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Sun Aug 6 16:12:44 2006 UTC (6 years, 9 months ago) by jjholt
File size: 1710 byte(s)
```Added tags.  --JH
```

```    1 ##DESCRIPTION
2 ##  Find slopes of secant lines of a curve at a point, then guess the slope of
3 ##  a tangent line at that point
4 ##ENDDESCRIPTION
5
6 ##KEYWORDS('Calculus')
7 ##Tagged by ynw2d
8
9 ##DBsubject('Calculus')
10 ##DBchapter('Limits and Derivatives')
11 ##DBsection('The Tangent and Velocity Problems')
12
13 DOCUMENT();        # This should be the first executable line in the problem.
14
16 "PG.pl",
17 "PGbasicmacros.pl",
18 "PGchoicemacros.pl",
20 "PGauxiliaryFunctions.pl"
21 );
22
23 TEXT(beginproblem());
24 \$showPartialCorrectAnswers = 1;
25
26 \$a1 = random(2,5,1);
27 \$b1= random(2,5,1);
28 \$x0 = 1/\$b1;
29 \$y0 = \$a1*\$b1;
30 \$x1 = \$x0 + 0.1;
31 \$x01 = \$x0 + 0.01;
32 \$x9 =  \$x0 - 0.1;
33 \$x99 = \$x0- 0.01;
34
35 TEXT(EV2(<<EOT));
36 The point \( P( \$x0 , \$y0 ) \) lies on the curve
37 \( y = \$a1 / x \).  If \( Q \) is the point
38 \( (x,  \$a1 / x ) \), find the slope of the secant line
39 \( PQ \) for the following values of \( x \).
40 \$BR
41 If \( x= \$x1 \), the slope of \( PQ \) is:
42 \{ans_rule(25) \}
43 \$BR
44 EOT
45
46 \$ans =-\$a1/(\$x0*\$x1);
47 ANS(num_cmp(\$ans));
48
49 TEXT(EV2(<<EOT));
50 and if \( x= \$x01 \), the slope of \( PQ \) is:
51 \{ans_rule(25)  \}
52 \$BR
53 EOT
54
55 \$ans =-\$a1/(\$x0*\$x01);
56 ANS(num_cmp(\$ans));
57
58 TEXT(EV2(<<EOT));
59 and if \( x= \$x9 \), the slope of \( PQ \) is:
60 \{ans_rule(25)  \}
61 \$BR
62 EOT
63
64 \$ans =-\$a1/(\$x0*\$x9);
65 ANS(num_cmp(\$ans));
66
67 TEXT(EV2(<<EOT));
68 and if \( x= \$x99 \), the slope of \( PQ \) is:
69 \{ans_rule(25) \}
70 \$BR
71 EOT
72
73 \$ans =-\$a1/(\$x0*\$x99);
74 ANS(num_cmp(\$ans));
75
76 TEXT(EV2(<<EOT));
77 Based on the above results, guess the slope of the tangent
78 line to the curve at \( P(\$x0 , \$y0 ) \).
79 \{ans_rule(25) \}
80 \$BR
81 EOT
82
83 \$ans =-\$a1/(\$x0*\$x0);
84
85 ANS(num_cmp(\$ans, relTol=>4));
86
87 ENDDOCUMENT();        # This should be the last executable line in the problem.
88
```

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