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Wed Oct 12 19:45:41 2005 UTC (7 years, 7 months ago) by gage
Original Path: branches/mg/NationalProblemLibrary/ma122DB/set5/s3_6_5.pg
File size: 1134 byte(s)
initial version of database problem library

1 ##DESCRIPTION
2 ##  Find a derivative of y at a point using implicit differentiation
3 ##ENDDESCRIPTION
4 ##KEYWORDS('derivatives', 'implicit')
5
6 ## Shotwell cleaned
7 ## tcao , PAID on 11-24-2003
8
9 ## DBsubject('Calculus')
10 ## DBchapter('Differentiation Rules')
11 ## DBsection('Implicit Differentiation')
12 ## Date('6/3/2002')
13 ## Author('')
14 ## Institution('')
15 ## TitleText1('Calculus Early Transcendentals')
16 ## EditionText1('4')
17 ## AuthorText1('Stewart')
18 ## Section1('3.6')
19 ## Problem1('1')
20
21 DOCUMENT();        # This should be the first executable line in the problem.
22
24 "PGbasicmacros.pl",
26 "PGauxiliaryFunctions.pl"
27 );
28
29 TEXT(beginproblem());
31
32 \$a1 = random(2,5,1);
33 \$b1 = random(2,5,1);
34 \$c1 = random(1,4,5);
35 \$x1 = random(1,5,1);
36 \$c2 = \$c1*\$x1;
37 \$y1 = \$c1-\$a1*\$x1-\$b1;
38 \$deriv1 = "-((2*\$a1*\$x1+\$b1+\$y1)/\$x1)";
39
40 BEGIN_TEXT
41 Let \( \$a1 x^2+ \$b1 x + xy = \$c2  \) and \( y( \$x1 ) = \$y1 \). Find
42 \( y'( \$x1 ) \) by implicit differentiation.
43 \$BR \$BR Answer: \{ans_rule(30) \}
44 \$BR
45 END_TEXT
46
47 ANS(num_cmp(\$deriv1));
48 ENDDOCUMENT();        # This should be the last executable line in the problem.
49