View of /trunk/NationalProblemLibrary/ma122DB/set3/s3_1_17.pg

    1 ##KEYWORDS('derivatives')
    2 ##DESCRIPTION
    3 ##  Find a derivative of a fraction of two
    4 ##  polynomials, evaluate it at a point
    5 ##ENDDESCRIPTION
    6 
    7 ## Shotwell cleaned
    8 ## tcao , PAID on 11-24-2003
    9 
   10 ## DBsubject('Calculus')
   11 ## DBchapter('Differentiation')
   12 ## DBsection('Derivatives of Polynomials and Exponential Functions')
   13 ## Date('6/3/2002')
   14 ## Author('')
   15 ## Institution('')
   16 ## TitleText1('Calculus: Early Transcendentals')
   17 ## EditionText1('6')
   18 ## AuthorText1('Stewart')
   19 ## Section1('3.1')
   20 ## Problem1('17')
   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 $a1 = random(2,7,1);
   34 $b1 = random(2,8,1);
   35 $c1 = random(2,7,1);
   36 $d1 = random(2,6,1);
   37 $n1 = random(3,7,1);
   38 $x1 = random(1,5,1);
   39 
   40 $deriv1 = (3/2)*$a1*$x1**.5 + ($b1/2)*$x1**(-.5) - ($c1/2)*$x1**(-1.5);
   41 $funct1 = "(3/2)*$a1*x**.5 + ($b1/2)*x**(-.5) - ($c1/2)*x**(-1.5)";
   42 
   43 BEGIN_TEXT
   44 Let
   45 \( f(x) =  \frac { $a1 x^2 + $b1 x + $c1 } {\sqrt{x} } \)
   46 Determine \( f'( x ) \). $BR
   47 $BR$BR Answer: \{ans_rule(48) \}
   48 $BR$BR
   49 
   50 
   51 Find \( f'( $x1 ) \).
   52 $BR$BR Answer: \{ans_rule(48) \}
   53 
   54 END_TEXT
   55 
   56 ANS(fun_cmp($funct1));
   57 ANS(num_cmp($deriv1));
   58 
   59 ENDDOCUMENT();        # This should be the last executable line in the problem.