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# View of /trunk/NationalProblemLibrary/ma122DB/set4b/s3_4_5.pg

Mon Oct 17 19:10:15 2005 UTC (7 years, 7 months ago) by jj
File size: 1669 byte(s)
Fixed some tags.


    1 ##KEYWORDS('derivatives', 'trigonometry', 'product rule')
2 ##DESCRIPTION
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 ## Shotwell cleaned
8 ## lcao , PAID on 11-24-2003
9
10 ## DBsubject('Calculus')
11 ## DBchapter('Differentiation')
12 ## DBsection('Derivatives of Trigonometric Functions')
13 ## Date('6/3/2002')
14 ## Author('')
15 ## Institution('')
16 ## TitleText1('Calculus Early Transcendentals')
17 ## EditionText1('4')
18 ## AuthorText1('Stewart')
19 ## Section1('3.4')
20 ## Problem1('5')
21
22 DOCUMENT();        # This should be the first executable line in the problem.
23
25 "PGbasicmacros.pl",
27 "PGauxiliaryFunctions.pl"
28 );
29
30 TEXT(beginproblem());
31 $showPartialCorrectAnswers = 1; 32 33 34$a_n = random(2,12,1);
35 $a_s = random(-1,1,2); 36$a   = $a_n *$a_s;
37
38 $x_d = random(3,6,1); 39 while ($x_d == 5) {$x_d = random(3,6,1);}; 40 41$q = random(0,1,1);
42 if ($q == 0) { 43$x_n = 1;
44     $x_s = -1; 45$x_sign = '-';
46     };
47 if ($q == 1) { 48$x_n = 1;
49     $x_s = 1; 50$x_sign = '';
51     };
52 if ($q == 2) { 53$x_n = $x_d - 1; 54$x_s = 1;
55     $x_sign = ''; 56 }; 57 if ($q == 3) {
58     $x_n =$x_d + 1;
59     $x_s = 1; 60$x_sign = '';
61     };
62 if ($q == 4) { 63$x_n = 2 * $x_d - 1; 64$x_s = 1;
65     $x_sign = ''; 66 }; 67 68 if ($x_n != 1) { $x_num =$x_n };
69 if ($x_n == 1) {$x_num = '' };
70
71 $x =$x_s*$x_n*$PI/$x_d; 72 73$funct1 ="($a*(sin(x)+cos(x))+$a*x*(cos(x)-sin(x)))";
74
75 BEGIN_TEXT
76 Let $$f(x) = a x( \sin x + \cos x)$$.
77 $BR$BR
78 $$f'( x ) =$$ \{ans_rule(45) \}
79
80 END_TEXT
81
82 ANS(fun_cmp(\$funct1));
83
84 ENDDOCUMENT();        # This should be the last executable line in the problem.