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# View of /trunk/NationalProblemLibrary/Rochester/setDerivatives4Trig/s2_4_27a.pg

Sun Mar 26 22:21:31 2006 UTC (7 years, 2 months ago) by jj
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Initial import


    1 ##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 DOCUMENT();        # This should be the first executable line in the problem.
8
10 "PG.pl",
11 "PGbasicmacros.pl",
12 "PGchoicemacros.pl",
14 "PGauxiliaryFunctions.pl"
15 );
16
17 TEXT(beginproblem());
18 $showPartialCorrectAnswers = 1; 19 20$pi = arccos(-1);
21
22 $a_n = random(2,12,1); 23$a_s = random(-1,1,2);
24 $a =$a_n * $a_s; 25 26$x_d = random(3,6,1);
27 while ($x_d == 5) {$x_d = random(3,6,1);};
28
29 $q = random(0,1,1); 30 if ($q == 0) {
31     $x_n = 1; 32$x_s = -1;
33     $x_sign = '-'; 34 }; 35 if ($q == 1) {
36     $x_n = 1; 37$x_s = 1;
38     $x_sign = ''; 39 }; 40 if ($q == 2) {
41     $x_n =$x_d - 1;
42     $x_s = 1; 43$x_sign = '';
44     };
45 if ($q == 3) { 46$x_n = $x_d + 1; 47$x_s = 1;
48     $x_sign = ''; 49 }; 50 if ($q == 4) {
51     $x_n = 2 *$x_d - 1;
52     $x_s = 1; 53$x_sign = '';
54     };
55
56 if ($x_n != 1) {$x_num = $x_n }; 57 if ($x_n == 1) { $x_num = '' }; 58 59$x = $x_s*$x_n*$pi/$x_d;
60
61 $deriv1 =($a*(sin($x)+cos($x))+ $a*$x*(cos($x)-sin($x)));
62 $funct1 ="($a*(sin(x)+cos(x))+ $a*x*(cos(x)-sin(x)))"; 63 64 TEXT(EV2(<<EOT)); 65 Let $f(x) = a x( \sin x + \cos x)$ 66$PAR
67 $$f'( x ) =$$
68 $PAR 69 \{ans_rule(45) \} 70$PAR
71 $$f'( x_sign \frac { x_num \pi } {x_d} ) =$$
72 $PAR 73 \{ans_rule(45) \} 74 75 EOT 76 77$ans = $funct1; 78 ANS(fun_cmp($ans));
79
80 $ans =$deriv1;
81 ANS(num_cmp(\$ans));
82
83 ENDDOCUMENT();        # This should be the last executable line in the problem.