42 : | ); | ||
| 43 : | |||
| 44 : | TEXT(beginproblem()); | ||
| 45 : | $showPartialCorrectAnswers = 1; | ||
| 46 : | |||
| 47 : | $a = non_zero_random(-3, 3, 1); | ||
| 48 : | do{$b = non_zero_random(-3, 3, 1)} until $b!=$a; | ||
| 49 : | $c = random(3,6,1); | ||
| 50 : | $d = $c-2; | ||
| 51 : | $e = non_zero_random(-2,2,1); | ||
| 52 : | $f = non_zero_random(-2,2,1); | ||
| 53 : | do{$k = non_zero_random(-5,5,1)} until ($k!=$a and $k!=$b); | ||
| 54 : | $F = Formula("($a x^$c+$b y^$c)/(x^2+y^2)")->reduce; | ||
| 55 : | $Feval = $F->eval(x=>$e,y=>$f); | ||
| 56 : | |||
| 57 : | $arg = '\left(\begin{array}{c} x\\y \end{array}\right)'; | ||
| 58 : | $P = ColumnVector($e,$f); | ||
| 59 : | |||
| 60 : | $ans = $k*$d*$Feval; | ||
| 61 : | |||
| 62 : | Context()->texStrings; | ||
| 63 : | |||
| 64 : | if ($k==1) {$kk = "";} | ||
| 65 : | else { | ||
| 66 : | if ($k==-1) {$kk = "-";} | ||
| 67 : | else {$kk = $k;}} | ||
| 68 : | |||
| 69 : | |||
| 70 : | BEGIN_TEXT | ||
| 71 : | Let \(f $arg = \displaystyle $F\ \) and \(\ \mathbf a = $P \). | ||
| 72 : | Find the directional derivative \(D_{$kk \mathbf a}f(\mathbf a)\). $BR | ||
| 73 : | |||
| 74 : | \{ans_rule(10)\} $BR | ||
| 75 : | |||
| 76 : | END_TEXT | ||
| 77 : | |||
| 78 : | ANS(num_cmp($ans)); | ||
| 79 : | |||
| 80 : | |||
| 81 : | |||
| 82 : | |||
| 83 : | ENDDOCUMENT(); # This should be the last executable line in the problem. |
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