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# View of /trunk/NationalProblemLibrary/UVA-Stew5e/setUVA-Stew5e-C03S06-ImplicitDiff/3-6-29.pg

Wed Jul 18 15:40:35 2007 UTC (5 years, 10 months ago) by jjholt
File size: 1409 byte(s)
```Added Stew6e tags.
```

```    1 ##DESCRIPTION
2 ##Calculus: Differentiation
3 ##ENDDESCRIPTION
4
5 ##KEYWORDS('calculus', 'differentiation')
6 ##Tagged by YJ
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Differentiation')
10 ## DBsection('Implicit Differentiation')
11 ## Date('5/26/2005')
12 ## Author('Jeff Holt')
13 ## Institution('UVA')
14 ## TitleText1('Calculus: Early Transcendentals')
15 ## EditionText1('5')
16 ## AuthorText1('Stewart')
17 ## Section1('3.6')
18 ## Problem1('29')
19
20 ## TitleText2('Calculus: Early Transcendentals')
21 ## EditionText2('6')
22 ## AuthorText2('Stewart')
23 ## Section2('3.5')
24 ## Problem2('')
25
26 DOCUMENT();        # This should be the first executable line in the problem.
27
29 "PG.pl",
30 "PGbasicmacros.pl",
31 "PGchoicemacros.pl",
33 "PGauxiliaryFunctions.pl"
34 );
35
36 TEXT(beginproblem());
38
39 \$x1 = random(-3,3,6);
40 \$y1 = random(-1,1,2);
41 \$m1 = (25*\$x1-4*\$x1*(\$x1*\$x1+\$y1*\$y1))/(4*(\$x1*\$x1+\$y1*\$y1)*\$y1+25*\$y1);
42
43 TEXT(EV2(<<EOT));
44 Find the equation of the tangent line to the curve (a lemniscate)
45  \( 2(x^2+y^2)^2 = 25(x^2-y^2) \)
46 at the point \( ( \$x1 , \$y1 ) \).
47 The equation of this tangent line can be written in the form \( y = mx+b \)
48 where
49 \$PAR
50 \( m \) = \{ans_rule(30) \}
51 \$BR
52 EOT
53 \$ans = \$m1;
54 ANS(num_cmp(\$ans));
55
56 TEXT(EV2(<<EOT));
57 and
58 \$PAR
59 \( b \) = \{ans_rule(30) \}
60 \$BR
61 EOT
62 \$ans = \$y1 -\$m1*\$x1;
63 ANS(num_cmp(\$ans));
64
65 ENDDOCUMENT();        # This should be the last executable line in the problem.
```