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| 1 : | jj | 145 | ##DESCRIPTION |
| 2 : | ##KEYWORDS('derivatives', 'trigonometry', 'product rule') | ||
| 3 : | ## Find a derivative of a function involving trigonometric functions, | ||
| 4 : | ## and evalute it at a given point; requires using product rule | ||
| 5 : | ##ENDDESCRIPTION | ||
| 6 : | |||
| 7 : | jjholt | 184 | ## Tagged by sawblade |
| 8 : | |||
| 9 : | ## DBsubject('Calculus') | ||
| 10 : | ## DBchapter('Differentiation') | ||
| 11 : | ## DBsection('Derivatives of Trigonometric Functions') | ||
| 12 : | ## Date('') | ||
| 13 : | ## Author('') | ||
| 14 : | ## Institution('Rochester') | ||
| 15 : | ## TitleText1('') | ||
| 16 : | ## EditionText1('') | ||
| 17 : | ## AuthorText1('') | ||
| 18 : | ## Section1('') | ||
| 19 : | ## Problem1('') | ||
| 20 : | sh002i | 556 | ## TitleText2('Calculus: Early Transcendentals') |
| 21 : | ## EditionText2('1') | ||
| 22 : | ## AuthorText2('Rogawski') | ||
| 23 : | ## Section2('3.6') | ||
| 24 : | ## Problem2('15') | ||
| 25 : | jjholt | 184 | |
| 26 : | jj | 145 | DOCUMENT(); # This should be the first executable line in the problem. |
| 27 : | |||
| 28 : | loadMacros( | ||
| 29 : | "PG.pl", | ||
| 30 : | "PGbasicmacros.pl", | ||
| 31 : | "PGchoicemacros.pl", | ||
| 32 : | "PGanswermacros.pl", | ||
| 33 : | "PGauxiliaryFunctions.pl" | ||
| 34 : | ); | ||
| 35 : | |||
| 36 : | TEXT(beginproblem()); | ||
| 37 : | $showPartialCorrectAnswers = 1; | ||
| 38 : | |||
| 39 : | $pi = arccos(-1); | ||
| 40 : | |||
| 41 : | $a_n = random(2,12,1); | ||
| 42 : | $a_s = random(-1,1,2); | ||
| 43 : | $a = $a_n * $a_s; | ||
| 44 : | |||
| 45 : | $x_d = random(3,6,1); | ||
| 46 : | while ($x_d == 5) {$x_d = random(3,6,1);}; | ||
| 47 : | |||
| 48 : | $q = random(0,1,1); | ||
| 49 : | if ($q == 0) { | ||
| 50 : | $x_n = 1; | ||
| 51 : | $x_s = -1; | ||
| 52 : | $x_sign = '-'; | ||
| 53 : | }; | ||
| 54 : | if ($q == 1) { | ||
| 55 : | $x_n = 1; | ||
| 56 : | $x_s = 1; | ||
| 57 : | $x_sign = ''; | ||
| 58 : | }; | ||
| 59 : | if ($q == 2) { | ||
| 60 : | $x_n = $x_d - 1; | ||
| 61 : | $x_s = 1; | ||
| 62 : | $x_sign = ''; | ||
| 63 : | }; | ||
| 64 : | if ($q == 3) { | ||
| 65 : | $x_n = $x_d + 1; | ||
| 66 : | $x_s = 1; | ||
| 67 : | $x_sign = ''; | ||
| 68 : | }; | ||
| 69 : | if ($q == 4) { | ||
| 70 : | $x_n = 2 * $x_d - 1; | ||
| 71 : | $x_s = 1; | ||
| 72 : | $x_sign = ''; | ||
| 73 : | }; | ||
| 74 : | |||
| 75 : | if ($x_n != 1) { $x_num = $x_n }; | ||
| 76 : | if ($x_n == 1) { $x_num = '' }; | ||
| 77 : | |||
| 78 : | $x = $x_s*$x_n*$pi/$x_d; | ||
| 79 : | |||
| 80 : | $deriv1 =($a*(sin($x)+cos($x))+ $a*$x*(cos($x)-sin($x))); | ||
| 81 : | $funct1 ="($a*(sin(x)+cos(x))+ $a*x*(cos(x)-sin(x)))"; | ||
| 82 : | |||
| 83 : | TEXT(EV2(<<EOT)); | ||
| 84 : | Let \[ f(x) = $a x( \sin x + \cos x) \] | ||
| 85 : | $PAR | ||
| 86 : | \( f'( x ) = \) | ||
| 87 : | $PAR | ||
| 88 : | \{ans_rule(45) \} | ||
| 89 : | $PAR | ||
| 90 : | \( f'( $x_sign \frac { $x_num \pi } {$x_d} ) = \) | ||
| 91 : | $PAR | ||
| 92 : | \{ans_rule(45) \} | ||
| 93 : | |||
| 94 : | EOT | ||
| 95 : | |||
| 96 : | $ans = $funct1; | ||
| 97 : | ANS(fun_cmp($ans)); | ||
| 98 : | |||
| 99 : | $ans = $deriv1; | ||
| 100 : | ANS(num_cmp($ans)); | ||
| 101 : | |||
| 102 : | ENDDOCUMENT(); # This should be the last executable line in the problem. |
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