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

    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 
   24 loadMacros(
   25 "PGbasicmacros.pl",
   26 "PGanswermacros.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.