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# View of /trunk/NationalProblemLibrary/Rochester/setLimitsRates1TangentVelocity/s1_1_2.pg

Fri May 28 14:52:41 2010 UTC (2 years, 11 months ago) by gage
File size: 1981 byte(s)
```updates to show problem source for model_Calculus_1
```

```    1 ##DESCRIPTION
2 ##  Find slope of secant lines of a curve, then guess the slope of
3 ##  a tangent line
4 ##ENDDESCRIPTION
5
6 ##KEYWORDS('Calculus')
7 ##Tagged by ynw2d
8
9 ##DBsubject('Calculus')
10 ##DBchapter('Limits and Derivatives')
11 ## DBsection('Tangents, Velocities, and Other Rates of Change')
12 ## TitleText1('Calculus: Early Transcendentals')
13 ## EditionText1('1')
14 ## AuthorText1('Rogawski')
15 ## Section1('2.1')
16 ## Problem1('19')
17 ## TitleText2('Calculus: Early Transcendentals')
18 ## EditionText2('1')
19 ## AuthorText2('Rogawski')
20 ## Section2('2.1')
21 ## Problem2('19')
22
23 DOCUMENT();        # This should be the first executable line in the problem.
24
26 "PG.pl",
27 "PGbasicmacros.pl",
28 "PGchoicemacros.pl",
30 "PGauxiliaryFunctions.pl",
31 "PGcourse.pl"
32 );
33
34 TEXT(beginproblem());
36
37 \$a1 = random(3,8,1);
38 \$x0 = random(2,5,1);
39 \$y0 = \$x0*\$x0 + \$x0 + \$a1;
40 \$x1 = \$x0 + 0.1;
41 \$x01 = \$x0 + 0.01;
42 \$x9 =  \$x0 - 0.1;
43 \$x99 = \$x0- 0.01;
44
45 TEXT(EV2(<<EOT));
46 The point \( P(\$x0 , \$y0 ) \) lies on the curve
47 \( y = x^2 + x + \$a1 \).  If \( Q \) is the point
48 \( (x, x^2 + x + \$a1 ) \), find the slope of the secant line
49 \( PQ \) for the following values of \( x \).
50 \$BR
51 If \( x= \$x1 \), the slope of \( PQ \) is:
52 \{ans_rule(25) \}
53 \$BR
54 EOT
55
56 \$ans = \$x0 +\$x1 + 1;
57 ANS(num_cmp(\$ans));
58
59 TEXT(EV2(<<EOT));
60 and if \( x= \$x01 \), the slope of \( PQ \) is:
61 \{ans_rule(25) \}
62 \$BR
63 EOT
64
65 \$ans = \$x0 +\$x01 + 1;
66 ANS(num_cmp(\$ans));
67
68 TEXT(EV2(<<EOT));
69 and if \( x= \$x9 \), the slope of \( PQ \) is:
70 \{ans_rule(25) \}
71 \$BR
72 EOT
73
74 \$ans = \$x0 +\$x9 + 1;
75 ANS(num_cmp(\$ans));
76
77 TEXT(EV2(<<EOT));
78 and if \( x= \$x99 \), the slope of \( PQ \) is:
79 \{ans_rule(25) \}
80 \$BR
81 EOT
82
83 \$ans = \$x0 +\$x99 + 1;
84 ANS(num_cmp(\$ans));
85
86 TEXT(EV2(<<EOT));
87 Based on the above results, guess the slope of the tangent
88 line to the curve at \( P(\$x0 , \$y0 ) \).
89 \{ans_rule(25) \}
90 \$BR
91 EOT
92
93 \$ans = 2*\$x0 + 1;
94 ANS(num_cmp(\$ans, relTol=>1));
95
96 ENDDOCUMENT();        # This should be the last executable line in the problem.
97
```